Regularized Non-Gaussian Image Denoising

TL;DR

This paper introduces a reparameterization method for non-Gaussian image denoising that enables the use of convex optimization techniques, improving reconstruction under complex noise models like Bernoulli, Poisson, and multiplicative noise.

Contribution

It proposes a simple reparameterization approach that transforms non-convex regularized denoising problems into convex ones, facilitating efficient optimization for non-Gaussian noise models.

Findings

Effective denoising under exponential family noise models.

Reparameterization enables convex optimization methods.

Improved image reconstruction quality.

Abstract

In image denoising problems, one widely-adopted approach is to minimize a regularized data-fit objective function, where the data-fit term is derived from a physical image acquisition model. Typically the regularizer is selected with two goals in mind: (a) to accurately reflect image structure, such as smoothness or sparsity, and (b) to ensure that the resulting optimization problem is convex and can be solved efficiently. The space of such regularizers in Gaussian noise settings is well studied; however, non-Gaussian noise models lead to data-fit expressions for which entirely different families of regularizers may be effective. These regularizers have received less attention in the literature because they yield non-convex optimization problems in Gaussian noise settings. This paper describes such regularizers and a simple reparameterization approach that allows image reconstruction to be accomplished using efficient convex optimization tools. The proposed approach essentially modifies the objective function to facilitate taking advantage of tools such as proximal denoising routines. We present examples of imaging denoising under exponential family (Bernoulli and Poisson) and multiplicative noise.