Semi-implicit finite volume scheme for solving nonlinear diffusion equations in image processing

We propose and prove a convergence of the semi-implicit finite volume appro ximation scheme for the numerical solution of the modified (in the sense of Catte, Lions, Morel and Coll) Perona-Malik nonlinear image selective smoot hing equation (called anisotropic diffusion in the image processing). The p roof is based on L-2 a-priori estimates and Kolmogorov's compactness theore m. The implementation aspects and computational results are discussed.