Explicit Algorithms for a New Time Dependent Model Based on Level Set Motion for Nonlinear Deblurring and Noise Removal

Abstract

In this paper we formulate a time dependent model to approximate the solution to the nonlinear total variation optimization problem for deblurring and noise removal introduced by Rudin and Osher [ Total variation based image restoration with free local constraints, in Proceedings IEEE Internat. Conf. Imag. Proc., IEEE Press, Piscataway, NJ, (1994), pp. 31--35] and Rudin, Osher, and Fatemi [ Phys. D, 60 (1992), pp. 259--268], respectively. Our model is based on level set motion whose steady state is quickly reached by means of an explicit procedure based on Roe's scheme [ J. Comput. Phys., 43 (1981), pp. 357--372], used in fluid dynamics. We show numerical evidence of the speed of resolution and stability of this simple explicit procedure in some representative 1D and 2D numerical examples.