Abstract
In this paper, we propose a novel variational model for decomposing images into their respective cartoon and texture parts. Our model characterizes certain non-local features of any Bounded Variation (BV) image by its Total Symmetric Variation (TSV). We demonstrate that TSV is effective in identifying regional boundaries. Based on this property, we introduce a weighted Meyer's $G$-norm to identify texture interiors without including contour edges. For BV images with bounded TSV, we show that the proposed model admits a solution. Additionally, we design a fast algorithm based on operator-splitting to tackle the associated non-convex optimization problem. The performance of our method is validated by a series of numerical experiments.
Abstract (translated)
在这篇论文中，我们提出了一种新颖的变分模型，用于将图像分解为其卡通部分和纹理部分。我们的模型通过总对称变化（TSV）来描述任何有界变差（BV）图像中的某些非局部特征。我们证明了TSV在识别区域边界方面是有效的。基于这一特性，我们引入了一种加权的Meyer $G$-范数，以在不包含轮廓边缘的情况下标识纹理内部。对于具有有界TSV的BV图像，我们展示了所提出的模型存在解。此外，我们设计了一种基于算子分裂的快速算法来解决相关的非凸优化问题。通过一系列数值实验验证了我们方法的有效性。
URL
https://arxiv.org/abs/2503.22560
