Image Decomposition with G-norm Weighted by Total Symmetric Variation
This work addresses image decomposition for computer vision applications, but it appears incremental as it builds on existing variational models with specific modifications.
The authors tackled the problem of decomposing images into cartoon and texture parts by proposing a variational model that uses Total Symmetric Variation to identify regional boundaries and a weighted G-norm to separate textures from edges, demonstrating its effectiveness through numerical experiments.
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.