Fast and Robust Reconstruction for Fluorescence Molecular Tomography via L_1-2 Regularization

Sparse reconstruction inspired by compressed sensing has attracted considerable attention in fluorescence molecular tomography (FMT). However, the columns of system matrix used for FMT reconstruction tend to be highly coherent, which means L₁ minimization may not produce the sparsest solution. In this paper, we propose a novel reconstruction method by minimization of the difference of L₁ and L₂ norms. To solve the nonconvex L_1-2 minimization problem, an iterative method based on the difference of convex algorithm (DCA) is presented. In each DCA iteration, the update of solution involves an L₁ minimization subproblem, which is solved by the alternating direction method of multipliers with an adaptive penalty. We investigated the performance of the proposed method with both simulated data and in vivo experimental data. The results demonstrate that the DCA for L_1-2 minimization outperforms the representative algorithms for L₁, L₂, L_1/2, and L₀ when the system matrix is highly coherent.