Image Decomposition with G-norm Weighted by Total Symmetric Variation

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.

@article{he2025_2503.22560,
  title={ Image Decomposition with G-norm Weighted by Total Symmetric Variation },
  author={ Roy Y. He and Martin Huska and Hao Liu },
  journal={arXiv preprint arXiv:2503.22560},
  year={ 2025 }
}