Source reconstruction for bioluminescence tomography via L1∕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 L1∕2 regularization to enhance sparsity of BLT solution and solve the nonconvex L1∕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