Infimal convolution of data discrepancies for mixed noise removal

TL;DR

This paper introduces a variational denoising model for images corrupted by mixed noise types, combining statistical derivation, numerical methods, and experimental validation to effectively separate and remove complex noise patterns.

Contribution

It proposes a novel infimal convolution-based data discrepancy model for mixed noise removal, with a statistical foundation and efficient numerical solution techniques.

Findings

Effective noise decomposition demonstrated in experiments

Model outperforms existing methods for mixed noise removal

Asymptotic recovery of classical single-noise models

Abstract

We consider the problem of image denoising in the presence of noise whose statistical properties are a combination of two different distributions. We focus on noise distributions that are frequently considered in applications, in particular mixtures of salt & pepper and Gaussian noise, and Gaussian and Poisson noise. We derive a variational image denoising model that features a total variation regularisation term and a data discrepancy that features the mixed noise as an infimal convolution of discrepancy terms of the single-noise distributions. We give a statistical derivation of this model by joint Maximum A-Posteriori (MAP) estimation, and discuss in particular its interpretation as the MAP of a so-called infinity convolution of two noise distributions. Moreover, classical single-noise models are recovered asymptotically as the weighting parameters go to infinity. The numerical solution of the model is computed using second order Newton-type methods. Numerical results show the decomposition of the noise into its constituting components. The paper is furnished with several numerical experiments and comparisons with other existing methods dealing with the mixed noise case are shown.