Junwei Shi

Efficient L1 regularization-based reconstruction for fluorescent molecular tomography using restarted nonlinear conjugate gradient

For the ill-posed fluorescent molecular tomography (FMT) inverse problem, the L1 regularization can protect the high-frequency information like edges while effectively reduce the image noise. However, the state-of-the-art L1 regularization-based algorithms for FMT reconstruction are expensive in memory, especially for large-scale problems. An efficient L1 regularization-based reconstruction algorithm based on nonlinear conjugate gradient with restarted strategy is proposed to increase the computational speed with low memory consumption. The reconstruction results from phantom experiments demonstrate that the proposed algorithm can obtain high spatial resolution and high signal-to-noise ratio, as well as high localization accuracy for fluorescence targets.

Enhanced spatial resolution in fluorescence molecular tomography using restarted L1-regularized nonlinear conjugate gradient algorithm

Abstract. Owing to the high degree of scattering of light through tissues, the ill-posedness of fluorescence molecular tomography (FMT) inverse problem causes relatively low spatial resolution in the reconstruction results. Unlike L2 regularization, L1 regularization can preserve the details and reduce the noise effectively. Reconstruction is obtained through a restarted L1 regularization-based nonlinear conjugate gradient (re-L1-NCG) algorithm, which has been proven to be able to increase the computational speed with low memory consumption. The algorithm consists of inner and outer iterations. In the inner iteration, L1-NCG is used to obtain the L1-regularized results. In the outer iteration, the restarted strategy is used to increase the convergence speed of L1-NCG. To demonstrate the performance of re-L1-NCG in terms of spatial resolution, simulation and physical phantom studies with fluorescent targets located with different edge-to-edge distances were carried out. The reconstruction results show that the re-L1-NCG algorithm has the ability to resolve targets with an edge-to-edge distance of 0.1 cm at a depth of 1.5 cm, which is a significant improvement for FMT.

Fluorescence molecular tomography reconstruction via discrete cosine transform-based regularization

Abstract. Fluorescence molecular tomography (FMT) as a noninvasive imaging modality has been widely used for biomedical preclinical applications. However, FMT reconstruction suffers from severe ill-posedness, especially when a limited number of projections are used. In order to improve the quality of FMT reconstruction results, a discrete cosine transform (DCT) based reweighted L1-norm regularization algorithm is proposed. In each iteration of the reconstruction process, different reweighted regularization parameters are adaptively assigned according to the values of DCT coefficients to suppress the reconstruction noise. In addition, the permission region of the reconstructed fluorophores is adaptively constructed to increase the convergence speed. In order to evaluate the performance of the proposed algorithm, physical phantom and in vivo mouse experiments with a limited number of projections are carried out. For comparison, different L1-norm regularization strategies are employed. By quantifying the signal-to-noise ratio (SNR) of the reconstruction results in the phantom and in vivo mouse experiments with four projections, the proposed DCT-based reweighted L1-norm regularization shows higher SNR than other L1-norm regularizations employed in this work.

Reconstruction of Fluorophore Concentration Variation in Dynamic Fluorescence Molecular Tomography

Dynamic fluorescence molecular tomography (DFMT) is a potential approach for drug delivery, tumor detection, diagnosis, and staging. The purpose of DFMT is to quantify the changes of fluorescent agents in the bodies, which offer important information about the underlying physiological processes. However, the conventional method requires that the fluorophore concentrations to be reconstructed are stationary during the data collection period. As thus, it cannot offer the dynamic information of fluorophore concentration variation within the data collection period. In this paper, a method is proposed to reconstruct the fluorophore concentration variation instead of the fluorophore concentration through a linear approximation. The fluorophore concentration variation rate is introduced by the linear approximation as a new unknown term to be reconstructed and is used to obtain the time courses of fluorophore concentration. Simulation and phantom studies are performed to validate the proposed method. The results show that the method is able to reconstruct the fluorophore concentration variation rates and the time courses of fluorophore concentration with relative errors less than 0.0218.

An adaptive support driven reweighted L1-regularization algorithm for fluorescence molecular tomography.

Fluorescence molecular tomography (FMT) is a promising in vivo functional imaging modality in preclinical study. When solving the ill-posed FMT inverse problem, L1 regularization can preserve the details and reduce the noise in the reconstruction results effectively. Moreover, compared with the regular L1 regularization, reweighted L1 regularization is recently reported to improve the performance. In order to realize the reweighted L1 regularization for FMT, an adaptive support driven reweighted L1-regularization (ASDR-L1) algorithm is proposed in this work. This algorithm has two integral parts: an adaptive support estimate and the iteratively updated weights. In the iteratively reweighted L1-minimization sub-problem, different weights are equivalent to different regularization parameters at different locations. Thus, ASDR-L1 can be considered as a kind of spatially variant regularization methods for FMT. Physical phantom and in vivo mouse experiments were performed to validate the proposed algorithm. The results demonstrate that the proposed reweighted L1-reguarization algorithm can significantly improve the performance in terms of relative quantitation and spatial resolution.

Iterative Correction Scheme Based on Discrete Cosine Transform and L1 Regularization for Fluorescence Molecular Tomography With Background Fluorescence

Goal: High-intensity background fluorescence is generally encountered in fluorescence molecular tomography (FMT), because of the accumulation of fluorescent probes in nontarget tissues or the existence of autofluorescence in biological tissues. The reconstruction results are affected or even distorted by the background fluorescence, especially when the distribution of fluorescent targets is relatively sparse. The purpose of this paper is to reduce the negative effect of background fluorescence on FMT reconstruction. Methods: After each iteration of the Tikhonov regularization algorithm, 3-D discrete cosine transform is adopted to filter the intermediate results. And then, a sparsity constraint step based on L1 regularization is applied to restrain the energy of the objective function. Results: Phantom experiments with different fluorescence intensities of homogeneous and heterogeneous background are carried out to validate the performance of the proposed scheme. The results show that the reconstruction quality can be improved with the proposed iterative correction scheme. Conclusion and Significance: The influence of background fluorescence in FMT can be reduced effectively because of the filtering of the intermediate results, the detail preservation, and noise suppression of L1 regularization.

Greedy reconstruction algorithm for fluorescence molecular tomography by means of truncated singular value decomposition conversion.

Fluorescence molecular tomography (FMT) is a promising imaging modality that enables three-dimensional visualization of fluorescent targets in vivo in small animals. L2-norm regularization methods are usually used for severely ill-posed FMT problems. However, the smoothing effects caused by these methods result in continuous distribution that lacks high-frequency edge-type features and hence limits the resolution of FMT. In this paper, the sparsity in FMT reconstruction results is exploited via compressed sensing (CS). First, in order to ensure the feasibility of CS for the FMT inverse problem, truncated singular value decomposition (TSVD) conversion is implemented for the measurement matrix of the FMT problem. Then, as one kind of greedy algorithm, an ameliorated stagewise orthogonal matching pursuit with gradually shrunk thresholds and a specific halting condition is developed for the FMT inverse problem. To evaluate the proposed algorithm, we compared it with a TSVD method based on L2-norm regularization in numerical simulation and phantom experiments. The results show that the proposed algorithm can obtain higher spatial resolution and higher signal-to-noise ratio compared with the TSVD method.

Depth compensation in fluorescence molecular tomography using an adaptive support driven reweighted L1-minimization algorithm

In fluorescence molecular tomography (FMT), the fluorophore distribution is reconstructed using the diffuse-light measurements obtained from the rotating source-detector pairs placed on the boundary of the tissues. Owing to the intensity attenuation of light when it propagates through tissues, the sensitivity of measurements deteriorates quickly with increased depth. Thus the inconsistent contrast of reconstructed fluorophores located at different depths is a major challenge in FMT. As a spatially variant regularization method, the adaptive support driven reweighted L1-minimization (ASDR-L1) algorithm is proposed here for depth compensation in FMT. ASDR-L1 is a modification of the restarted L1 regularization-based nonlinear conjugate gradient (re-L1-NCG) algorithm previously proposed by our laboratory. In ASDR-L1, the original L1-minimization problem is replaced by a sequence of weighted L1-minimization subproblems with spatially updated weights applied to the adaptive support estimate. Like re-L1-NCG, ASRDR-L1 adopts the restarted strategy in each outer iteration, which contributes to the adaptive support estimate. The updated weights for the next iteration spatially depend on the current solution. In the support estimate, spatially updated weights mean different regularization parameters for different locations. A large regularization parameter in the weighted L1-minimization subproblem makes the results concentrate on a small number of large values, whereas a small regularization parameter tends to make the values be evenly distributed. Thus depth compensation in FMT is achieved through the iteratively updated weights. Simulation experiments are conducted to confirm the feasibility of ASDR-L1. Through ASDR-L1, the reconstructed contrast between two identical fluorophores located at different depths is increased from 1:0.43 to 1:0.96.

Fast reconstruction of fluorescence molecular tomography via a permissible region extraction strategy.

In order to obtain precise reconstruction results in fluorescence molecular tomography (FMT), large-scale matrix equations would be solved in the inverse problem generally. Thus, much time and memory needs to be consumed. In this paper, a permissible region extraction strategy is proposed to solve this problem. First, a preliminary result is rapidly reconstructed using the weight matrix compressed by principal component analysis or uniform sampling. And then the reconstructed target area in this preliminary result is considered as the a priori permissible region to guide the final reconstruction. Phantom experiments with double fluorescent targets are performed to test the performance of the strategy. The results illustrate that the proposed strategy can significantly accelerate the image reconstruction in FMT almost without quality degradation.

Spectral selective fluorescence molecular imaging with volume holographic imaging system

A compact volume holographic imaging (VHI) method that can detect fluorescence objects located in diffusive medium in spectral selective imaging manner is presented. The enlargement of lateral field of view of the VHI system is realized by using broadband illumination and demagnification optics. Each target spectrum of fluorescence emitting from a diffusive medium is probed by tuning the inclination angle of the transmission volume holographic grating (VHG). With the use of the single transmission VHG, fluorescence images with different spectrum are obtained sequentially and precise three-dimensional (3D) information of deep fluorescent objects located in a diffusive medium can be reconstructed from these images. The results of phantom experiments demonstrate that two fluorescent objects with a sub-millimeter distance can be resolved by spectral selective imaging.