# Infimal convolution of data discrepancies for mixed noise removal

arXiv: https://arxiv.org/abs/1611.00690 · HTML: https://mlsanity.com/paper/1611.00690/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Nov 2016.

## Built on by (most cited first, 2 of 2)

- [ℓ1DecNet+: A new architecture framework by ℓ1 decomposition and iteration unfolding for sparse feature segmentation](https://mlsanity.com/paper/2203.02690/) (2022)
- [Image reconstruction in light-sheet microscopy: spatially varying deconvolution and mixed noise](https://mlsanity.com/paper/2108.03642/) (2021)

## Abstract (arXiv)

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.