Provably Convergent Plug & Play Linearized ADMM, applied to Deblurring Spatially Varying Kernels

TL;DR

This paper introduces a provably convergent Plug & Play linearized ADMM framework that enables solving inverse problems like deblurring with spatially varying kernels without computing complex proximal operators.

Contribution

It proposes a novel linearized ADMM-based Plug & Play method that guarantees convergence and handles intractable proximal operators in inverse imaging problems.

Findings

Converges reliably on deblurring and super-resolution tasks.

Effectively handles spatially varying kernels.

Outperforms existing methods in accuracy and stability.

Abstract

Plug & Play methods combine proximal algorithms with denoiser priors to solve inverse problems. These methods rely on the computability of the proximal operator of the data fidelity term. In this paper, we propose a Plug & Play framework based on linearized ADMM that allows us to bypass the computation of intractable proximal operators. We demonstrate the convergence of the algorithm and provide results on restoration tasks such as super-resolution and deblurring with non-uniform blur.