Relations Between Soft Wavelet Shrinkage and Total Variation Denoising

Soft wavelet shrinkage and total variation (TV) denoising are two frequently used nonlinear techniques for denoising signals and images, while preserving their discontinuities. In this talk we analyse conditions under which both methods are equivalent.

First we show that 1-D Haar wavelet shrinkage on a single scale is equivalent to a single step of space-discrete TV diffusion or regularisation of two-pixel pairs. This result is used to prove that a translationally invariant version of this single scale shrinkage can be regarded as a numerical scheme for TV diffusion. Finally, we show that wavelet shrinkage on multiple scales comes down to a single step TV diffusion filtering or regularisation of the so-called Laplacian pyramid of the signal.

This is joint work with Gabriele Steidl (University of Mannheim).