Jinchao Feng

A fast reconstruction algorithm for fluorescence molecular tomography with sparsity regularization

Through the reconstruction of the fluorescent probe distributions, fluorescence molecular tomography (FMT) can three-dimensionally resolve the molecular processes in small animals in vivo. In this paper, we propose an FMT reconstruction algorithm based on the iterated shrinkage method. By incorporating a surrogate function, the original optimization problem can be decoupled, which enables us to use the general sparsity regularization. Due to the sparsity characteristic of the fluorescent sources, the performance of this method can be greatly enhanced, which leads to a fast reconstruction algorithm. Numerical simulations and physical experiments were conducted. Compared to Newton method with Tikhonov regularization, the iterated shrinkage based algorithm can obtain more accurate results, even with very limited measurement data.

An optimal permissible source region strategy for multispectral bioluminescence tomography

Multispectral bioluminescence tomography (BLT) attracts increasing more attention in the area of small animal studies because multispectral data acquisition could help in the 3D location of bioluminescent sources. Generally, BLT problem is ill-posed and a priori information is indispensable to reconstruction bioluminescent source uniquely and quantitatively. In this paper, we propose a spectrally solved bioluminescence tomography algorithm with an optimal permissible source region strategy. Being the most different from earlier studies, an optimal permissible source region strategy which is automatically selected without human intervention is developed to reduce the ill-posedness of BLT and therefore improves the reconstruction quality. Furthermore, both numerical stability and computational efficiency benefit from the strategy. In the numerical experiments, a heterogeneous phantom is used to evaluate the proposed algorithm and the synthetic data is produced by Monte Carlo method for avoiding the inverse crime. The results demonstrate the feasibility and potential of our methodology for reconstructing the distribution of bioluminescent sources.

Cone beam micro-CT system for small animal imaging and performance evaluation

A prototype cone-beam micro-CT system for small animal imaging has been developed by our group recently, which consists of a microfocus X-ray source, a three-dimensional programmable stage with object holder, and a flat-panel X-ray detector. It has a large field of view (FOV), which can acquire the whole body imaging of a normal-size mouse in a single scan which usually takes about several minutes or tens of minutes. FDK method is adopted for 3D reconstruction with Graphics Processing Unit (GPU) acceleration. In order to reconstruct images with high spatial resolution and low artifacts, raw data preprocessing and geometry calibration are implemented before reconstruction. A method which utilizes a wire phantom to estimate the residual horizontal offset of the detector is proposed, and 1D point spread function is used to assess the performance of geometric calibration quantitatively. System spatial resolution, image uniformity and noise, and low contrast resolution have been studied. Mouse images with and without contrast agent are illuminated in this paper. Experimental results show that the system is suitable for small animal imaging and is adequate to provide high-resolution anatomic information for bioluminescence tomography to build a dual modality system.

Three-dimensional Bioluminescence Tomography based on Bayesian Approach

Bioluminescence tomography (BLT) poses a typical ill-posed inverse problem with a large number of unknowns and a relatively limited number of boundary measurements. It is indispensable to incorporate a priori information into the inverse problem formulation in order to obtain viable solutions. In the paper, Bayesian approach has been firstly suggested to incorporate multiple types of a priori information for BLT reconstruction. Meanwhile, a generalized adaptive Gaussian Markov random field (GAGMRF) prior model for unknown source density estimation is developed to further reduce the ill-posedness of BLT on the basis of finite element analysis. Then the distribution of bioluminescent source can be acquired by maximizing the log posterior probability with respect to a noise parameter and the unknown source density. Furthermore, the use of finite element method makes the algorithm appropriate for complex heterogeneous phantom. The algorithm was validated by numerical simulation of a 3-D micro-CT mouse atlas and physical phantom experiment. The reconstructed results suggest that we are able to achieve high computational efficiency and accurate localization of bioluminescent source.

Sparsity-Promoting Tomographic Fluorescence Imaging With Simplified Spherical Harmonics Approximation

Fluorescence molecular tomography has become a promising technique for in vivo small animal imaging and has many potential applications. Due to the ill-posed and the ill-conditioned nature of the problem, Tikhonov regularization is generally adopted to stabilize the solution. However, the result is usually over-smoothed. In this letter, the third-order simplified spherical harmonics approximation to radiative transfer equation is utilized to model the photon propagation within biological tissues. Considering the sparsity of the fluorescent sources, we replace Tikhonov method with an iteratively reweighted scheme. By dynamically updating the weight matrix, L1-norm regularization can be approximated, which can promote the sparsity of the solution. Simulation study shows that this method can preserve the sparsity of the fluorescent sources within heterogeneous medium, even with very limited measurement data.

Galerkin-based meshless methods for photon transport in the biological tissue

As an important small animal imaging technique, optical imaging has attracted increasing attention in recent years. However, the photon propagation process is extremely complicated for highly scattering property of the biological tissue. Furthermore, the light transport simulation in tissue has a significant influence on inverse source reconstruction. In this contribution, we present two Galerkin-based meshless methods (GBMM) to determine the light exitance on the surface of the diffusive tissue. The two methods are both based on moving least squares (MLS) approximation which requires only a series of nodes in the region of interest, so complicated meshing task can be avoided compared with the finite element method (FEM). Moreover, MLS shape functions are further modified to satisfy the delta function property in one method, which can simplify the processing of boundary conditions in comparison with the other. Finally, the performance of the proposed methods is demonstrated with numerical and physical phantom experiments.

Total variation regularization for bioluminescence tomography with the split Bregman method

Regularization methods have been broadly applied to bioluminescence tomography (BLT) to obtain stable solutions, including l2 and l1 regularizations. However, l2 regularization can oversmooth reconstructed images and l1 regularization may sparsify the source distribution, which degrades image quality. In this paper, the use of total variation (TV) regularization in BLT is investigated. Since a nonnegativity constraint can lead to improved image quality, the nonnegative constraint should be considered in BLT. However, TV regularization with a nonnegativity constraint is extremely difficult to solve due to its nondifferentiability and nonlinearity. The aim of this work is to validate the split Bregman method to minimize the TV regularization problem with a nonnegativity constraint for BLT. The performance of split Bregman-resolved TV (SBRTV) based BLT reconstruction algorithm was verified with numerical and in vivo experiments. Experimental results demonstrate that the SBRTV regularization can provide better regularization quality over l2 and l1 regularizations.

A trust region method in adaptive finite element framework for bioluminescence tomography

Bioluminescence tomography (BLT) is an effective molecular imaging (MI) modality. Because of the ill-posedness, the inverse problem of BLT is still open. We present a trust region method (TRM) for BLT source reconstruction. The TRM is applied in the source reconstruction procedure of BLT for the first time. The results of both numerical simulations and the experiments of cube phantom and nude mouse draw us to the conclusion that based on the adaptive finite element (AFE) framework, the TRM works in the source reconstruction procedure of BLT. To make our conclusion more reliable, we also compare the performance of the TRM and that of the famous Tikhonov regularization method after only one step of mesh refinement of the AFE framework. The conclusion is that the TRM can get faster and better results after only one mesh refinement step of AFE framework than the Tikhonov regularization method when handling large scale data. In the TRM, all the parameters are fixed, while in the Tikhonov method the regularization parameter needs to be well selected.

Adaptive improved element free Galerkin method for quasi- or multi-spectral bioluminescence tomography

Bioluminescence tomography (BLT) has become a powerful tool for whole-body small animal imaging. In this contribution, an adaptive improved element free Galerkin method (IEFGM) is presented to perform a quantitative reconstruction of the internal light source using quasi- or multi-spectral information, which not only can avoid the time-consuming mesh generation but also can reduce the ill-posedness of BLT effectively. In the algorithm, the reconstruction can be largely enhanced by an adaptive technology based on a posteriori error estimation. Finally, the numerical and physical phantom experiment results show that the bioluminescent source can be recovered accurately.

An adaptive regularization parameter choice strategy for multispectral bioluminescence tomography

PURPOSE Bioluminescence tomography (BLT) provides an effective tool for monitoring physiological and pathological activities in vivo. However, the measured data in bioluminescence imaging are corrupted by noise. Therefore, regularization methods are commonly used to find a regularized solution. Nevertheless, for the quality of the reconstructed bioluminescent source obtained by regularization methods, the choice of the regularization parameters is crucial. To date, the selection of regularization parameters remains challenging. With regards to the above problems, the authors proposed a BLT reconstruction algorithm with an adaptive parameter choice rule. METHODS The proposed reconstruction algorithm uses a diffusion equation for modeling the bioluminescent photon transport. The diffusion equation is solved with a finite element method. Computed tomography (CT) images provide anatomical information regarding the geometry of the small animal and its internal organs. To reduce the ill-posedness of BLT, spectral information and the optimal permissible source region are employed. Then, the relationship between the unknown source distribution and multiview and multispectral boundary measurements is established based on the finite element method and the optimal permissible source region. Since the measured data are noisy, the BLT reconstruction is formulated as l(2) data fidelity and a general regularization term. When choosing the regularization parameters for BLT, an efficient model function approach is proposed, which does not require knowledge of the noise level. This approach only requests the computation of the residual and regularized solution norm. With this knowledge, we construct the model function to approximate the objective function, and the regularization parameter is updated iteratively. RESULTS First, the micro-CT based mouse phantom was used for simulation verification. Simulation experiments were used to illustrate why multispectral data were used rather than monochromatic data. Furthermore, the study conducted using an adaptive regularization parameter demonstrated our ability to accurately localize the bioluminescent source. With the adaptively estimated regularization parameter, the reconstructed center position of the source was (20.37, 31.05, 12.95) mm, and the distance to the real source was 0.63 mm. The results of the dual-source experiments further showed that our algorithm could localize the bioluminescent sources accurately. The authors then presented experimental evidence that the proposed algorithm exhibited its calculated efficiency over the heuristic method. The effectiveness of the new algorithm was also confirmed by comparing it with the L-curve method. Furthermore, various initial speculations regarding the regularization parameter were used to illustrate the convergence of our algorithm. Finally, in vivo mouse experiment further illustrates the effectiveness of the proposed algorithm. CONCLUSIONS Utilizing numerical, physical phantom and in vivo examples, we demonstrated that the bioluminescent sources could be reconstructed accurately with automatic regularization parameters. The proposed algorithm exhibited superior performance than both the heuristic regularization parameter choice method and L-curve method based on the computational speed and localization error.