Bioluminescence tomography(BLT)is an important noninvasive optical molecular imaging modality in preclinical research.To improve the image quality,reconstruction algorithms have to deal with the inherent ill-posedness...Bioluminescence tomography(BLT)is an important noninvasive optical molecular imaging modality in preclinical research.To improve the image quality,reconstruction algorithms have to deal with the inherent ill-posedness of BLT inverse problem.The sparse characteristic of bioluminescent sources in spatial distribution has been widely explored in BLT and many L1-regularized methods have been investigated due to the sparsity-inducing properties of L1 norm.In this paper,we present a reconstruction method based on L_(1/2) regularization to enhance sparsity of BLT solution and solve the nonconvex L_(1/2) norm problem by converting it to a series of weighted L1 homotopy minimization problems with iteratively updated weights.To assess the performance of the proposed reconstruction algorithm,simulations on a heterogeneous mouse model are designed to compare it with three representative sparse reconstruction algorithms,including the weighted interior-point,L1 homotopy,and the Stagewise Orthogonal Matching Pursuit algorithm.Simulation results show that the proposed method yield stable reconstruction results under different noise levels.Quantitative comparison results demonstrate that the proposed algorithm outperforms the competitor algorithms in location accuracy,multiple-source resolving and image quality.展开更多
Reconstruction of 3D surface irradiance distribution using multiple views captured by charged coupled device(CCD)camera is the basis of solving the light source in bioluminescence tomography(BLT).A simple and convenie...Reconstruction of 3D surface irradiance distribution using multiple views captured by charged coupled device(CCD)camera is the basis of solving the light source in bioluminescence tomography(BLT).A simple and convenient mapping technique based on the pin-hole imaging model and Lambert′s cosine law was presented to establish the relationship between gray levels and irradiance intensities.Compared with previous integrating sphere camera calibration used in BLT,the proposed method can effectively avoid heavy burden of simulation experiment to obtain the corresponding relationship of gray levels and irradiance intensities.The accuracy and feasibility of the proposed method are validated with no more than 1mm location error by different types of phantom experiments.The mapping approach is also applicable to other noncontact optical imaging system.展开更多
Bioluminescence tomography(BLT)is a promising imaging modality that can provide noninvasive three-dimensional visualization information on tumor distribution.In BLT reconstruction,the widely used methods based on regu...Bioluminescence tomography(BLT)is a promising imaging modality that can provide noninvasive three-dimensional visualization information on tumor distribution.In BLT reconstruction,the widely used methods based on regularization or greedy strategy face problems such as over-sparsity,over-smoothing,spatial discontinuity,poor robustness,and poor multi-target resolution.To deal with these problems,combining the advantages of the greedy strategies as well as regularization methods,we propose a hybrid reconstruction framework for model-based multispectral BLT using the support set of a greedy strategy as a feasible region and the Alpha-divergence to combine the weighted solutions obtained by L1-norm and L2-norm regularization methods.In numerical simulations with digital mouse and in vivo experiments,the results show that the proposed framework has better localization accuracy,spatial resolution,and multi-target resolution.展开更多
Bioluminescence tomography(BLT)is a novel opt ical molecular imaging technique that advanced the conventional planar bioluminescence imaging(BLI)into a quantifiable three-dimensional(3D)approach in preclinical living ...Bioluminescence tomography(BLT)is a novel opt ical molecular imaging technique that advanced the conventional planar bioluminescence imaging(BLI)into a quantifiable three-dimensional(3D)approach in preclinical living animal studies in oncology.In order to solve the inverse problem and reconstruct tumor lesions inside animal body accurately,the prior structural information is com-monly obtained from X ray computed tomography(CT).This strategy requires a complicated hybrid imaging system,extensive post imaging analysis and involvement of ionizing radiation.Moreover,the overall robustness highly depends on the fusion accuracy between the optical and structural information.Here,we present a pure optical bioluminescence tomographic(POBT)system and a novel BLT workfow based on multi-view projection acquisition and 3D surface reconstruction.This met hod can reconstruct the 3D surface of an imaging subject based on a sparse set of planar white-light and bioluminescent images,so that the prior structural information can be offered for 3D tumor lesion reconstruction without the involvement of CT.The performance of this novel technique was evaluated through the comparison with a conventional dual-modality tomo-graphic(DMT)system and a commercialized optical imaging system(IVIS Spectrum)using three breast cancer xenografts.The results revealed that the new technique offered comparable in vivo tomographic accuracy with the DMT system(P>0.05)in much shorter data analysis time.It also offered significantly better accuracy comparing with the IVIS system(P<0.04)without sacrificing too much time.展开更多
Over the last couple of years molecular imaging has been rapidly developed to study physiological and pathological processes in vivo at the cellular and molecular levels. Among molecular imaging modalities, optical im...Over the last couple of years molecular imaging has been rapidly developed to study physiological and pathological processes in vivo at the cellular and molecular levels. Among molecular imaging modalities, optical imaging stands out for its unique advantages, especially performance and cost-effectiveness. Bioluminescence tomography （BLT） is an emerging optical imaging mode with promising biomedical advantages. In this survey paper, we explain the biomedical significance of BLT, summarize theoretical results on the analysis and numerical solution of a diffusion based BLT model, and comment on a few extensions for the study of BLT.展开更多
We present a sparse Bayesian reconstruction method based on multiple types of a priori information for multispectral bioluminescence tomography （BLT）. In the Bayesian approach, five kinds of a priori information are...We present a sparse Bayesian reconstruction method based on multiple types of a priori information for multispectral bioluminescence tomography （BLT）. In the Bayesian approach, five kinds of a priori information are incorporated, reducing the ill-posedness of BLT. Specifically, source sparsity characteristic is considered to promote reconstruction results. Considering the computational burden in the multispectral case, a series of strategies is adopted to improve computational efficiency, such as optimal permissible source region strategy and node model of the finite element method. The performance of the proposed algorithm is validated by a heterogeneous three-dimensional （3D） micron scale computed tomography atlas and a mouse-shaped phantom. Reconstructed results demonstrate the feasibility and effectiveness of the proposed algorithm.展开更多
Adaptive finite element method （AFEM） is broadly adopted to recover the internal source in biological tissues. In this letter, a novel dual-mesh alternation strategy （dual-mesh AFEM） is developed for bioluminescen...Adaptive finite element method （AFEM） is broadly adopted to recover the internal source in biological tissues. In this letter, a novel dual-mesh alternation strategy （dual-mesh AFEM） is developed for bioluminescence tomography. By comprehensively considering the error estimation of the finite element method solution on each mesh, two different adaptive strategies based on the error indicator of the reconstructed source and the photon flux density are used alternately in the process. Combined with the constantly adjusted permissible region in the adaptive process, the new algorithm can achieve a more accurate source location compared with the AFEM in the previous experiments.展开更多
To avoid the ill-posedness in the inverse problem of bioluminescence tomography, a moment searching algorithm fusing the finite element method （FEM） with the moment concept in theoretical mechanics is developed. In ...To avoid the ill-posedness in the inverse problem of bioluminescence tomography, a moment searching algorithm fusing the finite element method （FEM） with the moment concept in theoretical mechanics is developed. In the algorithm, the source＇s information is mapped to the surface photon flux density by FEM, and the source＇s position is modified with the feedback through the algorithm of barycenter searching, which makes full use of the position information of the photon flux density on surface. The position is modified in every iterative step and will finally converge to the real source＇s value theoretically.展开更多
In the bioluminescence tomography （BLT） problem, one constructs quantitatively the bioluminescence source distribution inside a small animal from optical signals detected on the animal＇s body surface. The BLT probl...In the bioluminescence tomography （BLT） problem, one constructs quantitatively the bioluminescence source distribution inside a small animal from optical signals detected on the animal＇s body surface. The BLT problem is ill-posed and often the Tikhonov regularization is used to obtain stable approximate solutions. In conventional Tikhonov regularization, it is crucial to choose a proper regularization parameter to balance the accuracy and stability of approximate solutions. In this paper, a parameter-dependent coupled complex boundary method （CCBM） based Tikhonov regularization is applied to the BLT problem governed by the radiative transfer equation （RTE）. By properly adjusting the parameter in the Robin boundary condition, we achieve one important property： the regularized solutions are uniformly stable with respect to the regularization parameter so that the regularization parameter can be chosen based solely on the consideration of the solution accuracy. The discrete-ordinate finite-element method is used to compute numerical solutions. Numerical results are provided to illustrate the performance of the proposed method.展开更多
A two-stage source reconstruction algorithm for bioluminescence tomography (BLT) is developed using hybrid finite element method (FEM). The proposed algorithm takes full advantages of linear and quadratic FEMs, which ...A two-stage source reconstruction algorithm for bioluminescence tomography (BLT) is developed using hybrid finite element method (FEM). The proposed algorithm takes full advantages of linear and quadratic FEMs, which can be used to localize and quantify bioluminescent source accurately. In the first stage, a large permissible region is roughly determined and then iteratively evolved to reduce matrix dimension using efficient linear FEM. In the final stage, high-convergence quadratic FEM is applied to improve reconstruction result. Both numerical simulation and physical experiment are performed to evaluate the proposed algorithm. The relevant results demonstrate that quantitative reconstruction can be well achieved in terms of computation efficiency, source position, power density, and total power when compared with previous studies.展开更多
In this paper,we introduce and study a new method for solving inverse source problems,through aworkingmodel that arises in bioluminescence tomography(BLT).In the BLT problem,one constructs quantitatively the biolumine...In this paper,we introduce and study a new method for solving inverse source problems,through aworkingmodel that arises in bioluminescence tomography(BLT).In the BLT problem,one constructs quantitatively the bioluminescence source distribution inside a small animal from optical signals detected on the animal’s body surface.The BLT problem possesses strong ill-posedness and often the Tikhonov regularization is used to obtain stable approximate solutions.In conventional Tikhonov regularization,it is crucial to choose a proper regularization parameter for trade off between the accuracy and stability of approximate solutions.The new method is based on a combination of the boundary condition and the boundary measurement in a parameter-dependent single complex Robin boundary condition,followed by the Tikhonov regularization.By properly adjusting the parameter in the Robin boundary condition,we achieve two important properties for our new method:first,the regularized solutions are uniformly stable with respect to the regularization parameter so that the regularization parameter can be chosen based solely on the consideration of the solution accuracy;second,the convergence order of the regularized solutions reaches one with respect to the noise level.Then,the finite element method is used to compute numerical solutions and a newfinite element error estimate is derived for discrete solutions.These results improve related results found in the existing literature.Several numerical examples are provided to illustrate the theoretical results.展开更多
基金supported by the National Natural Science Foundation of China(No.61401264,11574192)the Natural Science Research Plan Program in Shaanxi Province of China(No.2015JM6322)the Fundamental Research Funds for the Central Universities(No.GK201603025).
文摘Bioluminescence tomography(BLT)is an important noninvasive optical molecular imaging modality in preclinical research.To improve the image quality,reconstruction algorithms have to deal with the inherent ill-posedness of BLT inverse problem.The sparse characteristic of bioluminescent sources in spatial distribution has been widely explored in BLT and many L1-regularized methods have been investigated due to the sparsity-inducing properties of L1 norm.In this paper,we present a reconstruction method based on L_(1/2) regularization to enhance sparsity of BLT solution and solve the nonconvex L_(1/2) norm problem by converting it to a series of weighted L1 homotopy minimization problems with iteratively updated weights.To assess the performance of the proposed reconstruction algorithm,simulations on a heterogeneous mouse model are designed to compare it with three representative sparse reconstruction algorithms,including the weighted interior-point,L1 homotopy,and the Stagewise Orthogonal Matching Pursuit algorithm.Simulation results show that the proposed method yield stable reconstruction results under different noise levels.Quantitative comparison results demonstrate that the proposed algorithm outperforms the competitor algorithms in location accuracy,multiple-source resolving and image quality.
基金Supported by the National Natural Science Foundation of China(61171059)the Fundamental Research Funds for the Central Universities of China(NP2012202,NZ2014101)the Foundation of Graduate Innovation Center in Nanjing University of Aeronautics and Astronautics(kfjj201427)
文摘Reconstruction of 3D surface irradiance distribution using multiple views captured by charged coupled device(CCD)camera is the basis of solving the light source in bioluminescence tomography(BLT).A simple and convenient mapping technique based on the pin-hole imaging model and Lambert′s cosine law was presented to establish the relationship between gray levels and irradiance intensities.Compared with previous integrating sphere camera calibration used in BLT,the proposed method can effectively avoid heavy burden of simulation experiment to obtain the corresponding relationship of gray levels and irradiance intensities.The accuracy and feasibility of the proposed method are validated with no more than 1mm location error by different types of phantom experiments.The mapping approach is also applicable to other noncontact optical imaging system.
基金funded by the National Natural Science Foundation of China under Grants Nos.11871321,61901374,61906154,and 61971350Postdoctoral Innovative Talents Support Program under Grants No.BX20180254.
文摘Bioluminescence tomography(BLT)is a promising imaging modality that can provide noninvasive three-dimensional visualization information on tumor distribution.In BLT reconstruction,the widely used methods based on regularization or greedy strategy face problems such as over-sparsity,over-smoothing,spatial discontinuity,poor robustness,and poor multi-target resolution.To deal with these problems,combining the advantages of the greedy strategies as well as regularization methods,we propose a hybrid reconstruction framework for model-based multispectral BLT using the support set of a greedy strategy as a feasible region and the Alpha-divergence to combine the weighted solutions obtained by L1-norm and L2-norm regularization methods.In numerical simulations with digital mouse and in vivo experiments,the results show that the proposed framework has better localization accuracy,spatial resolution,and multi-target resolution.
基金the National Basic Research Program of China(973 Program)under Grant No.2015CB755500the National Natural Science Foundation of China under Grant No.81227901,61231004,81527805 and 61401462+3 种基金the Scienti¯c Research and Equipment Development Project of the Chinese Academy of Sciences under Grant No.YZ201359the Chinese Academy of Sciences under Grant No.KGZD-EW-T03the Chinese Academy of Sciences Fellowship for Young International Scientists under Grant No.2013Y1GA0004the Project funded by China Postdoctoral Science Foundation under Grant Nos.2014M550881,2015T80155.
文摘Bioluminescence tomography(BLT)is a novel opt ical molecular imaging technique that advanced the conventional planar bioluminescence imaging(BLI)into a quantifiable three-dimensional(3D)approach in preclinical living animal studies in oncology.In order to solve the inverse problem and reconstruct tumor lesions inside animal body accurately,the prior structural information is com-monly obtained from X ray computed tomography(CT).This strategy requires a complicated hybrid imaging system,extensive post imaging analysis and involvement of ionizing radiation.Moreover,the overall robustness highly depends on the fusion accuracy between the optical and structural information.Here,we present a pure optical bioluminescence tomographic(POBT)system and a novel BLT workfow based on multi-view projection acquisition and 3D surface reconstruction.This met hod can reconstruct the 3D surface of an imaging subject based on a sparse set of planar white-light and bioluminescent images,so that the prior structural information can be offered for 3D tumor lesion reconstruction without the involvement of CT.The performance of this novel technique was evaluated through the comparison with a conventional dual-modality tomo-graphic(DMT)system and a commercialized optical imaging system(IVIS Spectrum)using three breast cancer xenografts.The results revealed that the new technique offered comparable in vivo tomographic accuracy with the DMT system(P>0.05)in much shorter data analysis time.It also offered significantly better accuracy comparing with the IVIS system(P<0.04)without sacrificing too much time.
基金NIH grant EB001685Mathematical and Physical Sciences Funding Program fund of the University of Iowa
文摘Over the last couple of years molecular imaging has been rapidly developed to study physiological and pathological processes in vivo at the cellular and molecular levels. Among molecular imaging modalities, optical imaging stands out for its unique advantages, especially performance and cost-effectiveness. Bioluminescence tomography （BLT） is an emerging optical imaging mode with promising biomedical advantages. In this survey paper, we explain the biomedical significance of BLT, summarize theoretical results on the analysis and numerical solution of a diffusion based BLT model, and comment on a few extensions for the study of BLT.
基金supported by the National Basic Research Program of China (No. 2006CB705700)the National Natural Science Foundation of China (No.30970780)+3 种基金the Knowledge Innovation Project of the Chinese Academy of Sciences (No. KGCX2-YW-907)the Changjiang Scholars and Innovative Research Teamin University (No. IRT0645)the Chinese Academyof Sciences Hundred Talents Program, the Science and Technology Key Project of Beijing Municipal Education Commission (No. KZ200910005005)the Doctoral Fund of the Ministry of Education of China (No.20091103110005)
文摘We present a sparse Bayesian reconstruction method based on multiple types of a priori information for multispectral bioluminescence tomography （BLT）. In the Bayesian approach, five kinds of a priori information are incorporated, reducing the ill-posedness of BLT. Specifically, source sparsity characteristic is considered to promote reconstruction results. Considering the computational burden in the multispectral case, a series of strategies is adopted to improve computational efficiency, such as optimal permissible source region strategy and node model of the finite element method. The performance of the proposed algorithm is validated by a heterogeneous three-dimensional （3D） micron scale computed tomography atlas and a mouse-shaped phantom. Reconstructed results demonstrate the feasibility and effectiveness of the proposed algorithm.
基金supported by the National "973" Program of China (No.2011CB707702)the National Natural Science Foundation of China (Nos.81090272,81000632,and 30900334)+1 种基金the Shaanxi Provincial Natural Science Foundation Research Project (No.2009JQ8018)the Fundamental Research Funds for the Central Universities
文摘Adaptive finite element method （AFEM） is broadly adopted to recover the internal source in biological tissues. In this letter, a novel dual-mesh alternation strategy （dual-mesh AFEM） is developed for bioluminescence tomography. By comprehensively considering the error estimation of the finite element method solution on each mesh, two different adaptive strategies based on the error indicator of the reconstructed source and the photon flux density are used alternately in the process. Combined with the constantly adjusted permissible region in the adaptive process, the new algorithm can achieve a more accurate source location compared with the AFEM in the previous experiments.
基金supported by the program for Cheung Kong Scholars and Innovative Research Teamin University of China (No. IRT0645)the National Natural Science Foundation of China (No.60872137)+1 种基金the National Defence Foundation of China(No. 9140A01060408DZ0104)the National "973" Program of China (No. 2006CB705700)and the Programfor Chair Professors of Cheung Kong Scholars Program of China
文摘To avoid the ill-posedness in the inverse problem of bioluminescence tomography, a moment searching algorithm fusing the finite element method （FEM） with the moment concept in theoretical mechanics is developed. In the algorithm, the source＇s information is mapped to the surface photon flux density by FEM, and the source＇s position is modified with the feedback through the algorithm of barycenter searching, which makes full use of the position information of the photon flux density on surface. The position is modified in every iterative step and will finally converge to the real source＇s value theoretically.
文摘In the bioluminescence tomography （BLT） problem, one constructs quantitatively the bioluminescence source distribution inside a small animal from optical signals detected on the animal＇s body surface. The BLT problem is ill-posed and often the Tikhonov regularization is used to obtain stable approximate solutions. In conventional Tikhonov regularization, it is crucial to choose a proper regularization parameter to balance the accuracy and stability of approximate solutions. In this paper, a parameter-dependent coupled complex boundary method （CCBM） based Tikhonov regularization is applied to the BLT problem governed by the radiative transfer equation （RTE）. By properly adjusting the parameter in the Robin boundary condition, we achieve one important property： the regularized solutions are uniformly stable with respect to the regularization parameter so that the regularization parameter can be chosen based solely on the consideration of the solution accuracy. The discrete-ordinate finite-element method is used to compute numerical solutions. Numerical results are provided to illustrate the performance of the proposed method.
基金supported by National Basic Research Program of China (973 Program) (No. 2011CB707702)National Natural Science Foundation of China (Nos. 81090272, 81000632, and 30900334)+1 种基金the Shaanxi Provincial Natural Science Foundation (No. 2009JQ8018)the Fundamental Research Funds for the Central Universities
文摘A two-stage source reconstruction algorithm for bioluminescence tomography (BLT) is developed using hybrid finite element method (FEM). The proposed algorithm takes full advantages of linear and quadratic FEMs, which can be used to localize and quantify bioluminescent source accurately. In the first stage, a large permissible region is roughly determined and then iteratively evolved to reduce matrix dimension using efficient linear FEM. In the final stage, high-convergence quadratic FEM is applied to improve reconstruction result. Both numerical simulation and physical experiment are performed to evaluate the proposed algorithm. The relevant results demonstrate that quantitative reconstruction can be well achieved in terms of computation efficiency, source position, power density, and total power when compared with previous studies.
基金The work of the first author was supported by the Natural Science Foundation of China(Grant No.11401304)the Natural Science Foundation of Jiangsu Province(Grant No.BK20130780)+2 种基金the Fundamental Research Funds for the Central Universities(Grant No.NS2014078)The work of the second author was sup-ported by the Key Project of the Major Research Plan of NSFC(Grant No.91130004)The work of the third author was partially supported by NSF(Grant No.DMS-1521684)and Simons Foundation(Grant No.207052 and 228187).
文摘In this paper,we introduce and study a new method for solving inverse source problems,through aworkingmodel that arises in bioluminescence tomography(BLT).In the BLT problem,one constructs quantitatively the bioluminescence source distribution inside a small animal from optical signals detected on the animal’s body surface.The BLT problem possesses strong ill-posedness and often the Tikhonov regularization is used to obtain stable approximate solutions.In conventional Tikhonov regularization,it is crucial to choose a proper regularization parameter for trade off between the accuracy and stability of approximate solutions.The new method is based on a combination of the boundary condition and the boundary measurement in a parameter-dependent single complex Robin boundary condition,followed by the Tikhonov regularization.By properly adjusting the parameter in the Robin boundary condition,we achieve two important properties for our new method:first,the regularized solutions are uniformly stable with respect to the regularization parameter so that the regularization parameter can be chosen based solely on the consideration of the solution accuracy;second,the convergence order of the regularized solutions reaches one with respect to the noise level.Then,the finite element method is used to compute numerical solutions and a newfinite element error estimate is derived for discrete solutions.These results improve related results found in the existing literature.Several numerical examples are provided to illustrate the theoretical results.
