Accelerated Plug-and-Play Davis-Yin Splitting for Nonconvex Image Reconstruction

Abstract

In this work, we study a class of structured non-convex and non-smooth optimization problems arising in imaging applications, where the objective is the sum of three functions. We consider the Davis-Yin splitting method, a FISTA-type accelerated variant, along with a quasi-Newton line-search method and a plug-and-play (PnP) extension to solve the problem. We develop a unified convergence analysis based on the Davis-Yin envelope under mild assumptions, including the Kurdyka-Łojasiewicz property. Within this framework, we establish subsequential and global convergence of the iterates to stationary points, together with residual convergence rates. We demonstrate the performance of the proposed methods on image restoration and low-rank matrix completion problems. For low-rank matrix completion, we perform experiments on both synthetic data and public datasets to evaluate recovery accuracy and efficiency. In imaging tasks, including image deblurring, we compare the convergence behaviour and reconstruction quality of several algorithmic variants using peak signal-to-noise ratio (PSNR). The results show that FISTA-acceleration and line-search methods improve convergence, while PnP denoisers enhance image quality, and the proposed methods remain competitive on matrix completion tasks.