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Preprint (Vorabdruck) zugänglich unter
URN: urn:nbn:de:bsz:291-scidok-44427
URL: http://scidok.sulb.uni-saarland.de/volltexte/2012/4442/


Diffusion-inspired shrinkage functions and stability results for wavelet denoising

Mrázek, Pavel ; Weickert, Joachim ; Steidl, Gabriele

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Freie Schlagwörter (Englisch): image denoising , wavelet shrinkage , diffusion filtering
Institut: Fachrichtung 6.1 - Mathematik
DDC-Sachgruppe: Mathematik
Dokumentart: Preprint (Vorabdruck)
Schriftenreihe: Preprint / Fachrichtung Mathematik, Universität des Saarlandes
Bandnummer: 96
Sprache: Englisch
Erstellungsjahr: 2003
Publikationsdatum: 04.01.2012
Kurzfassung auf Englisch: 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.
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