A convergent Plug-and-Play Majorization-Minimization algorithm for Poisson inverse problems

TL;DR

This paper introduces a convergent plug-and-play algorithm for Poisson inverse problems that combines neural network regularization with likelihood-based data fidelity, achieving state-of-the-art results especially in high-noise scenarios.

Contribution

It proposes a novel majorization-minimization based plug-and-play method that guarantees convergence while integrating pre-trained neural denoisers for Poisson inverse problems.

Findings

State-of-the-art performance in deconvolution and tomography.

Superior results under high-noise conditions.

Convergence guarantees to a stationary point.

Abstract

In this paper, we present a novel variational plug-and-play algorithm for Poisson inverse problems. Our approach minimizes an explicit functional which is the sum of a Kullback-Leibler data fidelity term and a regularization term based on a pre-trained neural network. By combining classical likelihood maximization methods with recent advances in gradient-based denoisers, we allow the use of pre-trained Gaussian denoisers without sacrificing convergence guarantees. The algorithm is formulated in the majorization-minimization framework, which guarantees convergence to a stationary point. Numerical experiments confirm state-of-the-art performance in deconvolution and tomography under moderate noise, and demonstrate clear superiority in high-noise conditions, making this method particularly valuable for nuclear medicine applications.