Numerical analysis of the model of image processing with time-delay regularization

In this paper, we present a semi-implicit numerical scheme for the model of image processing with time-delay regularization, and prove its convergence by the related theory of viscosity solution. Based on the principle of contraction mapping and discrete functional analysis, we also establish the iterative convergence in the sense of L∞ norm. Numerical experiments with Gauss-Seidel iterative method of sparse matrix show that, compared with the explicit scheme, our numerical method make denoised image sharper.