Mixed-Noise Plug-and-Play with Infimal Convolution Fidelities and Multiple Priors

2026-09-27

AI Summary

This study addresses the challenges of proving convergence and insufficiently fusing multiple priors in plug-and-play (PnP) algorithms for inverse imaging under mixed noise. It proposes a novel multi-prior PnP paradigm based on Kullback–Leibler divergence, employing infimal convolution to construct the data fidelity term. By integrating Davis–Yin three-operator splitting, the method establishes a jointly estimable framework that preserves a Bayesian maximum a posteriori interpretation while guaranteeing provable convergence. Theoretically, it ensures stable convergence under complex mixed-noise conditions. Experimentally, the approach supports reconstruction with 38% high-level noise in Laplace–Gaussian noise scenarios, significantly outperforming existing methods in preserving fine textural details.

Abstract

Plug-and-Play (PnP) algorithms are a class of iterative methods for inverse imaging. Within an optimization algorithm, they combine a flexible fidelity term, encoding the forward operator, and a pretrained image denoiser, in order to deal with more severe corruptions such as blurring or downsampling when reconstructing an image. This work studies provably convergent PnP methods for mixed-noise forward processes by using the infimal convolution as a fidelity term, providing a statistical interpretation as a joint maximum a-posteriori estimator over both noises, and preserving the Bayesian MAP interpretation of PnP methods. Independently, we extend the PnP formulation to multiple prior terms using the Davis--Yin three-operator splitting. This extension can be combined with either standard fidelities or the proposed mixed-noise infimal-convolution fidelities. We verify that these generalized PnP methods are convergent under standard Kurdyka--Lojasiewicz conditions. Numerical experiments on Laplace-Gaussian and Poisson--Gaussian noise demonstrate stable convergence of single-prior and multiple-prior PnP methods, and divergence under fidelity mismatch. Furthermore, PnP with infimal convolution fidelities are able to scale to noise up to 38% standard deviation, with multiple priors reaching different stationary points that qualitatively preserve more textural properties.

Problem

• Plug-and-Play
• mixed-noise
• inverse imaging
• infimal convolution
• multiple priors

Innovation

• Plug-and-Play
• Infimal Convolution
• Mixed Noise
• Multiple Priors
• Davis-Yin Splitting