Fast Source Reconstruction for Bioluminescence Tomography Based on Sparse Regularization

Bioluminescence tomography (BLT) is an inherent ill-posed inverse problem to reconstruct the internal source in 3-D with limited measurements on the external surface. In most BLT studies so far, a relatively small permissible source region or multispectral approach is typically used to enhance the stability or quality of the solution. In this letter, considering the sparsity characteristic of the light source, BLT is reformulated as a least absolute shrinkage and selection operator (LASSO) problem with l₁ regularization, and then, a fast reconstruction algorithm named as stagewise fast LASSO is proposed for solving this problem. Numerical simulations of a 3-D mouse atlas under different noise levels demonstrate that the proposed algorithm is robust against measurement noise, and it can achieve high computational efficiency and accurate localization of source even without any permissible region constraint.