Regularization by Denoising via Fixed-Point Projection (RED-PRO)

TL;DR

This paper introduces RED-PRO, a convex optimization reformulation of RED that unifies it with PnP methods, providing convergence guarantees and improved image restoration results in deblurring and super-resolution tasks.

Contribution

It reformulates RED as a convex problem using fixed-point projections, unifies RED and PnP frameworks, and offers convergence guarantees with practical image processing applications.

Findings

RED-PRO improves image deblurring and super-resolution results.

It provides convergence guarantees for RED and PnP methods.

RED-PRO unifies and extends existing denoising-based regularization methods.

Abstract

Inverse problems in image processing are typically cast as optimization tasks, consisting of data-fidelity and stabilizing regularization terms. A recent regularization strategy of great interest utilizes the power of denoising engines. Two such methods are the Plug-and-Play Prior (PnP) and Regularization by Denoising (RED). While both have shown state-of-the-art results in various recovery tasks, their theoretical justification is incomplete. In this paper, we aim to bridge between RED and PnP, enriching the understanding of both frameworks. Towards that end, we reformulate RED as a convex optimization problem utilizing a projection (RED-PRO) onto the fixed-point set of demicontractive denoisers. We offer a simple iterative solution to this problem, by which we show that PnP proximal gradient method is a special case of RED-PRO, while providing guarantees for the convergence of both frameworks to globally optimal solutions. In addition, we present relaxations of RED-PRO that allow for handling denoisers with limited fixed-point sets. Finally, we demonstrate RED-PRO for the tasks of image deblurring and super-resolution, showing improved results with respect to the original RED framework.