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

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.