针对重尾噪声下的图像卡通纹理分解，提出更鲁棒的低秩先验模型。
A Robust Low-Rank Prior Model for Structured Cartoon-Texture Image Decomposition with Heavy-Tailed Noise
- 用Huber损失替代传统l2范数，提升抗噪能力
- 在强重尾噪声下仍能保持高精度分解效果
- 适合图像去噪、修复等含异常噪声场景
卡通-纹理图像分解是图像处理中的基础且具有挑战性的问题。观测图像中普遍存在的噪声严重干扰了分解的鲁棒性。为应对重尾噪声下的卡通-纹理分解难题，本文提出一种鲁棒的低秩先验模型。与传统方法不同，该模型采用Huber损失函数作为数据保真项，而非传统的ℓ₂-范数，同时保留总变差范数和核范数分别刻画卡通成分和纹理成分。考虑到内在结构，设计了两种可实现的算子分裂算法，适用于不同退化算子。大量数值实验，尤其是在高强度重尾噪声下的图像恢复任务中，充分验证了该模型的优越性能。
原文摘要 · Abstract (English)
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.
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