# Image Decomposition with G-norm Weighted by Total Symmetric Variation

arXiv: https://arxiv.org/abs/2503.22560 · HTML: https://mlsanity.com/paper/2503.22560/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 26 references that are in the map.
- First posted on arXiv 28 Mar 2025.

## Builds on (most cited first, 2 of 2)

- [Learning Texture Transformer Network for Image Super-Resolution](https://mlsanity.com/paper/2006.04139/) (2020)
- [Euler's Elastica Based Cartoon-Smooth-Texture Image Decomposition](https://mlsanity.com/paper/2407.02794/) (2024)

## Abstract (arXiv)

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.