2023/11/02 by Samuel Hurault, Hurault, Samuel, Antonin Chambolle +5 · 3 citations
Engineering · #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #FOS: Mathematics #Microwave Imaging and Scattering Analysis #Optimization and Control (math.OC) #Photoacoustic and Ultrasonic Imaging #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.2311.01216
openalex publication_date 2023/11/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
In this work, we present new proofs of convergence for Plug-and-Play (PnP) algorithms. PnP methods are efficient iterative algorithms for solving image inverse problems where regularization is performed by plugging a pre-trained denoiser in a proximal algorithm, such as Proximal Gradient Descent (PGD) or Douglas-Rachford Splitting (DRS). Recent research has explored convergence by incorporating a denoiser that writes exactly as a proximal operator. However, the corresponding PnP algorithm has then to be run with stepsize equal to 1. The stepsize condition for nonconvex convergence of the proximal algorithm in use then translates to restrictive conditions on the regularization parameter of the inverse problem. This can severely degrade the restoration capacity of the algorithm. In this paper, we present two remedies for this limitation. First, we provide a novel convergence proof for PnP-DRS that does not impose any restrictions on the regularization parameter. Second, we examine a relaxed version of the PGD algorithm that converges across a broader range of regularization parameters. Our experimental study, conducted on deblurring and super-resolution experiments, demonstrate that both of these solutions enhance the accuracy of image restoration.