In this paper, we propose an efficient numerical algorithm for solving large-scale ill-posed linear inverse problems encountered in image restoration. To boost computational efficiency, we extend the structured fast iterative shrinkage-thresholding algorithm (sFISTA) for addressing the corresponding l1-regularized minimization problem, and further introduce the over-relaxation technique to accelerate the algorithm. The proposed algorithm is termed structured over-relaxed monotone FISTA (sOMFISTA). The convergence analysis of sOMFISTA is also conducted. The algorithmic framework of sOMFISTA is universally applicable to any non-smooth convex regularization term, exhibiting remarkable flexibility. Extensive numerical experiments are carried out to systematically validate the superiority in efficiency and performance of the proposed sOMFISTA.
Chen et al. (Fri,) studied this question.