Volume 42, pp. 64-84, 2014.

Variational image denoising while constraining the distribution of the residual

Alessandro Lanza, Serena Morigi, Fiorella Sgallari, and Anthony J. Yezzi

Abstract

We present a denoising method aimed at restoring images corrupted by additive noise based on the assumption that the distribution of the noise process is known. The proposed variational model uses Total Variation (TV) regularization (chosen simply for its popularity; any other regularizer could be substituted as well) but constrains the distribution of the residual to fit a given target noise distribution. The residual distribution constraint constitutes the key novelty behind our approach. The restored image is efficiently computed by the constrained minimization of an energy functional using an Alternating Directions Methods of Multipliers (ADMM) procedure. Numerical examples show that the novel residual constraint indeed improves the quality of the image restorations.

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Key words

image denoising, variational models, image residual, probability distribution function

AMS subject classifications

68U10, 65K10, 65F22, 62E17

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