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.

翻译：本文提出了一种新颖的变分模型，用于将图像分解为卡通部分和纹理部分。该模型通过总对称变分（TSV）刻画有界变分（BV）图像的非局部特征。我们证明TSV能有效识别区域边界。基于此特性，我们引入加权Meyer $G$-范数以识别纹理内部区域，同时避免包含轮廓边缘。对于具有有界TSV的BV图像，我们证明了所提模型存在解。此外，我们设计了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本方法的性能。