Hybrid reconstruction framework for model-based multispectral bioluminescence tomography based on Alpha-divergence

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.

Source reconstruction for bioluminescence tomography via L_(1/2)regularization

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.

Three-Dimentional Surface Light Irradiance Reconstruction in Bioluminescence Tomography

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.

Fast in vivo bioluminescence tomography using a novel pure optical imaging technique

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.

BIOLUMINESCENCE TOMOGRAPHY:BIOMEDICAL BACKGROUND,MATHEMATICAL THEORY,AND NUMERICAL APPROXIMATION

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.

Two-stage Source Reconstruction Algorithm for Bioluminescence Tomography Using Hybrid FEM

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.

A New Coupled Complex BoundaryMethod for Bioluminescence Tomography

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.

ANALYSIS OF A NUMERICAL METHOD FOR RADIATIVE TRANSFER EQUATION BASED BIOLUMINESCENCE TOMOGRAPHY

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.

Recent Developments in Numerical Techniques for Transport-Based Medical Imaging Methods

The objective of this paper is to review recent developments in numerical reconstruction methods for inverse transport problems in imaging applications,mainly optical tomography,fluorescence tomography and bioluminescence tomography.In those inverse problems,one aims at reconstructing physical parameters,such as the absorption coefficient,the scattering coefficient and the fluorescence light source,inside heterogeneous media,from partial knowledge of transport solutions on the boundaries of the media.The physical parameters recovered can be used for diagnostic purpose.Numerical reconstruction techniques for those inverse transport problems can be roughly classified into two categories:linear reconstruction methods and nonlinear reconstruction methods.In the first type of methods,the inverse problems are linearized around some known background to obtain linear inverse problems.Classical regularization techniques are then applied to solve those inverse problems.The second type of methods are either based on regularized nonlinear least-square techniques or based on gradient-driven iterative methods for nonlinear operator equations.In either case,the unknown parameters are iteratively updated until the solutions of the transport equations with the those parameters match the measurements to a certain extent.We review linear and nonlinear reconstruction methods for inverse transport problems in medical imaging with stationary,frequency-domain and time-dependent data.The materials presented include both existing and new results.Meanwhile,we attempt to present similar algorithms for different problems in the same framework to make it more straightforward to generalize those algorithms to other inverse(transport)problems.