An improved OSV cartoon-texture decomposition model

Cartoon-texture decomposition of images is a hot research topic in image processing, its main goal is to decompose a given image into cartoon and texture parts measured by different norms. In the existing partial decomposition model, the H-1 functional is often used to measure the oscillation function, which is obtained by the Hodge decomposition. Because a divergence-free vector function is neglected in the calculation of the Hodge decomposition, some directional information will be lost in the texture part, which will affect the decomposition results. In this paper, a new cartoon-texture decomposition model with divergence-free vector field constraint is established by analyzing the theory of the vector field. Mathematically, the new model makes the texture more accurate and complete. In order to solve this model, we transform the constrained optimization problem into an unconstrained problem by using the augmented Lagrange method, and then solve it with the alternating direction method. The proposed cartoon-texture decomposition model contains the divergence-free vector field information, so it improves the decomposition effect obviously, and the experimental results confirm the validity of the proposed model.