Correspondences between wavelet shrinkage and nonlinear diffusion

Authors:
Pavel Mrázek;Joachim Weickert;Gabriele Steidl
Affiliations:
Mathematical Image Analysis Group, Faculty of Mathematics and Computer Science, Saarland University, Saarbrücken, Germany;Mathematical Image Analysis Group, Faculty of Mathematics and Computer Science, Saarland University, Saarbrücken, Germany;Faculty of Mathematics and Computer Science, University of Mannheim, Mannheim, Germany
Venue:
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
Year:
2003

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Abstract

We study the connections between discrete one-dimensional schemes for nonlinear diffusion and shift-invariant Haar wavelet shrinkage. We show that one step of (stabilised) explicit discretisation of nonlinear diffusion can be expressed in terms of wavelet shrinkage on a single spatial level. This equivalence allows a fruitful exchange of ideas between the two fields. In this paper we derive new wavelet shrinkage functions from existing diffusivity functions, and identify some previously used shrinkage functions as corresponding to well known diffusivities. We demonstrate experimentally that some of the diffusion-inspired shrinkage functions are among the best for translation-invariant multiscale wavelet shrinkage denoising.