Variable Step-Size Fast Iterative Shrinkage Thresholding Algorithm for Fluorescence Molecular tomography

The fast iterative shrinkage thresholding algorithm (FISTA) has been shown to be an efficient method for solving least squares with l1-norm regularization problems and has been applied to optical molecular tomography. It adopts a linear increase scheme to provide the Lipschitz constant, which determines the step-size of the internal gradient. The Lipschitz constant, however, will not change if the proximal gradient condition is satisfied after the linear increase. Then it restricts the convergence speed of FISTA further. In this work, a non-linear search scheme, which contains the gradient information, is proposed to obtain the suitable Lipschitz constant. It can provide a variable step-size in each iteration, which can accelerate the convergence of the standard FISTA. We called is as VFISTA. Phantom and in vivo experiments have been performed to show that VFISTA can speed up the reconstruction process effectively for the inverse problem of FMT compared to FISTA.