A multiscale tight frame-inspired scheme for nonlinear diffusion

Nonlinear diffusion and wavelet shrinkage are two successfully applied methods for discontinuity preserving denoising of signals and images. Recently, relations between both methods have been established taking into account wavelet shrinkage at one or multiscale. In this paper we show that one step of (stabilized) explicit discretization of nonlinear diffusion can be expressed in terms of tight frame shrinkage on a single spatial level or multiscale. We prove that our scheme permits larger steps while having more choices of shrinkage functions. Numerical examples demonstrate the behavior of our scheme for one or two scales.