On a reaction-diffusion system applied to image decomposition and restoration

In this paper, we study a reaction-diffusion system applied to image restoration and image decomposition into cartoon and texture, based on Osher, Solé and Vese's model in [S. Osher, A. Solé, L. Vese, Image decomposition and restoration using total variation minimization and the H−1 norm, SIAM Journal on Multiscale Modeling and Simulation 1 (3) (2003) 349-370]. By the regularization method, we establish the existence and uniqueness of entropy solutions to the system with BV initial data and Neumann boundary conditions. Finally, we also give an experimental approach to show the efficiency of this kind of model.