Vectorial Total Symmetric Variation and Applications to Color Image Decomposition

Image decomposition, which separates an image into distinct structural and textural components, underlies many fundamental tasks such as image denoising and cartoonization. A key challenge in this area lies in the effective separation of textures from edges due to their perceptual similarity, along with the prevention of color bleeding in color images. To address these issues, we propose a novel color image decomposition model. The model integrates a vectorial total variation term with a vectorial weighted G‑norm, where the weighting function operates as an edge indicator. For computing this weight, we introduce a vectorial total symmetric variation, which is a formulation that synthesizes image directional variations of all directions. An operator-splitting algorithm, enhanced with a restarting strategy, is developed to efficiently solve the resulting optimization problem. Numerical experiments demonstrate that the proposed approach successfully distinguishes textures from edges while preserving color consistency and maintaining sharp boundaries.