An Accelerated Double Forward-Backward Splitting Method with Applications in Image Restoration

期刊论文
发表日期：

2025年5月27日

查看全文

Zhi-Bin Zhu,
Xiao-Wen Zhu,
Zhen Tan

摘要

The forward-backward splitting method is an efficient method to solve the separable convex minimization problem, which is given by differentiable and non-differentiable terms. In this paper, inspired by Nesterov’s accelerated first-order iterative method, we propose an accelerated double forward-backward splitting method, which is based on two forward-backward steps and a modified extrapolation step. In addition, the proposed method is obtained by a convex combination at each iteration. Under general conditions, by exploiting the convexity of the function and applying a correction to the sequence $\{ t_k \}$ ${t_{k}}$ , we prove that the convergence rate of the new method is $O(1/{k^2} )$ $O (1 / k^{2})$ . Finally, we provide some numerical tests on image deblurring problem. Numerical experiments are performed to show that our proposed method is effective.