Sparsity reconstruction for bioluminescence tomography based on an augmented Lagrangian method

Bioluminescence imaging (BLI) is an optical molecular imaging modality for monitoring physiological and pathological activities at the molecular level. The information of bioluminescent probe distribution in small animals can be threedimensionally and quantitatively obtained by bioluminescence tomography (BLT). Due to ill-posed nature, BLT may bear multiple solutions and aberrant reconstruction in the presence of measurement noise and optical parameter mismatches. Among different regularization methods, L2-type regularization strategy is the most popular and commonly-applied method, which minimizes the output-least-square formulation incorporated with the l2-norm regularization term to stabilize the problem. However, it often imposes over-smoothing on the reconstruction results. In contrast, for many practical applications, such as early detection of tumors, the volumes of the bioluminescent sources are very small compared with the whole body. In this paper, L1 regularization is used to fully take advantage of the sparsity prior knowledge and improve both efficiency and stability. And then a reconstruction method based on the augmented Lagrangian approach is proposed, which considers the BLT problem as the constrained optimization problem and employs the Bregman iterative method to deal with it. By using "divide and conquer" approach, the optimization problem can be exactly and fast solved by iteratively solving a sequence of unconstrained subproblems. To evaluate the performance of the proposed method in turbid mouse geometry, stimulate experiments with a heterogeneous 3D mouse atlas are conducted. In addition, physical experiments further demonstrate the potential of the proposed algorithm in practical applications.