Convergent plug-and-play with proximal denoiser and unconstrained regularization parameter
This work addresses a convergence issue in image inverse problems for researchers and practitioners, but it is incremental as it builds on existing Plug-and-Play methods.
The authors tackled the limitation of Plug-and-Play algorithms requiring restrictive regularization parameters for convergence, by providing new convergence proofs that remove these restrictions and introducing a relaxed algorithm. Their experimental results on deblurring and super-resolution tasks showed improved image restoration accuracy.
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.