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.
Abstract (translated)
卡通-纹理分解是图像处理中一个基础且具有挑战性的问题。在实现精确分解时，一个主要障碍是观测图像中普遍存在的噪声，这会严重阻碍获得稳健的结果。为应对重尾噪声环境下卡通-纹理分解的难题，本文提出一种鲁棒低秩先验模型。该模型区别于传统方法：采用Huber损失函数作为数据保真项以替代传统的$\ell_2$范数，同时保留总变分范数和核范数分别刻画卡通成分与纹理成分。基于模型的内在结构，我们针对不同的退化算子设计了两类可实现的算子分裂算法。大量数值实验，特别是针对高强度重尾噪声下的图像复原任务，高效验证了本模型优越的性能。
URL
https://arxiv.org/abs/2603.27579
