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Li L, Zhang L, Zhao Y, Xie Q, He X, He X, Yi H. Dimension Reduction Based on Grouped Feature Selection Strategy for Fluorescence Molecular Tomography. ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. ANNUAL INTERNATIONAL CONFERENCE 2024; 2024:1-4. [PMID: 40039243 DOI: 10.1109/embc53108.2024.10782836] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/06/2025]
Abstract
Fluorescence Molecular Tomography (FMT) is an optical molecular imaging technique with high sensitivity. Multi-point excitation and multi-view measurement have improved the recovered results while also resulting in high computation and memory requirements. In this work, we proposed a grouped feature selection strategy (GFS) based on correlation and information entropy to reduce the size of the system matrix. It further reduced the computational complexity. Firstly, a similarity is constructed based on the correlation between the matrix rows. Then a group is created by the surface measurements. Secondly, information entropy is defined to measure the information contained in the surface measurement. Finally, these two measurement methods are combined with minimum redundancy and maximum relevance (mRMR) to construct the optimal subset of the original data, which completes the dimensionality reduction of the matrix. Numerical simulation experiments show that GFS outperforms the traditional principal component analysis (PCA) method in terms of reconstruction accuracy and reconstruction efficiency.Clinical Relevance- The primary objective of this work is to enhance the reconstruction speed of FMT. Current experiments are focused on simulation experiments, while the proposed downscaling strategy will facilitate rapid clinical diagnosis and treatment decisions in the future.
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Cheng X, Sun S, Xiao Y, Li W, Li J, Yu J, Guo H. Fluorescence molecular tomography based on an online maximum a posteriori estimation algorithm. JOURNAL OF THE OPTICAL SOCIETY OF AMERICA. A, OPTICS, IMAGE SCIENCE, AND VISION 2024; 41:844-851. [PMID: 38856571 DOI: 10.1364/josaa.519667] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/26/2024] [Accepted: 03/25/2024] [Indexed: 06/11/2024]
Abstract
Fluorescence molecular tomography (FMT) is a non-invasive, radiation-free, and highly sensitive optical molecular imaging technique for early tumor detection. However, inadequate measurement information along with significant scattering of near-infrared light within the tissue leads to high ill-posedness in the inverse problem of FMT. To improve the quality and efficiency of FMT reconstruction, we build a reconstruction model based on log-sum regularization and introduce an online maximum a posteriori estimation (OPE) algorithm to solve the non-convex optimization problem. The OPE algorithm approximates a stationary point by evaluating the gradient of the objective function at each iteration, and its notable strength lies in the remarkable speed of convergence. The results of simulations and experiments demonstrate that the OPE algorithm ensures good reconstruction quality and exhibits outstanding performance in terms of reconstruction efficiency.
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Zhao Y, Li S, Zhang L, Tang Z, Wei D, Zhang H, Xie Q, Yi H, He X. Two-step reconstruction framework of fluorescence molecular tomography based on energy statistical probability. JOURNAL OF BIOPHOTONICS 2024; 17:e202300480. [PMID: 38351740 DOI: 10.1002/jbio.202300480] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/17/2023] [Revised: 01/17/2024] [Accepted: 01/28/2024] [Indexed: 05/04/2024]
Abstract
Fluorescence molecular tomography (FMT), as a promising technique for early tumor detection, can non-invasively visualize the distribution of fluorescent marker probe three-dimensionally. However, FMT reconstruction is a severely ill-posed problem, which remains an obstacle to wider application of FMT. In this paper, a two-step reconstruction framework was proposed for FMT based on the energy statistical probability. First, the tissue structural information obtained from computed tomography (CT) is employed to associate the tissue optical parameters for rough solution in the global region. Then, according to the global-region reconstruction results, the probability that the target belongs to each region can be calculated. The region with the highest probability is delineated as region of interest to realize accurate and fast source reconstruction. Numerical simulations and in vivo experiments were carried out to evaluate the effectiveness of the proposed framework. The encouraging results demonstrate the significant effectiveness and potential of our method for practical FMT applications.
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Affiliation(s)
- Yizhe Zhao
- The Xi'an Key Laboratory of Radiomics and Intelligent Perception, Xi'an, China
- School of Information Sciences and Technology, Northwest University, Xi'an, China
| | - Shuangchen Li
- The Xi'an Key Laboratory of Radiomics and Intelligent Perception, Xi'an, China
- School of Information Sciences and Technology, Northwest University, Xi'an, China
| | - Lizhi Zhang
- The Xi'an Key Laboratory of Radiomics and Intelligent Perception, Xi'an, China
- School of Information Sciences and Technology, Northwest University, Xi'an, China
| | - Zijian Tang
- The Xi'an Key Laboratory of Radiomics and Intelligent Perception, Xi'an, China
- School of Information Sciences and Technology, Northwest University, Xi'an, China
| | - De Wei
- The Xi'an Key Laboratory of Radiomics and Intelligent Perception, Xi'an, China
- School of Information Sciences and Technology, Northwest University, Xi'an, China
| | - Heng Zhang
- The Xi'an Key Laboratory of Radiomics and Intelligent Perception, Xi'an, China
- School of Information Sciences and Technology, Northwest University, Xi'an, China
| | - Qiong Xie
- The First Hospital of Hunan University of Chinese Medicine, Changsha, Hunan, China
| | - Huangjian Yi
- The Xi'an Key Laboratory of Radiomics and Intelligent Perception, Xi'an, China
- School of Information Sciences and Technology, Northwest University, Xi'an, China
| | - Xiaowei He
- The Xi'an Key Laboratory of Radiomics and Intelligent Perception, Xi'an, China
- School of Information Sciences and Technology, Northwest University, Xi'an, China
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Zhang J, Zhang G, Chen Y, Li K, Zhao F, Yi H, Su L, Cao X. Regularized reconstruction based on joint smoothly clipped absolute deviation regularization and graph manifold learning for fluorescence molecular tomography. Phys Med Biol 2023; 68:195004. [PMID: 37647921 DOI: 10.1088/1361-6560/acf55a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2023] [Accepted: 08/30/2023] [Indexed: 09/01/2023]
Abstract
Objective.Fluorescence molecular tomography (FMT) is an optical imaging modality that provides high sensitivity and low cost, which can offer the three-dimensional distribution of biomarkers by detecting the fluorescently labeled probe noninvasively. In the field of preclinical cancer diagnosis and treatment, FMT has gained significant traction. Nonetheless, the current FMT reconstruction results suffer from unsatisfactory morphology and location accuracy of the fluorescence distribution, primarily due to the light scattering effect and the ill-posed nature of the inverse problem.Approach.To address these challenges, a regularized reconstruction method based on joint smoothly clipped absolute deviation regularization and graph manifold learning (SCAD-GML) for FMT is presented in this paper. The SCAD-GML approach combines the sparsity of the fluorescent sources with the latent manifold structure of fluorescent source distribution to achieve more accurate and sparse reconstruction results. To obtain the reconstruction results efficiently, the non-convex gradient descent iterative method is employed to solve the established objective function. To assess the performance of the proposed SCAD-GML method, a comprehensive evaluation is conducted through numerical simulation experiments as well asin vivoexperiments.Main results.The results demonstrate that the SCAD-GML method outperforms other methods in terms of both location and shape recovery of fluorescence biomarkers distribution.Siginificance.These findings indicate that the SCAD-GML method has the potential to advance the application of FMT inin vivobiological research.
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Affiliation(s)
- Jun Zhang
- School of Information Science and Technology, Northwest University, Xi'an, Shaanxi 710127, People's Republic of China
- National and Local Joint Engineering Research Center for Cultural Heritage Digitization, Xi'an, Shaanxi 710127, People's Republic of China
| | - Gege Zhang
- School of Information Science and Technology, Northwest University, Xi'an, Shaanxi 710127, People's Republic of China
- National and Local Joint Engineering Research Center for Cultural Heritage Digitization, Xi'an, Shaanxi 710127, People's Republic of China
| | - Yi Chen
- School of Information Science and Technology, Northwest University, Xi'an, Shaanxi 710127, People's Republic of China
- National and Local Joint Engineering Research Center for Cultural Heritage Digitization, Xi'an, Shaanxi 710127, People's Republic of China
| | - Kang Li
- School of Information Science and Technology, Northwest University, Xi'an, Shaanxi 710127, People's Republic of China
- National and Local Joint Engineering Research Center for Cultural Heritage Digitization, Xi'an, Shaanxi 710127, People's Republic of China
| | - Fengjun Zhao
- School of Information Science and Technology, Northwest University, Xi'an, Shaanxi 710127, People's Republic of China
| | - Huangjian Yi
- School of Information Science and Technology, Northwest University, Xi'an, Shaanxi 710127, People's Republic of China
| | - Linzhi Su
- School of Information Science and Technology, Northwest University, Xi'an, Shaanxi 710127, People's Republic of China
- National and Local Joint Engineering Research Center for Cultural Heritage Digitization, Xi'an, Shaanxi 710127, People's Republic of China
| | - Xin Cao
- School of Information Science and Technology, Northwest University, Xi'an, Shaanxi 710127, People's Republic of China
- National and Local Joint Engineering Research Center for Cultural Heritage Digitization, Xi'an, Shaanxi 710127, People's Republic of China
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Cong W, Wang G. Fluorescence molecular tomography for quantum yield and lifetime. APPLIED OPTICS 2023; 62:5926-5931. [PMID: 37706945 DOI: 10.1364/ao.495129] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/10/2023] [Accepted: 07/09/2023] [Indexed: 09/15/2023]
Abstract
Fluorescence molecular tomography (FMT) is a promising modality for noninvasive imaging of internal fluorescence agents in biological tissues, especially in small animal models, with applications in diagnosis, therapy, and drug design. In this paper, we present a fluorescent reconstruction algorithm that combines time-resolved fluorescence imaging data with photon-counting microcomputed tomography (PCMCT) images to estimate the quantum yield and lifetime of fluorescent markers in a mouse model. By incorporating PCMCT images, a permissible region of interest of fluorescence yield and lifetime can be roughly estimated as prior knowledge, reducing the number of unknown variables in the inverse problem and improving the image reconstruction stability. Our numerical experiments demonstrate the accuracy and stability of the proposed reconstruction method in the presence of data noise, achieving a reconstruction error of 0.02 ns for the fluorescence lifetime and an average relative error of 18% for quantum yield reconstruction.
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Yuan Y, Yi H, Kang D, Yu J, Guo H, He X, He X. Robust transformed l 1 metric for fluorescence molecular tomography. COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE 2023; 234:107503. [PMID: 37015182 DOI: 10.1016/j.cmpb.2023.107503] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/27/2022] [Revised: 02/27/2023] [Accepted: 03/21/2023] [Indexed: 06/19/2023]
Abstract
BACKGROUND AND OBJECTIVE Fluorescence molecular tomography (FMT) is a non-invasive molecular imaging modality that can be used to observe the three-dimensional distribution of fluorescent probes in vivo. FMT is a promising imaging technique in clinical and preclinical research that has attracted significant attention. Numerous regularization based reconstruction algorithms have been proposed. However, traditional algorithms that use the squared l2-norm distance usually exaggerate the influence of noise and measurement and calculation errors, and their robustness cannot be guaranteed. METHODS In this study, we propose a novel robust transformed l1 (TL1) metric that interpolates l0 and l1 norms through a nonnegative parameter α∈(0,+∞). The TL1 metric looks like the lp-norm with p∈(0,1). These are markedly different because TL1 metric has two properties, boundedness and Lipschitz-continuity, which make the TL1 criterion suitable distance metric, particularly for robustness, owing to its stronger noise suppression. Subsequently, we apply the proposed metric to FMT and build a robust model to reduce the influence of noise. The nonconvexity of the proposed model made direct optimization difficult, and a continuous optimization method was developed to solve the model. The problem was converted into a difference in convex programming problem for the TL1 metric (DCATL1), and the corresponding algorithm converged linearly. RESULTS Various numerical simulations and in vivo bead-implanted mouse experiments were conducted to verify the performance of the proposed method. The experimental results show that the DCATL1 algorithm is more robust than the state-of-the-art approaches and achieves better source localization and morphology recovery. CONCLUSIONS The in vivo experiments showed that DCATL1 can be used to visualize the distribution of fluorescent probes inside biological tissues and promote preclinical application in small animals, demonstrating the feasibility and effectiveness of the proposed method.
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Affiliation(s)
- Yating Yuan
- The Xi'an Key Laboratory of Radiomics and Intelligent Perception, Xi'an, China; School of Information Sciences and Technology, Northwest University, Xi'an, 710127, China
| | - Huangjian Yi
- The Xi'an Key Laboratory of Radiomics and Intelligent Perception, Xi'an, China; School of Information Sciences and Technology, Northwest University, Xi'an, 710127, China
| | - Dizhen Kang
- The Xi'an Key Laboratory of Radiomics and Intelligent Perception, Xi'an, China; School of Information Sciences and Technology, Northwest University, Xi'an, 710127, China
| | - Jingjing Yu
- School of Physics and Information Technology, Shaanxi Normal University, Xi'an, 710119, China
| | - Hongbo Guo
- The Xi'an Key Laboratory of Radiomics and Intelligent Perception, Xi'an, China; School of Information Sciences and Technology, Northwest University, Xi'an, 710127, China
| | - Xuelei He
- The Xi'an Key Laboratory of Radiomics and Intelligent Perception, Xi'an, China; School of Information Sciences and Technology, Northwest University, Xi'an, 710127, China
| | - Xiaowei He
- The Xi'an Key Laboratory of Radiomics and Intelligent Perception, Xi'an, China; School of Information Sciences and Technology, Northwest University, Xi'an, 710127, China.
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Chen Y, Du M, Zhang J, Zhang G, Su L, Li K, Zhao F, Yi H, Wang L, Cao X. Generalized conditional gradient method with adaptive regularization parameters for fluorescence molecular tomography. OPTICS EXPRESS 2023; 31:18128-18146. [PMID: 37381530 DOI: 10.1364/oe.486339] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/24/2023] [Accepted: 04/08/2023] [Indexed: 06/30/2023]
Abstract
Fluorescence molecular tomography (FMT) is an optical imaging technology with the ability of visualizing the three-dimensional distribution of fluorescently labelled probes in vivo. However, due to the light scattering effect and ill-posed inverse problems, obtaining satisfactory FMT reconstruction is still a challenging problem. In this work, to improve the performance of FMT reconstruction, we proposed a generalized conditional gradient method with adaptive regularization parameters (GCGM-ARP). In order to make a tradeoff between the sparsity and shape preservation of the reconstruction source, and to maintain its robustness, elastic-net (EN) regularization is introduced. EN regularization combines the advantages of L1-norm and L2-norm, and overcomes the shortcomings of traditional Lp-norm regularization, such as over-sparsity, over-smoothness, and non-robustness. Thus, the equivalent optimization formulation of the original problem can be obtained. To further improve the performance of the reconstruction, the L-curve is adopted to adaptively adjust the regularization parameters. Then, the generalized conditional gradient method (GCGM) is used to split the minimization problem based on EN regularization into two simpler sub-problems, which are determining the direction of the gradient and the step size. These sub-problems are addressed efficiently to obtain more sparse solutions. To assess the performance of our proposed method, a series of numerical simulation experiments and in vivo experiments were implemented. The experimental results show that, compared with other mathematical reconstruction methods, GCGM-ARP method has the minimum location error (LE) and relative intensity error (RIE), and the maximum dice coefficient (Dice) in the case of different sources number or shape, or Gaussian noise of 5%-25%. This indicates that GCGM-ARP has superior reconstruction performance in source localization, dual-source resolution, morphology recovery, and robustness. In conclusion, the proposed GCGM-ARP is an effective and robust strategy for FMT reconstruction in biomedical application.
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Chu M, Guo H, He X, Wang B, Liu Y, Hu X, Yu J, He X. A Graph-guided Hybrid Regularization Method For Bioluminescence Tomography. COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE 2023; 230:107329. [PMID: 36608432 DOI: 10.1016/j.cmpb.2022.107329] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/13/2022] [Revised: 12/19/2022] [Accepted: 12/28/2022] [Indexed: 06/17/2023]
Abstract
BACKGROUND AND OBJECTIVE Bioluminescence tomography (BLT) is a powerful and sensitive imaging technique having great potential in preclinical application, such as tumor imaging, monitoring and therapy, etc. Regularization plays an important role in BLT reconstruction for considering the priori information to overcome the inherent ill-posedness of the inverse problem. Therefore, well-designed regularization term and sophisticated algorithm for solving the consequent optimization problem are key to improve the BLT quality. METHODS To balance the sparsity, smoothness and morphological characteristics of the bioluminescence targets, we constructed a novel Graph-Guided Hybrid Regularization (GGHR) method by combining graph-guided penalty term with L1 and L2 norm regularizer. To solve the corresponding minimization problem with hybrid penalties, the dual decomposition and Nesterov's smoothing technique were adopted to decouple and transform the non-separable and non-smooth graph-guided penalty term into a differential smooth approximation form, which was solved by the fast iterative shrinkage thresholding algorithm. RESULTS The performance of the proposed GGHR method was verified and evaluated through a series of simulation, phantom and in vivo experiments. The comparison results demonstrated that the GGHR method outperformed current mainstream reconstruction algorithms in spatial localization, morphology recovery and in vivo practicality. CONCLUSIONS The proposed GGHR method is a robust and practicality reconstruction algorithm for further highlighting the positive effect of hybrid regularization on BLT applications.
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Affiliation(s)
- Mengxiang Chu
- The Xi'an Key Laboratory of Radiomics and Intelligent Perception, Xi'an, China; School of Network and Data Center, Northwest University, Xi'an, 710127, China; School of Information Sciences and Technology, Northwest University, Xi'an, 710127, China.
| | - Hongbo Guo
- The Xi'an Key Laboratory of Radiomics and Intelligent Perception, Xi'an, China; School of Information Sciences and Technology, Northwest University, Xi'an, 710127, China.
| | - Xuelei He
- The Xi'an Key Laboratory of Radiomics and Intelligent Perception, Xi'an, China; School of Information Sciences and Technology, Northwest University, Xi'an, 710127, China
| | - Beilei Wang
- The Xi'an Key Laboratory of Radiomics and Intelligent Perception, Xi'an, China; School of Information Sciences and Technology, Northwest University, Xi'an, 710127, China
| | - Yanqiu Liu
- The Xi'an Key Laboratory of Radiomics and Intelligent Perception, Xi'an, China; School of Information Sciences and Technology, Northwest University, Xi'an, 710127, China
| | - Xiangong Hu
- The Xi'an Key Laboratory of Radiomics and Intelligent Perception, Xi'an, China; School of Network and Data Center, Northwest University, Xi'an, 710127, China
| | - Jingjing Yu
- School of Physics and Information Technology, Shaanxi Normal University, Xi'an, 710062, China
| | - Xiaowei He
- The Xi'an Key Laboratory of Radiomics and Intelligent Perception, Xi'an, China; School of Network and Data Center, Northwest University, Xi'an, 710127, China; School of Information Sciences and Technology, Northwest University, Xi'an, 710127, China.
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Konovalov AB, Vlasov VV, Samarin SI, Soloviev ID, Savitsky AP, Tuchin VV. Reconstruction of fluorophore absorption and fluorescence lifetime using early photon mesoscopic fluorescence molecular tomography: a phantom study. JOURNAL OF BIOMEDICAL OPTICS 2022; 27:126001. [PMID: 36519075 PMCID: PMC9743783 DOI: 10.1117/1.jbo.27.12.126001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/27/2022] [Accepted: 11/18/2022] [Indexed: 06/17/2023]
Abstract
SIGNIFICANCE Fluorescence molecular lifetime tomography (FMLT) plays an increasingly important role in experimental oncology. The article presents and experimentally verifies an original method of mesoscopic time domain FMLT, based on an asymptotic approximation to the fluorescence source function, which is valid for early arriving photons. AIM The aim was to justify the efficiency of the method by experimental scanning and reconstruction of a phantom with a fluorophore. The experimental facility included the TCSPC system, the pulsed supercontinuum Fianium laser, and a three-channel fiber probe. Phantom scanning was done in mesoscopic regime for three-dimensional (3D) reflectance geometry. APPROACH The sensitivity functions were simulated with a Monte Carlo method. A compressed-sensing-like reconstruction algorithm was used to solve the inverse problem for the fluorescence parameter distribution function, which included the fluorophore absorption coefficient and fluorescence lifetime distributions. The distributions were separated directly in the time domain with the QR-factorization least square method. RESULTS 3D tomograms of fluorescence parameters were obtained and analyzed using two strategies for the formation of measurement data arrays and sensitivity matrices. An algorithm is developed for the flexible choice of optimal strategy in view of attaining better reconstruction quality. Variants on how to improve the method are proposed, specifically, through stepped extraction and further use of a posteriori information about the object. CONCLUSIONS Even if measurement data are limited, the proposed method is capable of giving adequate reconstructions but their quality depends on available a priori (or a posteriori) information. Further research aims to improve the method by implementing the variants proposed.
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Affiliation(s)
- Alexander B. Konovalov
- Federal State Unitary Enterprise “Russian Federal Nuclear Center – Zababakhin All-Russia Research Institute of Technical Physics,” Snezhinsk, Russia
- Bach Institute of Biochemistry, Research Center of Biotechnology of the Russian Academy of Sciences, Moscow, Russia
| | - Vitaly V. Vlasov
- Federal State Unitary Enterprise “Russian Federal Nuclear Center – Zababakhin All-Russia Research Institute of Technical Physics,” Snezhinsk, Russia
- Bach Institute of Biochemistry, Research Center of Biotechnology of the Russian Academy of Sciences, Moscow, Russia
| | - Sergei I. Samarin
- Federal State Unitary Enterprise “Russian Federal Nuclear Center – Zababakhin All-Russia Research Institute of Technical Physics,” Snezhinsk, Russia
| | - Ilya D. Soloviev
- Bach Institute of Biochemistry, Research Center of Biotechnology of the Russian Academy of Sciences, Moscow, Russia
| | - Alexander P. Savitsky
- Bach Institute of Biochemistry, Research Center of Biotechnology of the Russian Academy of Sciences, Moscow, Russia
| | - Valery V. Tuchin
- Bach Institute of Biochemistry, Research Center of Biotechnology of the Russian Academy of Sciences, Moscow, Russia
- Saratov State University, Saratov, Russia
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Chen Y, Du M, Li W, Su L, Yi H, Zhao F, Li K, Wang L, Cao X. ABPO-TVSCAD: alternating Bregman proximity operators approach based on TVSCAD regularization for bioluminescence tomography. Phys Med Biol 2022; 67:215013. [PMID: 36220011 DOI: 10.1088/1361-6560/ac994c] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/26/2022] [Accepted: 10/11/2022] [Indexed: 06/16/2023]
Abstract
Objective.Bioluminescence tomography (BLT) is a promising non-invasive optical medical imaging technique, which can visualize and quantitatively analyze the distribution of tumor cells in living tissues. However, due to the influence of photon scattering effect and ill-conditioned inverse problem, the reconstruction result is unsatisfactory. The purpose of this study is to improve the reconstruction performance of BLT.Approach.An alternating Bregman proximity operators (ABPO) method based on TVSCAD regularization is proposed for BLT reconstruction. TVSCAD combines the anisotropic total variation (TV) regularization constraints and the non-convex smoothly clipped absolute deviation (SCAD) penalty constraints, to make a trade-off between the sparsity and edge preservation of the source. ABPO approach is used to solve the TVSCAD model (ABPO-TVSCAD for short). In addition, to accelerate the convergence speed of the ABPO, we adapt the strategy of shrinking the permission source region, which further improves the performance of ABPO-TVSCAD.Main results.The results of numerical simulations andin vivoxenograft mouse experiment show that our proposed method achieved superior accuracy in spatial localization and morphological reconstruction of bioluminescent source.Significance.ABPO-TVSCAD is an effective and robust reconstruction method for BLT, and we hope that this method can promote the development of optical molecular tomography.
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Affiliation(s)
- Yi Chen
- School of Information Sciences and Technology, Northwest University, Xi'an 710127, People's Republic of China
| | - Mengfei Du
- School of Information Sciences and Technology, Northwest University, Xi'an 710127, People's Republic of China
| | - Weitong Li
- School of Information Sciences and Technology, Northwest University, Xi'an 710127, People's Republic of China
| | - Linzhi Su
- School of Information Sciences and Technology, Northwest University, Xi'an 710127, People's Republic of China
| | - Huangjian Yi
- School of Information Sciences and Technology, Northwest University, Xi'an 710127, People's Republic of China
| | - Fengjun Zhao
- School of Information Sciences and Technology, Northwest University, Xi'an 710127, People's Republic of China
| | - Kang Li
- School of Information Sciences and Technology, Northwest University, Xi'an 710127, People's Republic of China
| | - Lin Wang
- School of Computer Science and Engineering, Xi'an University of Technology, Xi'an 710048, People's Republic of China
| | - Xin Cao
- School of Information Sciences and Technology, Northwest University, Xi'an 710127, People's Republic of China
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Zhang P, Liu J, Yin L, An Y, Zhang S, Tong W, Hui H, Tian J. Adaptive permissible region based random Kaczmarz reconstruction method for localization of carotid atherosclerotic plaques in fluorescence molecular tomography. Phys Med Biol 2022; 67. [DOI: 10.1088/1361-6560/ac8718] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/23/2022] [Accepted: 08/04/2022] [Indexed: 11/12/2022]
Abstract
Abstract
Objective. In this study, we propose the adaptive permissible region based random Kaczmarz method as an improved reconstruction method to recover small carotid atherosclerotic plaque targets in rodents with high resolution in fluorescence molecular tomography (FMT). Approach. We introduce the random Kaczmarz method as an advanced minimization method to solve the FMT inverse problem. To satisfy the special condition of this method, we proposed an adaptive permissible region strategy based on traditional permissible region methods to flexibly compress the dimension of the solution space. Main results. Monte Carlo simulations, phantom experiments, and in vivo experiments demonstrate that the proposed method can recover the small carotid atherosclerotic plaque targets with high resolution and accuracy, and can achieve lower root mean squared error and distance error (DE) than other traditional methods. For targets with 1.5 mm diameter and 0.5 mm separation, the DE indicators can be improved by up to 40%. Moreover, the proposed method can be utilized for in vivo locating atherosclerotic plaques with high accuracy and robustness. Significance. We applied the random Kaczmarz method to solve the inverse problem in FMT and improve the reconstruction result via this advanced minimization method. We verified that the FMT technology has a great potential to locate and quantify atherosclerotic plaques with higher accuracy, and can be expanded to more preclinical research.
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Zhang P, Ma C, Song F, Fan G, Sun Y, Feng Y, Ma X, Liu F, Zhang G. A review of advances in imaging methodology in fluorescence molecular tomography. Phys Med Biol 2022; 67. [DOI: 10.1088/1361-6560/ac5ce7] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/08/2021] [Accepted: 03/11/2022] [Indexed: 01/03/2023]
Abstract
Abstract
Objective. Fluorescence molecular tomography (FMT) is a promising non-invasive optical molecular imaging technology with strong specificity and sensitivity that has great potential for preclinical and clinical studies in tumor diagnosis, drug development and therapeutic evaluation. However, the strong scattering of photons and insufficient surface measurements make it very challenging to improve the quality of FMT image reconstruction and its practical application for early tumor detection. Therefore, continuous efforts have been made to explore more effective approaches or solutions in the pursuit of high-quality FMT reconstructions. Approach. This review takes a comprehensive overview of advances in imaging methodology for FMT, mainly focusing on two critical issues in FMT reconstructions: improving the accuracy of solving the forward physical model and mitigating the ill-posed nature of the inverse problem from a methodological point of view. More importantly, numerous impressive and practical strategies and methods for improving the quality of FMT reconstruction are summarized. Notably, deep learning methods are discussed in detail to illustrate their advantages in promoting the imaging performance of FMT thanks to large datasets, the emergence of optimized algorithms and the application of innovative networks. Main results. The results demonstrate that the imaging quality of FMT can be effectively promoted by improving the accuracy of optical parameter modeling, combined with prior knowledge, and reducing dimensionality. In addition, the traditional regularization-based methods and deep neural network-based methods, especially end-to-end deep networks, can enormously alleviate the ill-posedness of the inverse problem and improve the quality of FMT image reconstruction. Significance. This review aims to illustrate a variety of effective and practical methods for the reconstruction of FMT images that may benefit future research. Furthermore, it may provide some valuable research ideas and directions for FMT in the future, and could promote, to a certain extent, the development of FMT and other methods of optical tomography.
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Wang H, Feng T, Dong X, Zhao Z, Han G, Wang J, Ma W, Wang R, Liu M, Miao J. Method for improving the accuracy of fluorescence molecular tomography based on multi-wavelength concurrent reconstruction. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2022; 93:044102. [PMID: 35489912 DOI: 10.1063/5.0056883] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/15/2021] [Accepted: 02/28/2022] [Indexed: 06/14/2023]
Abstract
A Concurrent-wavelength Reconstruction Algorithm (CRA) based on multi-wavelength information fusion is proposed in this paper that aims to further improve the accuracy of Fluorescence Molecular Tomography (FMT) reconstruction. Combining multi-spectral data with FMT technology, the information of 650 and 750 nm wavelengths near-infrared was used to increase the feature information of the dominant 850 nm wavelength near-infrared effectively. Principal component analysis, which can remove redundant information and achieve data dimensionality reduction, was then utilized to extract the feature information. Finally, tomographic reconstruction of the anomalies was performed based on the stacked auto-encoder neural network model. The comparison results of numerical experiments showed that the reconstruction effect of CRA was superior to the performance of the single wavelength model. The correlation coefficient between CRA reconstructed anomalies' fluorescence yield values and the real fluorescence yield values remained at 0.95 or more under the noise of different levels of signal-to-noise ratios. Therefore, the CRA proposed in this paper could effectively improve on the ill-posedness of the inverse problem, which could further enhance the accuracy of FMT reconstruction.
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Affiliation(s)
- Huiquan Wang
- School of Life Sciences, Tiangong University, Tianjin 300387, China
| | - Tianzi Feng
- School of Electronic and Information Engineering, Tiangong University, Tianjin 300387, China
| | - Xinming Dong
- The Center of Tianjin Rehabilitation and Sanatorium, Tianjin 300387, China
| | - Zhe Zhao
- School of Life Sciences, Tiangong University, Tianjin 300387, China
| | - Guang Han
- School of Life Sciences, Tiangong University, Tianjin 300387, China
| | - Jinhai Wang
- School of Life Sciences, Tiangong University, Tianjin 300387, China
| | - Wenjuan Ma
- Department of Breast Imaging, Tianjin Medical University Cancer Institute and Hospital, National Clinical Research Center for Cancer, Tianjin 300060, China
| | - Rong Wang
- School of Life Sciences, Tiangong University, Tianjin 300387, China
| | - Minghu Liu
- School of Life Sciences, Tiangong University, Tianjin 300387, China
| | - Jinghong Miao
- School of Life Sciences, Tiangong University, Tianjin 300387, China
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14
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An Y, Bian C, Yan D, Wang H, Wang Y, Du Y, Tian J. A Fast and Automated FMT/XCT Reconstruction Strategy Based on Standardized Imaging Space. IEEE TRANSACTIONS ON MEDICAL IMAGING 2022; 41:657-666. [PMID: 34648436 DOI: 10.1109/tmi.2021.3120011] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/25/2023]
Abstract
The traditional finite element method-based fluorescence molecular tomography (FMT)/ X-ray computed tomography (XCT) imaging reconstruction suffers from complicated mesh generation and dual-modality image data fusion, which limits the application of in vivo imaging. To solve this problem, a novel standardized imaging space reconstruction (SISR) method for the quantitative determination of fluorescent probe distributions inside small animals was developed. In conjunction with a standardized dual-modality image data fusion technology, and novel reconstruction strategy based on Laplace regularization and L1-fused Lasso method, the in vivo distribution can be calculated rapidly and accurately, which enables standardized and algorithm-driven data process. We demonstrated the method's feasibility through numerical simulations and quantitatively monitored in vivo programmed death ligand 1 (PD-L1) expression in mouse tumor xenografts, and the results demonstrate that our proposed SISR can increase data throughput and reproducibility, which helps to realize the dynamically and accurately in vivo imaging.
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15
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Zhang H, He X, Yu J, He X, Guo H, Hou Y. L1-L2 norm regularization via forward-backward splitting for fluorescence molecular tomography. BIOMEDICAL OPTICS EXPRESS 2021; 12:7807-7825. [PMID: 35003868 PMCID: PMC8713696 DOI: 10.1364/boe.435932] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/06/2021] [Revised: 11/08/2021] [Accepted: 11/08/2021] [Indexed: 05/07/2023]
Abstract
Fluorescent molecular tomography (FMT) is a highly sensitive and noninvasive imaging approach for providing three-dimensional distribution of fluorescent marker probes. However, owing to its light scattering effect and the ill-posedness of inverse problems, it is challenging to develop an efficient reconstruction algorithm that can achieve the exact location and morphology of the fluorescence source. In this study, therefore, in order to satisfy the need for early tumor detection and improve the sparsity of solution, we proposed a novel L 1-L 2 norm regularization via the forward-backward splitting method for enhancing the FMT reconstruction accuracy and the robustness. By fully considering the highly coherent nature of the system matrix of FMT, it operates by splitting the objective to be minimized into simpler functions, which are dealt with individually to obtain a sparser solution. An analytic solution of L 1-L 2 norm proximal operators and a forward-backward splitting algorithm were employed to efficiently solve the nonconvex L 1-L 2 norm minimization problem. Numerical simulations and an in-vivo glioma mouse model experiment were conducted to evaluate the performance of our algorithm. The comparative results of these experiments demonstrated that the proposed algorithm obtained superior reconstruction performance in terms of spatial location, dual-source resolution, and in-vivo practicability. It was believed that this study would promote the preclinical and clinical applications of FMT in early tumor detection.
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Affiliation(s)
- Heng Zhang
- The Xi'an Key Laboratory of Radiomics and Intelligent Perception, Xi'an, China
- School of Information Sciences and Technology, Northwest University, Xi'an, 710127, China
| | - Xiaowei He
- The Xi'an Key Laboratory of Radiomics and Intelligent Perception, Xi'an, China
- School of Information Sciences and Technology, Northwest University, Xi'an, 710127, China
| | - Jingjing Yu
- School of Physics and Information Technology, Shaanxi Normal University, Xi'an, 710062, China
| | - Xuelei He
- The Xi'an Key Laboratory of Radiomics and Intelligent Perception, Xi'an, China
- School of Information Sciences and Technology, Northwest University, Xi'an, 710127, China
| | - Hongbo Guo
- The Xi'an Key Laboratory of Radiomics and Intelligent Perception, Xi'an, China
- School of Information Sciences and Technology, Northwest University, Xi'an, 710127, China
| | - Yuqing Hou
- The Xi'an Key Laboratory of Radiomics and Intelligent Perception, Xi'an, China
- School of Information Sciences and Technology, Northwest University, Xi'an, 710127, China
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16
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Wang H, Bian C, Kong L, An Y, Du Y, Tian J. A Novel Adaptive Parameter Search Elastic Net Method for Fluorescent Molecular Tomography. IEEE TRANSACTIONS ON MEDICAL IMAGING 2021; 40:1484-1498. [PMID: 33556004 DOI: 10.1109/tmi.2021.3057704] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
Fluorescence molecular tomography (FMT) is a new type of medical imaging technology that can quantitatively reconstruct the three-dimensional distribution of fluorescent probes in vivo. Traditional Lp norm regularization techniques used in FMT reconstruction often face problems such as over-sparseness, over-smoothness, spatial discontinuity, and poor robustness. To address these problems, this paper proposes an adaptive parameter search elastic net (APSEN) method that is based on elastic net regularization, using weight parameters to combine the L1 and L2 norms. For the selection of elastic net weight parameters, this approach introduces the L0 norm of valid reconstruction results and the L2 norm of the residual vector, which are used to adjust the weight parameters adaptively. To verify the proposed method, a series of numerical simulation experiments were performed using digital mice with tumors as experimental subjects, and in vivo experiments of liver tumors were also conducted. The results showed that, compared with the state-of-the-art methods with different light source sizes or distances, Gaussian noise of 5%-25%, and the brute-force parameter search method, the APSEN method has better location accuracy, spatial resolution, fluorescence yield recovery ability, morphological characteristics, and robustness. Furthermore, the in vivo experiments demonstrated the applicability of APSEN for FMT.
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Konovalov AB, Vlasov VV, Uglov AS. Early-photon reflectance fluorescence molecular tomography for small animal imaging: Mathematical model and numerical experiment. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2021; 37:e03408. [PMID: 33094558 DOI: 10.1002/cnm.3408] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/26/2020] [Revised: 10/04/2020] [Accepted: 10/17/2020] [Indexed: 06/11/2023]
Abstract
The paper presents an original approach to time-domain reflectance fluorescence molecular tomography (FMT) of small animals. It is based on the use of early arriving photons and state-of-the-art compressed-sensing-like reconstruction algorithms and aims to improve the spatial resolution of fluorescent images. We deduce the fundamental equation that models the imaging operator and derive analytical representations for the sensitivity functions which are responsible for the reconstruction of the fluorophore absorption coefficient. The idea of fluorescence lifetime tomography with our approach is also discussed. We conduct a numerical experiment on 3D reconstruction of box phantoms with spherical fluorescent inclusions of small diameters. For modeling measurement data and constructing the sensitivity matrix we assume a virtual fluorescence tomograph with a scanning fiber probe that illuminates and collects light in reflectance geometry. It provides for large source-receiver separations which correspond to the macroscopic regime. Two compressed-sensing-like reconstruction algorithms are used to solve the inverse problem. These are the algebraic reconstruction technique with total variation regularization and our modification of the fast iterative shrinkage-thresholding algorithm. Results of our numerical experiment show that our approach is capable of achieving as good spatial resolution as 0.2 mm and even better at depths to 9 mm inclusive.
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Affiliation(s)
- Alexander B Konovalov
- Computational Center, Federal State Unitary Enterprise "Russian Federal Nuclear Center - Zababakhin All-Russia Research Institute of Technical Physics,", Snezhinsk, Russia
- Laboratory of Molecular Imaging, Bach Institute of Biochemistry, Research Center of Biotechnology of the Russian Academy of Sciences, Moscow, Russia
| | - Vitaly V Vlasov
- Computational Center, Federal State Unitary Enterprise "Russian Federal Nuclear Center - Zababakhin All-Russia Research Institute of Technical Physics,", Snezhinsk, Russia
- Laboratory of Molecular Imaging, Bach Institute of Biochemistry, Research Center of Biotechnology of the Russian Academy of Sciences, Moscow, Russia
| | - Alexander S Uglov
- Computational Center, Federal State Unitary Enterprise "Russian Federal Nuclear Center - Zababakhin All-Russia Research Institute of Technical Physics,", Snezhinsk, Russia
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Meng H, Gao Y, Yang X, Wang K, Tian J. K-Nearest Neighbor Based Locally Connected Network for Fast Morphological Reconstruction in Fluorescence Molecular Tomography. IEEE TRANSACTIONS ON MEDICAL IMAGING 2020; 39:3019-3028. [PMID: 32286961 DOI: 10.1109/tmi.2020.2984557] [Citation(s) in RCA: 27] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
Fluorescence molecular tomography (FMT) is a highly sensitive and noninvasive imaging modality for three-dimensional visualization of fluorescence probe distribution in small animals. However, the simplified photon propagation model and ill-posed inverse problem limit the improvement of FMT reconstruction. In this work, we proposed a novel K-nearest neighbor based locally connected (KNN-LC) network to improve the performance of morphological reconstruction in FMT. It directly builds the inverse process of photon transmission by learning the mapping relation between the surface photon intensity and the distribution of fluorescent source. KNN-LC network cascades a fully connected (FC) sub-network with a locally connected (LC) sub-network, where the FC part provides a coarse reconstruction result and LC part fine-tunes the morphological quality of reconstructed result. To assess the performance of our proposed network, we implemented both numerical simulation and in vivo studies. Furthermore, split Bregman-resolved total variation (SBRTV) regularization method and inverse problem simulation (IPS) method were utilized as baselines in all comparisons. The results demonstrated that KNN-LC network achieved accurate reconstruction in both source localization and morphology recovery in a short time. This promoted the in vivo application of FMT for visualizing the distribution of biomarkers inside biological tissue.
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Cao X, Li K, Xu XL, Deneen KMV, Geng GH, Chen XL. Development of tomographic reconstruction for three-dimensional optical imaging: From the inversion of light propagation to artificial intelligence. Artif Intell Med Imaging 2020; 1:78-86. [DOI: 10.35711/aimi.v1.i2.78] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 06/05/2020] [Revised: 08/01/2020] [Accepted: 08/21/2020] [Indexed: 02/06/2023] Open
Abstract
Optical molecular tomography (OMT) is an imaging modality which uses an optical signal, especially near-infrared light, to reconstruct the three-dimensional information of the light source in biological tissue. With the advantages of being low-cost, noninvasive and having high sensitivity, OMT has been applied in preclinical and clinical research. However, due to its serious ill-posedness and ill-condition, the solution of OMT requires heavy data analysis and the reconstruction quality is limited. Recently, the artificial intelligence (commonly known as AI)-based methods have been proposed to provide a different tool to solve the OMT problem. In this paper, we review the progress on OMT algorithms, from conventional methods to AI-based methods, and we also give a prospective towards future developments in this domain.
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Affiliation(s)
- Xin Cao
- School of Information Science and Technology, Northwest University, Xi’an 710069, Shaanxi Province, China
| | - Kang Li
- School of Information Science and Technology, Northwest University, Xi’an 710069, Shaanxi Province, China
| | - Xue-Li Xu
- School of Information Science and Technology, Northwest University, Xi’an 710069, Shaanxi Province, China
| | - Karen M von Deneen
- Engineering Research Center of Molecular and Neuro Imaging, Ministry of Education, and School of Life Science and Technology, Xidian University, Xi’an 710126, Shaanxi Province, China
| | - Guo-Hua Geng
- School of Information Science and Technology, Northwest University, Xi’an 710069, Shaanxi Province, China
| | - Xue-Li Chen
- Engineering Research Center of Molecular and Neuro Imaging, Ministry of Education, and School of Life Science and Technology, Xidian University, Xi’an 710126, Shaanxi Province, China
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20
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Sun C, Nakamura G, Nishimura G, Jiang Y, Liu J, Machida M. Fast and robust reconstruction algorithm for fluorescence diffuse optical tomography assuming a cuboid target. JOURNAL OF THE OPTICAL SOCIETY OF AMERICA. A, OPTICS, IMAGE SCIENCE, AND VISION 2020; 37:231-239. [PMID: 32118903 DOI: 10.1364/josaa.37.000231] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/16/2019] [Accepted: 12/04/2019] [Indexed: 06/10/2023]
Abstract
A fast algorithm for fluorescence diffuse optical tomography is proposed. The algorithm is robust against the choice of initial guesses. We estimate the position of a fluorescent target by assuming a cuboid (rectangular parallelepiped) for the fluorophore target. The proposed numerical algorithm is verified by a numerical experiment and an experiment with a meat phantom. The target position is reconstructed with a cuboid from measurements in the time domain. Moreover, the long-time behavior of the emission light is investigated making use of the analytical solution to the diffusion equation.
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21
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Kong L, An Y, Liang Q, Yin L, Du Y, Tian J. Reconstruction for Fluorescence Molecular Tomography via Adaptive Group Orthogonal Matching Pursuit. IEEE Trans Biomed Eng 2020; 67:2518-2529. [PMID: 31905129 DOI: 10.1109/tbme.2019.2963815] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
OBJECTIVE Fluorescence molecular tomography (FMT) is a promising medical imaging technology aimed at the non-invasive, specific, and sensitive detection of the distribution of fluorophore. Conventional sparsity prior-based methods of FMT commonly face problems such as over-sparseness, spatial discontinuity, and poor robustness, due to the neglect of the interrelation within the local subspace. To address this, we propose an adaptive group orthogonal matching pursuit (AGOMP) method. METHODS AGOMP is based on a novel local spatial-structured sparse regularization, which leverages local spatial interrelations as group sparsity without the hard prior of the tumor region. The adaptive grouped subspace matching pursuit method was adopted to enhance the interrelatedness of elements within a group, which alleviates the over-sparsity problem to some extent and improves the accuracy, robustness, and morphological similarity of FMT reconstruction. A series of numerical simulation experiments, based on digital mouse with both one and several tumors, were conducted, as well as in vivo mouse experiments. RESULTS The results demonstrated that the proposed AGOMP method achieved better location accuracy, fluorescent yield reconstruction, relative sparsity, and morphology than state-of-the-art methods under complex conditions for levels of Gaussian noise ranging from 5-25%. Furthermore, the in vivo mouse experiments demonstrated the practical application of FMT with AGOMP. CONCLUSION The proposed AGOMP can improve the accuracy and robustness for FMT reconstruction in biomedical application.
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22
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Jiang S, Liu J, An Y, Gao Y, Meng H, Wang K, Tian J. Fluorescence Molecular Tomography Based on Group Sparsity Priori for Morphological Reconstruction of Glioma. IEEE Trans Biomed Eng 2019; 67:1429-1437. [PMID: 31449004 DOI: 10.1109/tbme.2019.2937354] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
OBJECTIVE Fluorescence molecular tomography (FMT) is an important tool for life science, which can noninvasive real-time three-dimensional (3-D) visualization for fluorescence source location. FMT is widely used in tumor research due to its high-sensitive and low cost. However, the reconstruction of FMT is difficult. Although the reconstruction methods of FMT have developed rapidly in recent years, the morphological reconstruction of FMT is still a challenge problem. Thus, the purpose of this study is to realize the morphological reconstruction performance of FMT in glioma research. METHODS In this study, group sparsity was used as a new priori information for FMT. Besides sparsity, group sparsity also takes the group structure of the fluorescent sources, which can maintain the morphological information of the sources. Fused LASSO method (FLM) was proved it can efficiently model the group sparsity prior. Thus, we utilize FLM to reconstruct the morphological information of glioma. Furthermore, to reduce the influence of the high scattering of skull, we modified the FLM for improving the accuracy of morphological reconstruction. RESULTS Glioma numerical simulation model and in vivo glioma model were established to evaluate the performance of morphological reconstruction of the proposed method. The results demonstrated that the proposed method was efficient to reconstruct the morphological information of glioma. CONCLUSION Group sparsity priori can effectively improve the morphological accuracy of FMT reconstruction. SIGNIFICANCE Group sparsity can maintain the morphological information of fluorescent sources effectively, which has great application potential in FMT. The group sparsity based methods can realize the morphological reconstruction, which is of great practical significance in tumor research.
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He X, Yu J, Wang X, Yi H, Chen Y, Song X, He X. Half Thresholding Pursuit Algorithm for Fluorescence Molecular Tomography. IEEE Trans Biomed Eng 2018; 66:1468-1476. [PMID: 30296209 DOI: 10.1109/tbme.2018.2874699] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
OBJECTIVE Fluorescence Molecular Tomography (FMT) is a promising optical tool for small animal imaging. The l1/2-norm regularization has attracted attention in the field of FMT due to its ability in enhancing sparsity of solution and coping with the high ill-posedness of the inverse problem. However, efficient algorithm for solving the nonconvex regularized model deserve to explore. METHOD A Half Thresholding Pursuit Algorithm (HTPA) combined with parameter optimization is proposed in this paper to efficiently solve the nonconvex optimization model. Specifically, the half thresholding iteration method is utilized to solve l1/2-norm model, pursuit strategy is used to accelerate the process of iteration, and the parameter optimization scheme is designed to obtain robust parameter. RESULTS Analysis and assessment on simulated and experimental data demonstrate that the proposed HTPA performs better in location accuracy and reconstructed fluorescent yield in less time cost, compared with the state-of-the-art reconstruction algorithms. CONCLUSION The proposed HTPA combined with the parameter optimization scheme is an efficient and robust reconstruction approach to FMT.
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Jiang S, Liu J, Zhang G, An Y, Meng H, Gao Y, Wang K, Tian J. Reconstruction of Fluorescence Molecular Tomography via a Fused LASSO Method Based on Group Sparsity Prior. IEEE Trans Biomed Eng 2018; 66:1361-1371. [PMID: 30281432 DOI: 10.1109/tbme.2018.2872913] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Abstract
OBJECTIVE The aim of this paper is to improve the reconstruction accuracy in both position and source region of fluorescence molecular tomography (FMT). METHODS The reconstruction of the FMT is challenging due to its serious ill-posedness and ill-condition. Currently, to obtain the fluorescent sources accurately, more a priori information of the fluorescent sources is utilized and more efficient and practical methods are proposed. In this paper, we took the group sparsity of the fluorescent sources as a new type of priori information in the FMT, and proposed the fused LASSO method (FLM) for FMT. The FLM based on group sparsity prior not only takes advantage of the sparsity of the fluorescent sources, but also utilizes the structure of the sources, thus making the reconstruction results more accuracy and morphologically similar to the sources. To further improve the reconstruction efficiency, we adopt Nesterov's method to solve the FLM. RESULTS Both heterogeneous numerical simulation experiments and in vivo mouse experiments were carried out to verify the property of the FLM. The results have verified the superiority of the FLM over conventional methods in tumor detection and tumor morphological reconstruction. Furthermore, the in vivo experiments had demonstrated that the FLM has great potential in preclinical application of the FMT. SIGNIFICANCE The reconstruction method based on group sparsity prior has a great potential in the FMT study, it can further improve the reconstruction quality, which has practical significance in preclinical research.
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Zhang S, Ma X, Wang Y, Wu M, Meng H, Chai W, Wang X, Wei S, Tian J. Robust Reconstruction of Fluorescence Molecular Tomography Based on Sparsity Adaptive Correntropy Matching Pursuit Method for Stem Cell Distribution. IEEE TRANSACTIONS ON MEDICAL IMAGING 2018; 37:2176-2184. [PMID: 29993826 DOI: 10.1109/tmi.2018.2825102] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
Fluorescence molecular tomography (FMT), as a promising imaging modality in preclinical research, can obtain the three-dimensional (3-D) position information of the stem cell in mice. However, because of the ill-posed nature and sensitivity to noise of the inverse problem, it is a challenge to develop a robust reconstruction method, which can accurately locate the stem cells and define the distribution. In this paper, we proposed a sparsity adaptive correntropy matching pursuit (SACMP) method. SACMP method is independent on the noise distribution of measurements and it assigns small weights on severely corrupted entries of data and large weights on clean ones adaptively. These properties make it more suitable for in vivo experiment. To analyze the performance in terms of robustness and practicability of SACMP, we conducted numerical simulation and in vivo mice experiments. The results demonstrated that the SACMP method obtained the highest robustness and accuracy in locating stem cells and depicting stem cell distribution compared with stagewise orthogonal matching pursuit and sparsity adaptive subspace pursuit reconstruction methods. To the best of our knowledge, this is the first study that acquired such accurate and robust FMT distribution reconstruction for stem cell tracking in mice brain. This promotes the application of FMT in locating stem cell and distribution reconstruction in practical mice brain injury models.
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26
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An Y, Wang K, Tian J. Recent methodology advances in fluorescence molecular tomography. Vis Comput Ind Biomed Art 2018; 1:1. [PMID: 32240398 PMCID: PMC7098398 DOI: 10.1186/s42492-018-0001-6] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2018] [Accepted: 06/30/2018] [Indexed: 12/26/2022] Open
Abstract
Molecular imaging (MI) is a novel imaging discipline that has been continuously developed in recent years. It combines biochemistry, multimodal imaging, biomathematics, bioinformatics, cell & molecular physiology, biophysics, and pharmacology, and it provides a new technology platform for the early diagnosis and quantitative analysis of diseases, treatment monitoring and evaluation, and the development of comprehensive physiology. Fluorescence Molecular Tomography (FMT) is a type of optical imaging modality in MI that captures the three-dimensional distribution of fluorescence within a biological tissue generated by a specific molecule of fluorescent material within a biological tissue. Compared with other optical molecular imaging methods, FMT has the characteristics of high sensitivity, low cost, and safety and reliability. It has become the research frontier and research hotspot of optical molecular imaging technology. This paper took an overview of the recent methodology advances in FMT, mainly focused on the photon propagation model of FMT based on the radiative transfer equation (RTE), and the reconstruction problem solution consist of forward problem and inverse problem. We introduce the detailed technologies utilized in reconstruction of FMT. Finally, the challenges in FMT were discussed. This survey aims at summarizing current research hotspots in methodology of FMT, from which future research may benefit.
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Affiliation(s)
- Yu An
- Key Laboratory of Molecular Imaging, Institute of Automation, Chinese Academy of Sciences, Beijing, China
| | - Kun Wang
- Key Laboratory of Molecular Imaging, Institute of Automation, Chinese Academy of Sciences, Beijing, China
| | - Jie Tian
- Key Laboratory of Molecular Imaging, Institute of Automation, Chinese Academy of Sciences, Beijing, China.
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27
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Liu Y, Jiang S, Liu J, An Y, Zhang G, Gao Y, Wang K, Tian J. Reconstruction method for fluorescence molecular tomography based on L1-norm primal accelerated proximal gradient. JOURNAL OF BIOMEDICAL OPTICS 2018; 23:1-11. [PMID: 30109802 DOI: 10.1117/1.jbo.23.8.085002] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/20/2018] [Accepted: 07/30/2018] [Indexed: 06/08/2023]
Abstract
Fluorescence molecular tomography (FMT) has been widely used in preclinical tumor imaging, which enables three-dimensional imaging of the distribution of fluorescent probes in small animal bodies via image reconstruction method. However, the reconstruction results are usually unsatisfactory in the term of robustness and efficiency because of the ill-posed and ill-conditioned of FMT problem. In this study, an FMT reconstruction method based on primal accelerated proximal gradient (PAPG) descent and L1-norm regularized projection (L1RP) is proposed. The proposed method utilizes the current and previous iterations to obtain a search point at each iteration. To achieve fast convergence, the PAPG method is applied to efficiently solve the search point, and then L1RP is performed to obtain the robust and accurate reconstruction. To verify the performance of the proposed method, simulation experiments are conducted. The comparative results revealed that it held advantages of robustness, accuracy, and efficiency in FMT reconstructions. Furthermore, a phantom experiment and an in vivo mouse experiment were also performed, which proved the potential and feasibility of the proposed method for practical applications.
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Affiliation(s)
- Yuhao Liu
- Beijing Jiaotong University, School of Computer and Information Technology, Haidian District, Beijin, China
- Institute of Automation, CAS Key Laboratory of Molecular Imaging, Chinese Academy of Sciences, Beiji, China
| | - Shixin Jiang
- Beijing Jiaotong University, School of Computer and Information Technology, Haidian District, Beijin, China
- Institute of Automation, CAS Key Laboratory of Molecular Imaging, Chinese Academy of Sciences, Beiji, China
| | - Jie Liu
- Beijing Jiaotong University, School of Computer and Information Technology, Haidian District, Beijin, China
| | - Yu An
- Institute of Automation, CAS Key Laboratory of Molecular Imaging, Chinese Academy of Sciences, Beiji, China
| | - Guanglei Zhang
- Beihang University, School of Biological Science and Medical Engineering, Beijing Advanced Innovatio, China
| | - Yuan Gao
- Institute of Automation, CAS Key Laboratory of Molecular Imaging, Chinese Academy of Sciences, Beiji, China
| | - Kun Wang
- Institute of Automation, CAS Key Laboratory of Molecular Imaging, Chinese Academy of Sciences, Beiji, China
- University of Chinese Academy of Sciences, Beijing, China
| | - Jie Tian
- Institute of Automation, CAS Key Laboratory of Molecular Imaging, Chinese Academy of Sciences, Beiji, China
- University of Chinese Academy of Sciences, Beijing, China
- Beijing Key Laboratory of Molecular Imaging, Beijing, China
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Zhu Y, Jha AK, Wong DF, Rahmim A. Image reconstruction in fluorescence molecular tomography with sparsity-initialized maximum-likelihood expectation maximization. BIOMEDICAL OPTICS EXPRESS 2018; 9:3106-3121. [PMID: 29984086 PMCID: PMC6033581 DOI: 10.1364/boe.9.003106] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/04/2018] [Revised: 05/16/2018] [Accepted: 05/23/2018] [Indexed: 06/08/2023]
Abstract
We present a reconstruction method involving maximum-likelihood expectation maximization (MLEM) to model Poisson noise as applied to fluorescence molecular tomography (FMT). MLEM is initialized with the output from a sparse reconstruction-based approach, which performs truncated singular value decomposition-based preconditioning followed by fast iterative shrinkage-thresholding algorithm (FISTA) to enforce sparsity. The motivation for this approach is that sparsity information could be accounted for within the initialization, while MLEM would accurately model Poisson noise in the FMT system. Simulation experiments show the proposed method significantly improves images qualitatively and quantitatively. The method results in over 20 times faster convergence compared to uniformly initialized MLEM and improves robustness to noise compared to pure sparse reconstruction. We also theoretically justify the ability of the proposed approach to reduce noise in the background region compared to pure sparse reconstruction. Overall, these results provide strong evidence to model Poisson noise in FMT reconstruction and for application of the proposed reconstruction framework to FMT imaging.
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Affiliation(s)
- Yansong Zhu
- Department of Electrical and Computer Engineering, Johns Hopkins University, Baltimore, MD,
USA
- Department of Radiology and Radiological Science, Johns Hopkins University, Baltimore, MD,
USA
| | - Abhinav K. Jha
- Department of Radiology and Radiological Science, Johns Hopkins University, Baltimore, MD,
USA
- Department of Biomedical Engineering, Washington University in St. Louis, St. Louis, MO,
USA
- Mallinckrodt Institute of Radiology, Washington University in St. Louis, St. Louis, MO,
USA
| | - Dean F. Wong
- Department of Radiology and Radiological Science, Johns Hopkins University, Baltimore, MD,
USA
- Department of Neuroscience, Johns Hopkins University, Baltimore, MD,
USA
- Department of Psychiatry and Behavioral Science, Johns Hopkins University, Baltimore, MD,
USA
- Department of Neurology, Johns Hopkins University, Baltimore, MD,
USA
| | - Arman Rahmim
- Department of Electrical and Computer Engineering, Johns Hopkins University, Baltimore, MD,
USA
- Department of Radiology and Radiological Science, Johns Hopkins University, Baltimore, MD,
USA
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Gao Y, Wang K, Jiang S, Liu Y, Ai T, Tian J. Bioluminescence Tomography Based on Gaussian Weighted Laplace Prior Regularization for In Vivo Morphological Imaging of Glioma. IEEE TRANSACTIONS ON MEDICAL IMAGING 2017; 36:2343-2354. [PMID: 28796614 DOI: 10.1109/tmi.2017.2737661] [Citation(s) in RCA: 28] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
Bioluminescence tomography (BLT) is a powerful non-invasive molecular imaging tool for in vivo studies of glioma in mice. However, because of the light scattering and resulted ill-posed problems, it is challenging to develop a sufficient reconstruction method, which can accurately locate the tumor and define the tumor morphology in three-dimension. In this paper, we proposed a novel Gaussian weighted Laplace prior (GWLP) regularization method. It considered the variance of the bioluminescence energy between any two voxels inside an organ had a non-linear inverse relationship with their Gaussian distance to solve the over-smoothed tumor morphology in BLT reconstruction. We compared the GWLP with conventional Tikhonov and Laplace regularization methods through various numerical simulations and in vivo orthotopic glioma mouse model experiments. The in vivo magnetic resonance imaging and ex vivo green fluorescent protein images and hematoxylin-eosin stained images of whole head cryoslicing specimens were utilized as gold standards. The results demonstrated that GWLP achieved the highest accuracy in tumor localization and tumor morphology preservation. To the best of our knowledge, this is the first study that achieved such accurate BLT morphological reconstruction of orthotopic glioma without using any segmented tumor structure from any other structural imaging modalities as the prior for reconstruction guidance. This enabled BLT more suitable and practical for in vivo imaging of orthotopic glioma mouse models.
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Zhang S, Wang K, Liu H, Leng C, Gao Y, Tian J. Reconstruction Method for In Vivo Bioluminescence Tomography Based on the Split Bregman Iterative and Surrogate Functions. Mol Imaging Biol 2017; 19:245-255. [PMID: 27580914 DOI: 10.1007/s11307-016-1002-5] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
Abstract
PURPOSE Bioluminescence tomography (BLT) can provide in vivo three-dimensional (3D) images for quantitative analysis of biological processes in preclinical small animal studies, which is superior than the conventional planar bioluminescence imaging. However, to reconstruct light sources under the skin in 3D with desirable accuracy and efficiency, BLT has to face the ill-posed and ill-conditioned inverse problem. In this paper, we developed a new method for BLT reconstruction, which utilized the mathematical strategies of the split Bregman iterative and surrogate functions (SBISF) method. PROCEDURES The proposed method considered the sparsity characteristic of the reconstructed sources. Thus, the sparsity itself was regarded as a kind of a priori information, and the sparse regularization is incorporated, which can accurately locate the position of the sources. Numerical simulation experiments of multisource cases with comparative analyses were performed to evaluate the performance of the proposed method. Then, a bead-implanted mouse and a breast cancer xenograft mouse model were employed to validate the feasibility of this method in in vivo experiments. RESULTS The results of both simulation and in vivo experiments indicated that comparing with the L1-norm iteration shrinkage method and non-monotone spectral projected gradient pursuit method, the proposed SBISF method provided the smallest position error with the least amount of time consumption. CONCLUSIONS The SBISF method is able to achieve high accuracy and high efficiency in BLT reconstruction and hold great potential for making BLT more practical in small animal studies.
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Affiliation(s)
- Shuang Zhang
- Sino-Dutch Biomedical and Information Engineering School, Northeastern University, Shenyang, 110819, China
- Key Laboratory of Molecular Imaging, Institute of Automation, Chinese Academy of Sciences, Beijing, 100190, People's Republic of China
| | - Kun Wang
- Key Laboratory of Molecular Imaging, Institute of Automation, Chinese Academy of Sciences, Beijing, 100190, People's Republic of China.
- Beijing Key Laboratory of Molecular Imaging, Zhongguancun East Road #95, Haidian Dist., Beijing, 100190, People's Republic of China.
| | - Hongbo Liu
- Key Laboratory of Molecular Imaging, Institute of Automation, Chinese Academy of Sciences, Beijing, 100190, People's Republic of China
- Beijing Key Laboratory of Molecular Imaging, Zhongguancun East Road #95, Haidian Dist., Beijing, 100190, People's Republic of China
| | - Chengcai Leng
- Key Laboratory of Molecular Imaging, Institute of Automation, Chinese Academy of Sciences, Beijing, 100190, People's Republic of China
- Beijing Key Laboratory of Molecular Imaging, Zhongguancun East Road #95, Haidian Dist., Beijing, 100190, People's Republic of China
| | - Yuan Gao
- Key Laboratory of Molecular Imaging, Institute of Automation, Chinese Academy of Sciences, Beijing, 100190, People's Republic of China
- Beijing Key Laboratory of Molecular Imaging, Zhongguancun East Road #95, Haidian Dist., Beijing, 100190, People's Republic of China
| | - Jie Tian
- Key Laboratory of Molecular Imaging, Institute of Automation, Chinese Academy of Sciences, Beijing, 100190, People's Republic of China.
- Beijing Key Laboratory of Molecular Imaging, Zhongguancun East Road #95, Haidian Dist., Beijing, 100190, People's Republic of China.
- Chinese Society for Molecular Imaging, Beijing, People's Republic of China.
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Ye J, Du Y, An Y, Mao Y, Jiang S, Shang W, He K, Yang X, Wang K, Chi C, Tian J. Sparse Reconstruction of Fluorescence Molecular Tomography Using Variable Splitting and Alternating Direction Scheme. Mol Imaging Biol 2017; 20:37-46. [DOI: 10.1007/s11307-017-1088-4] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
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Wang B, Wan W, Wang Y, Ma W, Zhang L, Li J, Zhou Z, Zhao H, Gao F. An L p (0 ≤ p ≤ 1)-norm regularized image reconstruction scheme for breast DOT with non-negative-constraint. Biomed Eng Online 2017; 16:32. [PMID: 28253881 PMCID: PMC5439119 DOI: 10.1186/s12938-017-0318-y] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/20/2016] [Accepted: 01/30/2017] [Indexed: 11/12/2022] Open
Abstract
Background In diffuse optical tomography (DOT), the image reconstruction is often an ill-posed inverse problem, which is even more severe for breast DOT since there are considerably increasing unknowns to reconstruct with regard to the achievable number of measurements. One common way to address this ill-posedness is to introduce various regularization methods. There has been extensive research regarding constructing and optimizing objective functions. However, although these algorithms dramatically improved reconstruction images, few of them have designed an essentially differentiable objective function whose full gradient is easy to obtain to accelerate the optimization process. Methods This paper introduces a new kind of non-negative prior information, designing differentiable objective functions for cases of L1-norm, Lp (0 < p < 1)-norm and L0-norm. Incorporating this non-negative prior information, it is easy to obtain the gradient of these differentiable objective functions, which is useful to guide the optimization process. Results Performance analyses are conducted using both numerical and phantom experiments. In terms of spatial resolution, quantitativeness, gray resolution and execution time, the proposed methods perform better than the conventional regularization methods without this non-negative prior information. Conclusions The proposed methods improves the reconstruction images using the introduced non-negative prior information. Furthermore, the non-negative constraint facilitates the gradient computation, accelerating the minimization of the objective functions.
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Affiliation(s)
- Bingyuan Wang
- College of Precision Instruments and Optoelectronics Engineering, Tianjin University, Tianjin, 300072, China
| | - Wenbo Wan
- College of Precision Instruments and Optoelectronics Engineering, Tianjin University, Tianjin, 300072, China
| | - Yihan Wang
- College of Precision Instruments and Optoelectronics Engineering, Tianjin University, Tianjin, 300072, China
| | - Wenjuan Ma
- Cancer Institute and Hospital, Tianjin Medical University, Tianjin, 300060, China
| | - Limin Zhang
- College of Precision Instruments and Optoelectronics Engineering, Tianjin University, Tianjin, 300072, China
| | - Jiao Li
- College of Precision Instruments and Optoelectronics Engineering, Tianjin University, Tianjin, 300072, China
| | - Zhongxing Zhou
- College of Precision Instruments and Optoelectronics Engineering, Tianjin University, Tianjin, 300072, China
| | - Huijuan Zhao
- College of Precision Instruments and Optoelectronics Engineering, Tianjin University, Tianjin, 300072, China. .,Tianjin Key Laboratory of Biomedical Detecting Techniques and Instruments, Tianjin, 300072, China.
| | - Feng Gao
- College of Precision Instruments and Optoelectronics Engineering, Tianjin University, Tianjin, 300072, China. .,Tianjin Key Laboratory of Biomedical Detecting Techniques and Instruments, Tianjin, 300072, China.
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An Y, Liu J, Zhang G, Jiang S, Ye J, Chi C, Tian J. Compactly Supported Radial Basis Function-Based Meshless Method for Photon Propagation Model of Fluorescence Molecular Tomography. IEEE TRANSACTIONS ON MEDICAL IMAGING 2017; 36:366-373. [PMID: 27552744 DOI: 10.1109/tmi.2016.2601311] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Fluorescence Molecular Tomography (FMT) is a powerful imaging modality for the research of cancer diagnosis, disease treatment and drug discovery. Via three-dimensional (3-D) imaging reconstruction, it can quantitatively and noninvasively obtain the distribution of fluorescent probes in biological tissues. Currently, photon propagation of FMT is conventionally described by the Finite Element Method (FEM), and it can obtain acceptable image quality. However, there are still some inherent inadequacies in FEM, such as time consuming, discretization error and inflexibility in mesh generation, which partly limit its imaging accuracy. To further improve the solving accuracy of photon propagation model (PPM), we propose a novel compactly supported radial basis functions (CSRBFs)-based meshless method (MM) to implement the PPM of FMT. We introduced a series of independent nodes and continuous CSRBFs to interpolate the PPM, which can avoid complicated mesh generation. To analyze the performance of the proposed MM, we carried out numerical heterogeneous mouse simulation to validate the simulated surface fluorescent measurement. Then we performed an in vivo experiment to observe the tomographic reconstruction. The experimental results confirmed that our proposed MM could obtain more similar surface fluorescence measurement with the golden standard (Monte-Carlo method), and more accurate reconstruction result was achieved via MM in in vivo application.
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Jiang S, Liu J, An Y, Zhang G, Ye J, Mao Y, He K, Chi C, Tian J. Novel l 2,1-norm optimization method for fluorescence molecular tomography reconstruction. BIOMEDICAL OPTICS EXPRESS 2016; 7:2342-59. [PMID: 27375949 PMCID: PMC4918587 DOI: 10.1364/boe.7.002342] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/11/2016] [Revised: 05/09/2016] [Accepted: 05/12/2016] [Indexed: 05/23/2023]
Abstract
Fluorescence molecular tomography (FMT) is a promising tomographic method in preclinical research, which enables noninvasive real-time three-dimensional (3-D) visualization for in vivo studies. The ill-posedness of the FMT reconstruction problem is one of the many challenges in the studies of FMT. In this paper, we propose a l 2,1-norm optimization method using a priori information, mainly the structured sparsity of the fluorescent regions for FMT reconstruction. Compared to standard sparsity methods, the structured sparsity methods are often superior in reconstruction accuracy since the structured sparsity utilizes correlations or structures of the reconstructed image. To solve the problem effectively, the Nesterov's method was used to accelerate the computation. To evaluate the performance of the proposed l 2,1-norm method, numerical phantom experiments and in vivo mouse experiments are conducted. The results show that the proposed method not only achieves accurate and desirable fluorescent source reconstruction, but also demonstrates enhanced robustness to noise.
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Affiliation(s)
- Shixin Jiang
- Department of Biomedical Engineering, School of Computer and Information Technology, Beijing Jiaotong University, No. 3 Shangyuancun, Haidian District, Beijing 100044, China
| | - Jie Liu
- Department of Biomedical Engineering, School of Computer and Information Technology, Beijing Jiaotong University, No. 3 Shangyuancun, Haidian District, Beijing 100044, China
| | - Yu An
- Department of Biomedical Engineering, School of Computer and Information Technology, Beijing Jiaotong University, No. 3 Shangyuancun, Haidian District, Beijing 100044, China
| | - Guanglei Zhang
- Department of Biomedical Engineering, School of Computer and Information Technology, Beijing Jiaotong University, No. 3 Shangyuancun, Haidian District, Beijing 100044, China
| | - Jinzuo Ye
- Key Laboratory of Molecular Imaging of Chinese Academy of Sciences, Institute of Automation, Chinese Academy of Sciences, No. 95 Zhongguancun East Road, Haidian District, Beijing 100190, China
| | - Yamin Mao
- Key Laboratory of Molecular Imaging of Chinese Academy of Sciences, Institute of Automation, Chinese Academy of Sciences, No. 95 Zhongguancun East Road, Haidian District, Beijing 100190, China
| | - Kunshan He
- Key Laboratory of Molecular Imaging of Chinese Academy of Sciences, Institute of Automation, Chinese Academy of Sciences, No. 95 Zhongguancun East Road, Haidian District, Beijing 100190, China
| | - Chongwei Chi
- Key Laboratory of Molecular Imaging of Chinese Academy of Sciences, Institute of Automation, Chinese Academy of Sciences, No. 95 Zhongguancun East Road, Haidian District, Beijing 100190, China
- Beijing Key Laboratory of Molecular Imaging, Institute of Automation, Chinese Academy of Sciences, No. 95 Zhongguancun East Road, Haidian District, Beijing 100190, China
| | - Jie Tian
- Key Laboratory of Molecular Imaging of Chinese Academy of Sciences, Institute of Automation, Chinese Academy of Sciences, No. 95 Zhongguancun East Road, Haidian District, Beijing 100190, China
- Beijing Key Laboratory of Molecular Imaging, Institute of Automation, Chinese Academy of Sciences, No. 95 Zhongguancun East Road, Haidian District, Beijing 100190, China
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Zhu D, Li C. Accelerated image reconstruction in fluorescence molecular tomography using a nonuniform updating scheme with momentum and ordered subsets methods. JOURNAL OF BIOMEDICAL OPTICS 2016; 21:16004. [PMID: 26762246 DOI: 10.1117/1.jbo.21.1.016004] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/13/2015] [Accepted: 12/08/2015] [Indexed: 05/03/2023]
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36
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An Y, Liu J, Zhang G, Ye J, Mao Y, Jiang S, Shang W, Du Y, Chi C, Tian J. Meshless reconstruction method for fluorescence molecular tomography based on compactly supported radial basis function. JOURNAL OF BIOMEDICAL OPTICS 2015; 20:105003. [PMID: 26451513 DOI: 10.1117/1.jbo.20.10.105003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/02/2015] [Accepted: 09/15/2015] [Indexed: 05/05/2023]
Abstract
Fluorescence molecular tomography (FMT) is a promising tool in the study of cancer, drug discovery, and disease diagnosis, enabling noninvasive and quantitative imaging of the biodistribution of fluorophores in deep tissues via image reconstruction techniques. Conventional reconstruction methods based on the finite-element method (FEM) have achieved acceptable stability and efficiency. However, some inherent shortcomings in FEM meshes, such as time consumption in mesh generation and a large discretization error, limit further biomedical application. In this paper, we propose a meshless method for reconstruction of FMT (MM-FMT) using compactly supported radial basis functions (CSRBFs). With CSRBFs, the image domain can be accurately expressed by continuous CSRBFs, avoiding the discretization error to a certain degree. After direct collocation with CSRBFs, the conventional optimization techniques, including Tikhonov, L1-norm iteration shrinkage (L1-IS), and sparsity adaptive matching pursuit, were adopted to solve the meshless reconstruction. To evaluate the performance of the proposed MM-FMT, we performed numerical heterogeneous mouse experiments and in vivo bead-implanted mouse experiments. The results suggest that the proposed MM-FMT method can reduce the position error of the reconstruction result to smaller than 0.4 mm for the double-source case, which is a significant improvement for FMT.
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Affiliation(s)
- Yu An
- Beijing Jiaotong University, School of Computer and Information, Department of Biomedical Engineering, No. 3 Shangyuancun Road, Beijing 100044, ChinabChinese Academy of Sciences, Institute of Automation, Key Laboratory of Molecular Imaging of Chinese Acad
| | - Jie Liu
- Beijing Jiaotong University, School of Computer and Information, Department of Biomedical Engineering, No. 3 Shangyuancun Road, Beijing 100044, China
| | - Guanglei Zhang
- Beijing Jiaotong University, School of Computer and Information, Department of Biomedical Engineering, No. 3 Shangyuancun Road, Beijing 100044, China
| | - Jinzuo Ye
- Chinese Academy of Sciences, Institute of Automation, Key Laboratory of Molecular Imaging of Chinese Academy of Sciences, No. 95 Zhongguancun East Road, Beijing, China
| | - Yamin Mao
- Chinese Academy of Sciences, Institute of Automation, Key Laboratory of Molecular Imaging of Chinese Academy of Sciences, No. 95 Zhongguancun East Road, Beijing, China
| | - Shixin Jiang
- Beijing Jiaotong University, School of Computer and Information, Department of Biomedical Engineering, No. 3 Shangyuancun Road, Beijing 100044, China
| | - Wenting Shang
- Chinese Academy of Sciences, Institute of Automation, Key Laboratory of Molecular Imaging of Chinese Academy of Sciences, No. 95 Zhongguancun East Road, Beijing, China
| | - Yang Du
- Chinese Academy of Sciences, Institute of Automation, Key Laboratory of Molecular Imaging of Chinese Academy of Sciences, No. 95 Zhongguancun East Road, Beijing, China
| | - Chongwei Chi
- Chinese Academy of Sciences, Institute of Automation, Key Laboratory of Molecular Imaging of Chinese Academy of Sciences, No. 95 Zhongguancun East Road, Beijing, China
| | - Jie Tian
- Chinese Academy of Sciences, Institute of Automation, Key Laboratory of Molecular Imaging of Chinese Academy of Sciences, No. 95 Zhongguancun East Road, Beijing, ChinacChinese Academy of Sciences, Institute of Automation, Beijing Key Laboratory of Molecul
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Zou W, Wang J, Hu D, Wang W. A reconstruction approach in wavelet domain for fluorescent molecular tomography via rotated sources illumination. Biomed Eng Online 2015; 14:86. [PMID: 26419738 PMCID: PMC4589093 DOI: 10.1186/s12938-015-0080-y] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2015] [Accepted: 09/10/2015] [Indexed: 11/23/2022] Open
Abstract
Background Fluorescent molecular tomography (FMT) aims at reconstructing the spatial map of optical and fluorescence parameters from fluence measurements. Basically, solving large-scale matrix equations is computationally expensive for image reconstruction of FMT. Despite the reconstruction quality can be improved with more sources, it may result in higher computational costs for reconstruction. This article presents a novel method in the wavelet domain with rotated sources illumination. Methods We use the finite element method for the computation of the forward model. The global inverse problem is solved based on wavelet in conjunction with principal component analysis. The iterative reconstruction is implemented with sources rotated in a certain angle. The original excitation light sources are used to reconstruct the image in the first iteration. Then, upon the sources are rotated by a certain angle, they are employed for the next iteration of reconstruction. Results Simulation results demonstrate that our method can considerably reduce the time taken for the computation of inverse problem in FMT. Furthermore, the approach proposed is also shown to largely outperform the traditional method in terms of the precision of inverse solutions. Conclusions Our method has the capability to locate the inclusions. The proposed method can significantly speed up the reconstruction process with the high reconstruction quality.
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Affiliation(s)
- Wei Zou
- School of Electronic and Information Engineering, Soochow University, Suzhou, 215006, China. .,Department of Electronic and Information Engineering, Hong Kong Polytechnic University, Kowloon, Hong Kong. .,School of Information Technologies, The University of Sydney, Sydney, NSW, 2006, Australia.
| | - Jiajun Wang
- School of Electronic and Information Engineering, Soochow University, Suzhou, 215006, China. .,Department of Electronic and Information Engineering, Hong Kong Polytechnic University, Kowloon, Hong Kong. .,School of Information Technologies, The University of Sydney, Sydney, NSW, 2006, Australia.
| | - Danfeng Hu
- School of Electronic and Information Engineering, Soochow University, Suzhou, 215006, China.
| | - Wenxia Wang
- School of Electronic and Information Engineering, Soochow University, Suzhou, 215006, China.
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Deng Y, Luo Z, Jiang X, Xie W, Luo Q. Accurate quantification of fluorescent targets within turbid media based on a decoupled fluorescence Monte Carlo model. OPTICS LETTERS 2015; 40:3129-3132. [PMID: 26125384 DOI: 10.1364/ol.40.003129] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We propose a method based on a decoupled fluorescence Monte Carlo model for constructing fluorescence Jacobians to enable accurate quantification of fluorescence targets within turbid media. The effectiveness of the proposed method is validated using two cylindrical phantoms enclosing fluorescent targets within homogeneous and heterogeneous background media. The results demonstrate that our method can recover relative concentrations of the fluorescent targets with higher accuracy than the perturbation fluorescence Monte Carlo method. This suggests that our method is suitable for quantitative fluorescence diffuse optical tomography, especially for in vivo imaging of fluorophore targets for diagnosis of different diseases and abnormalities.
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Temporal Unmixing of Dynamic Fluorescent Images by Blind Source Separation Method with a Convex Framework. COMPUTATIONAL AND MATHEMATICAL METHODS IN MEDICINE 2015; 2015:713424. [PMID: 26089974 PMCID: PMC4458298 DOI: 10.1155/2015/713424] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/18/2014] [Revised: 04/20/2015] [Accepted: 04/23/2015] [Indexed: 11/17/2022]
Abstract
By recording a time series of tomographic images, dynamic fluorescence molecular tomography (FMT) allows exploring perfusion, biodistribution, and pharmacokinetics of labeled substances in vivo. Usually, dynamic tomographic images are first reconstructed frame by frame, and then unmixing based on principle component analysis (PCA) or independent component analysis (ICA) is performed to detect and visualize functional structures with different kinetic patterns. PCA and ICA assume sources are statistically uncorrelated or independent and don't perform well when correlated sources are present. In this paper, we deduce the relationship between the measured imaging data and the kinetic patterns and present a temporal unmixing approach, which is based on nonnegative blind source separation (BSS) method with a convex analysis framework to separate the measured data. The presented method requires no assumption on source independence or zero correlations. Several numerical simulations and phantom experiments are conducted to investigate the performance of the proposed temporal unmixing method. The results indicate that it is feasible to unmix the measured data before the tomographic reconstruction and the BSS based method provides better unmixing quality compared with PCA and ICA.
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Lu Y, Darne CD, Tan IC, Zhu B, Rightmer R, Rasmussen JC, Sevick-Muraca EM. Experimental Comparison of Continuous-Wave and Frequency-Domain Fluorescence Tomography in a Commercial Multi-Modal Scanner. IEEE TRANSACTIONS ON MEDICAL IMAGING 2015; 34:1197-1211. [PMID: 25438307 DOI: 10.1109/tmi.2014.2375193] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
The performance evaluation of a variety of small animal tomography measurement approaches and algorithms for recovery of fluorescent absorption cross section has not been conducted. Herein, we employed an intensified CCD system installed in a commercial small animal CT (Computed Tomography) scanner to compare image reconstructions from time-independent, continuous wave (CW) measurements and from time-dependent, frequency domain (FD) measurements in a series of physical phantoms specifically designed for evaluation. Comparisons were performed as a function of (1) number of projections, (2) the level of preprocessing filters used to improve the signal-to-noise ratio (SNR), (3) endogenous heterogeneity of optical properties, as well as in the cases of (4) two fluorescent targets and (5) a mouse-shaped phantom. Assessment of quantitative recovery of fluorescence absorption cross section was performed using a fully parallel, regularization-free, linear reconstruction algorithm with diffusion approximation (DA) and high order simplified spherical harmonics ( SPN) approximation to the radiative transport equation (RTE). The results show that while FD measurements may result in superior image reconstructions over CW measurements, data acquisition times are significantly longer, necessitating further development of multiple detector/source configurations, improved data read-out rates, and detector technology. FD measurements with SP3 reconstructions enabled better quantitative recovery of fluorescent target strength, but required increased computational expense. Despite the developed parallel reconstruction framework being able to achieve more than 60 times speed increase over sequential implementation, further development in faster parallel acceleration strategies for near-real time and real-time image recovery and more precise forward solution is necessary.
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Guo H, Yu J, He X, Hou Y, Dong F, Zhang S. Improved sparse reconstruction for fluorescence molecular tomography with L1/2 regularization. BIOMEDICAL OPTICS EXPRESS 2015; 6:1648-64. [PMID: 26137370 PMCID: PMC4467700 DOI: 10.1364/boe.6.001648] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/19/2015] [Revised: 04/04/2015] [Accepted: 04/05/2015] [Indexed: 05/23/2023]
Abstract
Fluorescence molecular tomography (FMT) is a promising imaging technique that allows in vivo visualization of molecular-level events associated with disease progression and treatment response. Accurate and efficient 3D reconstruction algorithms will facilitate the wide-use of FMT in preclinical research. Here, we utilize L1/2-norm regularization for improving FMT reconstruction. To efficiently solve the nonconvex L1/2-norm penalized problem, we transform it into a weighted L1-norm minimization problem and employ a homotopy-based iterative reweighting algorithm to recover small fluorescent targets. Both simulations on heterogeneous mouse model and in vivo experiments demonstrated that the proposed L1/2-norm method outperformed the comparative L1-norm reconstruction methods in terms of location accuracy, spatial resolution and quantitation of fluorescent yield. Furthermore, simulation analysis showed the robustness of the proposed method, under different levels of measurement noise and number of excitation sources.
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Affiliation(s)
- Hongbo Guo
- School of Information Sciences and Technology, Northwest University, Xi’an, 710069,
China
| | - Jingjing Yu
- School of Physics and Information Technology, Shaanxi Normal University, Xi’an, 710062,
China
| | - Xiaowei He
- School of Information Sciences and Technology, Northwest University, Xi’an, 710069,
China
| | - Yuqing Hou
- School of Information Sciences and Technology, Northwest University, Xi’an, 710069,
China
| | - Fang Dong
- School of Information Sciences and Technology, Northwest University, Xi’an, 710069,
China
| | - Shuling Zhang
- School of Information Sciences and Technology, Northwest University, Xi’an, 710069,
China
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An Y, Liu J, Zhang G, Ye J, Du Y, Mao Y, Chi C, Tian J. A Novel Region Reconstruction Method for Fluorescence Molecular Tomography. IEEE Trans Biomed Eng 2015; 62:1818-26. [PMID: 25706503 DOI: 10.1109/tbme.2015.2404915] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Abstract
Fluorescence molecular tomography (FMT) could exploit the distribution of fluorescent biomarkers that target tumors accurately and effectively, which enables noninvasive real-time 3-D visualization as well as quantitative analysis of small tumors in small animal studies in vivo. Due to the difficulties of reconstruction, continuous efforts are being made to find more practical and efficient approaches to accurately obtain the characteristics of fluorescent regions inside biological tissues. In this paper, we propose a region reconstruction method for FMT, which is defined as an L1-norm regularization piecewise constant level set approach. The proposed approach adopts a priori information including the sparsity of the fluorescent sources and the fluorescent contrast between the target and background. When the contrast of different fluorescent sources is low to a certain degree, our approach can simultaneously solve the detection and characterization problems for the reconstruction of FMT. To evaluate the performance of the region reconstruction method, numerical phantom experiments and in vivo bead-implanted mouse experiments were performed. The results suggested that the proposed region reconstruction method was able to reconstruct the features of the fluorescent regions accurately and effectively, and the proposed method was able to be feasibly adopted in in vivo application.
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Ye J, Du Y, An Y, Chi C, Tian J. Reconstruction of fluorescence molecular tomography via a nonmonotone spectral projected gradient pursuit method. JOURNAL OF BIOMEDICAL OPTICS 2014; 19:126013. [PMID: 25539059 DOI: 10.1117/1.jbo.19.12.126013] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/22/2014] [Accepted: 11/18/2014] [Indexed: 05/15/2023]
Abstract
Fluorescence molecular tomography (FMT) is a promising imaging technique in preclinical research, enabling three-dimensional location of the specific tumor position for small animal imaging. However, FMT presents a challenging inverse problem that is quite ill-posed and ill-conditioned. Thus, the reconstruction of FMT faces various challenges in its robustness and efficiency. We present an FMT reconstruction method based on nonmonotone spectral projected gradient pursuit (NSPGP) with /₁-norm optimization. At each iteration, a spectral gradient-projection method approximately minimizes a least-squares problem with an explicit one-norm constraint. A nonmonotone line search strategy is utilized to get the appropriate updating direction, which guarantees global convergence. Additionally, the Barzilai-Borwein step length is applied to build the optimal step length, further improving the convergence speed of the proposed method. Several numerical simulation studies, including multisource cases as well as comparative analyses, have been performed to evaluate the performance of the proposed method. The results indicate that the proposed NSPGP method is able to ensure the accuracy, robustness, and efficiency of FMT reconstruction. Furthermore, an in vivo experiment based on a heterogeneous mouse model was conducted, and the results demonstrated that the proposed method held the potential for practical applications of FMT.
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Affiliation(s)
- Jinzuo Ye
- Chinese Academy of Sciences, Key Laboratory of Molecular Imaging of Chinese Academy of Sciences, Institute of Automation, No.95 Zhongguancun East Road, Haidian District, Beijing 100190, China
| | - Yang Du
- Chinese Academy of Sciences, Key Laboratory of Molecular Imaging of Chinese Academy of Sciences, Institute of Automation, No.95 Zhongguancun East Road, Haidian District, Beijing 100190, China
| | - Yu An
- Beijing Jiaotong University, School of Computer and Information Technology, Department of Biomedical Engineering, No.3 Shangyuancun, Haidian District, Beijing 100044, China
| | - Chongwei Chi
- Chinese Academy of Sciences, Key Laboratory of Molecular Imaging of Chinese Academy of Sciences, Institute of Automation, No.95 Zhongguancun East Road, Haidian District, Beijing 100190, China
| | - Jie Tian
- Chinese Academy of Sciences, Key Laboratory of Molecular Imaging of Chinese Academy of Sciences, Institute of Automation, No.95 Zhongguancun East Road, Haidian District, Beijing 100190, China
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Zhu D, Li C. Nonuniform update for sparse target recovery in fluorescence molecular tomography accelerated by ordered subsets. BIOMEDICAL OPTICS EXPRESS 2014; 5:4249-59. [PMID: 26623173 PMCID: PMC4285603 DOI: 10.1364/boe.5.004249] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/25/2014] [Revised: 10/18/2014] [Accepted: 10/24/2014] [Indexed: 05/20/2023]
Abstract
Fluorescence molecular tomography (FMT) is a promising imaging modality and has been actively studied in the past two decades since it can locate the specific tumor position three-dimensionally in small animals. However, it remains a challenging task to obtain fast, robust and accurate reconstruction of fluorescent probe distribution in small animals due to the large computational burden, the noisy measurement and the ill-posed nature of the inverse problem. In this paper we propose a nonuniform preconditioning method in combination with L (1) regularization and ordered subsets technique (NUMOS) to take care of the different updating needs at different pixels, to enhance sparsity and suppress noise, and to further boost convergence of approximate solutions for fluorescence molecular tomography. Using both simulated data and phantom experiment, we found that the proposed nonuniform updating method outperforms its popular uniform counterpart by obtaining a more localized, less noisy, more accurate image. The computational cost was greatly reduced as well. The ordered subset (OS) technique provided additional 5 times and 3 times speed enhancements for simulation and phantom experiments, respectively, without degrading image qualities. When compared with the popular L (1) algorithms such as iterative soft-thresholding algorithm (ISTA) and Fast iterative soft-thresholding algorithm (FISTA) algorithms, NUMOS also outperforms them by obtaining a better image in much shorter period of time.
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Xie W, Deng Y, Wang K, Yang X, Luo Q. Reweighted L1 regularization for restraining artifacts in FMT reconstruction images with limited measurements. OPTICS LETTERS 2014; 39:4148-4151. [PMID: 25121673 DOI: 10.1364/ol.39.004148] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
In fluorescence molecular tomography (FMT), many artifacts exist in the reconstructed images because of the inherently ill-posed nature of the FMT inverse problem, especially with limited measurements. A new method based on iterative reweighted L1 (IRL1) regularization is proposed for reducing artifacts with limited measurements. Phantom experiments demonstrate that the reconstructed images have fewer artifacts even with very limited measurements. This indicates that FMT based on IRL1 can obtain high-quality images and thus has the potential to observe dynamic changes in fluorescence-targeted molecules.
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Okawa S, Ikehara T, Oda I, Yamada Y. Reconstruction of localized fluorescent target from multi-view continuous-wave surface images of small animal with lp sparsity regularization. BIOMEDICAL OPTICS EXPRESS 2014; 5:1839-60. [PMID: 24940544 PMCID: PMC4052914 DOI: 10.1364/boe.5.001839] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/17/2014] [Revised: 05/05/2014] [Accepted: 05/06/2014] [Indexed: 05/10/2023]
Abstract
Fluorescence diffuse optical tomography using a multi-view continuous-wave and non-contact measurement system and an algorithm incorporating the lp (0 < p ≤ 1) sparsity regularization reconstructs a localized fluorescent target in a small animal. The measurement system provides a total of 25 fluorescence surface 2D-images of an object, which are acquired by a CCD camera from five different angles of view with excitation from five different angles. Fluorescence surface emissions from five different angles of view are simultaneously imaged on the CCD sensor, thus leading to fast acquisition of the 25 images within three minutes. The distributions of the fluorophore are reconstructed by solving the inverse problem based on the photon diffusion equations. In the reconstruction process incorporating the lp sparsity regularization, the regularization term is reformulated as a differentiable function for gradient-based non-linear optimization. Numerical simulations and phantom experiments show that the use of the lp sparsity regularization improves the localization of the target and quantitativeness of the fluorophore concentration. A mouse experiment demonstrates that a localized fluorescent target in a mouse is successfully reconstructed.
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Affiliation(s)
- Shinpei Okawa
- Department of Medical Engineering, National Defense Medical College, 3-2 Namiki, Tokorozawa, Saitama 359-8513,
Japan
| | - Tatsuya Ikehara
- Shimadzu Corporation, 3-9-4 Hikaridai, Seikachou, Souraku-gun, Kyoto 619-0237,
Japan
| | - Ichiro Oda
- Shimadzu Corporation, 3-9-4 Hikaridai, Seikachou, Souraku-gun, Kyoto 619-0237,
Japan
| | - Yukio Yamada
- Department of Mechanical Engineering and Intelligent Systems, The University of Electro-Communications, 1-5-1 Chofugaoka, Chofu, Tokyo 182-8585,
Japan
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Zhu D, Li C. Nonconvex regularizations in fluorescence molecular tomography for sparsity enhancement. Phys Med Biol 2014; 59:2901-12. [PMID: 24828748 DOI: 10.1088/0031-9155/59/12/2901] [Citation(s) in RCA: 57] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Abstract
In vivo fluorescence imaging has been a popular functional imaging modality in preclinical imaging. Near infrared probes used in fluorescence molecular tomography (FMT) are designed to localize in the targeted tissues, hence sparse solution to the FMT image reconstruction problem is preferred. Nonconvex regularization methods are reported to enhance sparsity in the fields of statistical learning, compressed sensing etc. We investigated such regularization methods in FMT for small animal imaging with numerical simulations and phantom experiments. We adopted a majorization-minimization algorithm for the iterative reconstruction process and compared the reconstructed images using our proposed nonconvex regularizations with those using the well known L(1) regularization. We found that the proposed nonconvex methods outperform L(1) regularization in accurately recovering sparse targets in FMT.
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Affiliation(s)
- Dianwen Zhu
- School of Engineering, University of California Merced, Merced, CA 95343, USA
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Wang D, He J, Qiao H, Song X, Fan Y, Li D. High-performance fluorescence molecular tomography through shape-based reconstruction using spherical harmonics parameterization. PLoS One 2014; 9:e94317. [PMID: 24732826 PMCID: PMC3986074 DOI: 10.1371/journal.pone.0094317] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/11/2013] [Accepted: 03/14/2014] [Indexed: 12/25/2022] Open
Abstract
Fluorescence molecular tomography in the near-infrared region is becoming a powerful modality for mapping the three-dimensional quantitative distributions of fluorochromes in live small animals. However, wider application of fluorescence molecular tomography still requires more accurate and stable reconstruction tools. We propose a shape-based reconstruction method that uses spherical harmonics parameterization, where fluorophores are assumed to be distributed as piecewise constants inside disjointed subdomains and the remaining background. The inverse problem is then formulated as a constrained nonlinear least-squares problem with respect to shape parameters, which decreases ill-posedness because of the significantly reduced number of unknowns. Since different shape parameters contribute differently to the boundary measurements, a two-step and modified block coordinate descent optimization algorithm is introduced to stabilize the reconstruction. We first evaluated our method using numerical simulations under various conditions for the noise level and fluorescent background; it showed significant superiority over conventional voxel-based methods in terms of the spatial resolution, reconstruction accuracy with regard to the morphology and intensity, and robustness against the initial estimated distribution. In our phantom experiment, our method again showed better spatial resolution and more accurate intensity reconstruction. Finally, the results of an in vivo experiment demonstrated its applicability to the imaging of mice.
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Affiliation(s)
- Daifa Wang
- State Key Laboratory of Software Development Environment, Beihang University, Beijing, China,
- Key Laboratory for Biomechanics and Mechanobiology of Ministry of Education, School of Biological Science and Medical Engineering, Beihang University, Beijing, China
| | - Jin He
- Key Laboratory for Biomechanics and Mechanobiology of Ministry of Education, School of Biological Science and Medical Engineering, Beihang University, Beijing, China
| | - Huiting Qiao
- Key Laboratory for Biomechanics and Mechanobiology of Ministry of Education, School of Biological Science and Medical Engineering, Beihang University, Beijing, China
| | - Xiaolei Song
- The Russell H. Morgan Department of Radiology and Radiological Sciences, Division of MR Research, Johns Hopkins University School of Medicine, Baltimore, Maryland, United States of America
| | - Yubo Fan
- Key Laboratory for Biomechanics and Mechanobiology of Ministry of Education, School of Biological Science and Medical Engineering, Beihang University, Beijing, China
| | - Deyu Li
- Key Laboratory for Biomechanics and Mechanobiology of Ministry of Education, School of Biological Science and Medical Engineering, Beihang University, Beijing, China
- * E-mail:
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Behrooz A, Eftekhar AA, Adibi A. Hadamard multiplexed fluorescence tomography. BIOMEDICAL OPTICS EXPRESS 2014; 5:763-77. [PMID: 24688812 PMCID: PMC3959853 DOI: 10.1364/boe.5.000763] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/21/2013] [Revised: 01/10/2014] [Accepted: 02/05/2014] [Indexed: 05/22/2023]
Abstract
Depth-resolved three-dimensional (3D) reconstruction of fluorophore-tagged inclusions in fluorescence tomography (FT) poses a highly ill-conditioned problem as depth information must be extracted from boundary data. Due to the ill-posed nature of the FT inverse problem, noise and errors in the data can severely impair the accuracy of the 3D reconstructions. The signal-to-noise ratio (SNR) of the FT data strongly affects the quality of the reconstructions. Additionally, in FT scenarios where the fluorescent signal is weak, data acquisition requires lengthy integration times that result in excessive FT scan periods. Enhancing the SNR of FT data contributes to the robustness of the 3D reconstructions as well as the speed of FT scans. A major deciding factor in the SNR of the FT data is the power of the radiation illuminating the subject to excite the administered fluorescent reagents. In existing single-point illumination FT systems, the source power level is limited by the skin maximum radiation exposure levels. In this paper, we introduce and study the performance of a multiplexed fluorescence tomography system with orders-of-magnitude enhanced data SNR over existing systems. The proposed system allows for multi-point illumination of the subject without jeopardizing the information content of the FT measurements and results in highly robust reconstructions of fluorescent inclusions from noisy FT data. Improvements offered by the proposed system are validated by numerical and experimental studies.
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