Fast and robust reconstruction approach for sparse fluorescence tomography based on adaptive matching pursuit

Fluorescence molecular tomography (FMT) has been receiving more and more attention for its applications in in vivo small animal imaging. Fluorescent sources to be reconstructed are usually small and sparse, which can be considered as a priori information. The stage-wise orthogonal matching pursuit algorithm (StOMP) with L1 regularization has been applied in FMT problem to get a sparse solution and proved efficient and at least 2 orders of magnitude faster than iterated-shrinkage-based algorithms. A sparsity factor that indicates the number of unknowns is determined by estimation in advance in StOMP. However, different FMT experiments have different sparsity factors and the StOMP algorithm doesn´t provide a way to determine a specific sparsity factor accurately. Estimation of sparsity factor empirically in StOMP makes the algorithm not robust and applicable in different FMT experiments, which usually results in unacceptable results. In this paper, we propose a novel approach based on adaptive matching pursuit to make reconstruction results more stable and method easier to use. The proposed algorithm is able to find an optimal sparsity factor and a satisfactory solution always, no matter what value of the initial sparsity factor is estimated. Besides, the proposed algorithm adopts an automatical updating strategy. It ends after only a few iterations and doesn´t add extral time burden compared to StOMP. So the proposed algorithm is still as fast as the StOMP algorithm. Comparisons are made between the StOMP algorithm and the proposed algorithm in numerical experiments to show the advantages of our method.