L_p Regularization for Bioluminescence Tomography Based on the Split Bregman Method

Purpose: Bioluminescence tomography (BLT) is a promising in vivo optical imaging technique in preclinical research at cellular and molecular levels. The problem of BLT reconstruction is quite ill-posed and ill-conditioned. In order to achieve high accuracy and efficiency for its inverse reconstruction, we proposed a novel approach based on L_p regularization with the Split Bregman method. Procedures: The diffusion equation was used as the forward model. Then, we defined the objective function of L_p regularization and developed a Split Bregman iteration algorithm to optimize this function. After that, we conducted numerical simulations and in vivo experiments to evaluate the accuracy and efficiency of the proposed method. Results: The results of the simulations indicated that compared with the conjugate gradient and iterative shrinkage methods, the proposed method is more accurate and faster for multisource reconstructions. Furthermore, in vivo imaging suggested that it could clearly distinguish the viable and apoptotic tumor regions. Conclusions: The Split Bregman iteration method is able to minimize the L_p regularization problem and achieve fast and accurate reconstruction in BLT.