A Multiscale Wavelet-Inspired Scheme for Nonlinear Diffusion

Nonlinear diffusion filtering 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 scale. In this paper, we propose a new explicit scheme for nonlinear diffusion which directly incorporates ideas from multiscale Haar wavelet shrinkage. We prove that our scheme permits larger time steps while preserving convergence to the mean signal value. Numerical examples demonstrate the behavior of our scheme for two and three scales. Mathematics Subject Classification 2000. 65T60, 65M06, 65M12, 94A12.