Please use this identifier to cite or link to this item: doi:10.22028/D291-26249
Title: Diffusion-inspired shrinkage functions and stability results for wavelet denoising
Author(s): Mrázek, Pavel
Weickert, Joachim
Steidl, Gabriele
Language: English
Year of Publication: 2003
Free key words: image denoising
wavelet shrinkage
diffusion filtering
DDC notations: 510 Mathematics
Publikation type: Other
Abstract: We study the connections between discrete 1-D schemes for non-linear diffusion and shift-invariant Haar wavelet shrinkage. We show that one step of a (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 denoising. Moreover, by transferring stability notions from diffusion filtering to wavelet shrinkage, we derive conditions on the shrinkage function that ensure that shift invariant single-level Haar wavelet shrinkage is maximum-minimum stable, monotonicity preserving, and variation diminishing.
Link to this record: urn:nbn:de:bsz:291-scidok-44427
Series name: Preprint / Fachrichtung Mathematik, Universität des Saarlandes
Series volume: 96
Date of registration: 4-Jan-2012
Faculty: MI - Fakultät für Mathematik und Informatik
Department: MI - Mathematik
Collections:SciDok - Der Wissenschaftsserver der Universität des Saarlandes

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