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 B V initial data and Neumann boundary conditions. Finally, we also give an experimental approach to show the efficiency of this kind of model.