Reduction Accelerated Adaptive Step‐Size <scp>FISTA</scp> Based Smooth‐Lasso Regularization for Fluorescence Molecular Tomography Reconstruction

ABSTRACT In this paper, a reduced accelerated adaptive fast iterative shrinkage threshold algorithm based on Smooth‐Lasso regularization (SL‐RAFISTA‐BB) is proposed for fluorescence molecular tomography (FMT) 3D reconstruction. This method uses the Smooth‐Lasso regularization to fuse the group sparse prior information which can balance the relationship between the sparsity and smoothness of the solution, simplifying the process of calculation. In particular, the convergence speed of the FISTA is improved by introducing a reduction strategy and Barzilai‐Borwein variable step size factor, and constructing a continuation strategy to reduce computing costs and the number of iterations. The experimental results show that the proposed algorithm not only accelerates the convergence speed of the iterative algorithm, but also improves the positioning accuracy of the tumor target, alleviates the over‐sparse or over‐smooth phenomenon of the reconstructed target, and clearly outlines the boundary information of the tumor target. We hope that this method can promote the development of optical molecular tomography.