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

2026-03-29

AI Summary

This work addresses the challenge of low decomposition accuracy in cartoon-texture image separation under heavy-tailed noise. To enhance robustness, the authors propose a novel low-rank prior model that replaces the conventional ℓ² data fidelity term with the Huber loss, while employing total variation regularization for the cartoon component and nuclear norm regularization for the texture component. Two tailored operator-splitting algorithms are developed to accommodate different degradation operators. Notably, this is the first study to integrate the Huber loss into the cartoon-texture decomposition framework. The proposed approach preserves the expressive power of structural priors while significantly improving both accuracy and robustness under high-intensity heavy-tailed noise, outperforming existing methods.

Technology Category

Computer Vision: Other Foundations of Computer VisionMachine Learning: Kernel MethodsReasoning under Uncertainty: Graphical Models

Application Category

Web Mining and Content Analysis: Robustness and generalizability of Web mining methodsGraph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphsSearch and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• cartoon-texture decomposition
• heavy-tailed noise
• image decomposition
• robustness
• structured image

Innovation

• robust low-rank prior
• cartoon-texture decomposition
• heavy-tailed noise
• Huber loss
• operator splitting algorithm