A new similarity measure for nonlocal filtering in the presence of multiplicative noise

  • This paper presents a new similarity measure and nonlocal filters for images corrupted by multiplicative noise. The considered filters are generalizations of the nonlocal means filter of Buades et al., which is known to be well suited for removing additive Gaussian noise. To adapt to different noise models, the patch comparison involved in this filter has first of all to be performed by a suitable noise dependent similarity measure. To this purpose, we start by studying a probabilistic measure recently proposed for general noise models by Deledalle et al. We analyze this measure in the context of conditional density functions and examine its properties for images corrupted by additive and multiplicative noise. Since it turns out to have unfavorable properties for multiplicative noise we deduce a new similarity measure consisting of a probability density function specially chosen for this type of noise. The properties of our new measure are studied theoretically as well as by numerical experiments. To obtain the final nonlocal filters we apply a weighted maximum likelihood estimation framework, which also incorporates the noise statistics. Moreover, we define the weights occurring in these filters using our new similarity measure and propose different adaptations to further improve the results. Finally, restoration results for images corrupted by multiplicative Gamma and Rayleigh noise are presented to demonstrate the very good performance of our nonlocal filters.

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Metadaten
Verfasserangaben:Tanja Teuber, Annika Lang
URN (Permalink):urn:nbn:de:hbz:386-kluedo-23104
Dokumentart:Preprint
Sprache der Veröffentlichung:Englisch
Jahr der Fertigstellung:2011
Jahr der Veröffentlichung:2011
Veröffentlichende Institution:Technische Universität Kaiserslautern
Datum der Publikation (Server):11.04.2011
Freies Schlagwort / Tag:Similarity measures; image restoration; maximum likelihood estimation; multiplicative noise; non-local filtering
Fachbereiche / Organisatorische Einheiten:Fachbereich Mathematik
DDC-Sachgruppen:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Sammlungen:Schriften der AG Mathematische Bildverbarbeitung und Datenanalyse
Lizenz (Deutsch):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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