A Robust Low-Rank Prior Model for Structured Cartoon-Texture Image Decomposition with Heavy-Tailed Noise

TL;DR

This paper introduces a robust low-rank prior model for cartoon-texture image decomposition that effectively handles heavy-tailed noise using Huber loss and operator splitting algorithms.

Contribution

It proposes a novel model combining Huber loss with total variation and nuclear norms, improving robustness against heavy-tailed noise in image decomposition.

Findings

Outperforms existing models in high-noise scenarios

Efficiently restores images with heavy-tailed noise

Demonstrates superior performance in numerical experiments

Abstract

Cartoon-texture image decomposition is a fundamental yet challenging problem in image processing. A significant hurdle in achieving accurate decomposition is the pervasive presence of noise in the observed images, which severely impedes robust results. To address the challenging problem of cartoon-texture decomposition in the presence of heavy-tailed noise, we in this paper propose a robust low-rank prior model. Our approach departs from conventional models by adopting the Huber loss function as the data-fidelity term, rather than the traditional $\ell_2$-norm, while retaining the total variation norm and nuclear norm to characterize the cartoon and texture components, respectively. Given the inherent structure, we employ two implementable operator splitting algorithms, tailored to different degradation operators. Extensive numerical experiments, particularly on image restoration tasks under high-intensity heavy-tailed noise, efficiently demonstrate the superior performance of our model.