Structured Over-Relaxed Monotone FISTA for Linear Inverse Problems in Image Restoration

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 $l_1$-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.