A variational model for cartoon-texture decomposition of a color image

Image decomposition is one of the most important tasks in image processing. In this paper, we develop a novel saturation-value total variation model for color image decomposition. The approach is to propose a variational model containing an energy functional to derive the cartoon and texture decomposition in the saturation-value color space so that the color can be kept in the resulting cartoon component. The proposed idea is different from existing color image decomposition model where color information usually exists in both cartoon and texture components. In the variational model, saturation-value total variation is incorporated for regularizing the cartoon component of a color image, meanwhile, L1 norm is considered for modeling the texture component in the saturation-value color space. Theoretically, we develop a smooth approximation approach to study the existence of the solution of the proposed optimization problem. We formulate an effective and efficient algorithm to solve the proposed minimization problem based on the framework of alternating direction method of multipliers. Numerical examples are presented to demonstrate that the performance of the proposed model is better than that of other testing methods for several testing color images.