用对称总变差加权的G范数分解图像，更精准分离轮廓与纹理。
Image Decomposition with G-norm Weighted by Total Symmetric Variation
- 引入总对称变差识别区域边界，提升图像结构感知能力
- 加权G范数有效避免轮廓边缘干扰纹理区域检测
- 适用于需要精细纹理分离的图像处理任务
本文提出一种新的变分模型，用于将图像分解为卡通和纹理两部分。该模型通过总对称变差（TSV）刻画有界变差（BV）图像的非局部特征，证明其在识别区域边界方面具有有效性。基于此特性，引入加权Meyer的G-范数，以识别纹理内部而不包含轮廓边缘。对于具有有界TSV的BV图像，证明了所提模型存在解。此外，设计了一种基于算子分裂的快速算法，解决相关的非凸优化问题。通过一系列数值实验验证了方法的有效性。
原文摘要 · Abstract (English)
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.
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