Explicit algorithms for a new time dependent model based on level set motion for nonlinear deblurring and noise removal

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 base 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.