Analysis of the CCFD method for MC-based image denoising problems

Image denoising using mean curvature leads to the problem of solving a nonlinear fourth-order integro-differential equation. The term comes from regularization functional. In this paper, we treat high-order nonlinearity by reducing equation system first-order equations. Then cell-centered finite difference scheme is applied system. With lexicographical ordering unknowns, discretization functional block pentadiagonal matrix. Our contributions are fourfold: (i) give new method for treating term; (ii) express in terms simple matrices; (iii) an analysis and establish that error first order; (iv) verify theoretical result illustrating convergence rates numerical experiments.