Removing multiplicative noise by Douglas-Rachford splitting methods

Steidl, Gabriele ; Teuber, Tanja

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URN: urn:nbn:de:bsz:180-madoc-22714
Document Type: Working paper
Year of publication: 2009
The title of a journal, publication series: Preprints / Department of Mathematics
Volume: 08-02
Place of publication: Mannheim
Publication language: English
Institution: School of Business Informatics and Mathematics > Sonstige - Fakultät für Mathematik und Informatik
MADOC publication series: Veröffentlichungen der Fakultät für Mathematik und Informatik > Institut für Mathematik > Preprints
Subject: 510 Mathematics
Subject headings (SWD): Bildverarbeitung , Rauschunterdrückung
Keywords (English): Denoising , multiplicative noise , Douglas-Rachford splitting , I-divergence , total variation , nonlocal means
Abstract: Multiplicative noise appears in various image processing applications, e.g., in synthetic aperture radar (SAR), ultrasound imaging or in connection with blur in electronic microscopy, single particle emission computed tomography (SPECT) and positron emission tomography (PET). In this paper, we consider a variational restoration model consisting of the I-divergence as data fitting term and the total variation semi-norm or nonlocal means as regularizer. Although the I-divergence is the typical data fitting term when dealing with Poisson noise we substantiate why it is also appropriate for cleaning Gamma noise. We propose to compute the minimizer of our restoration functional by applying Douglas-Rachford splitting techniques, resp. alternating split Bregman methods, combined with an efficient algorithm to solve the involved nonlinear systems of equations. We prove the Q-linear convergence of the latter algorithm. Finally, we demonstrate the performance of our whole scheme by numerical examples. It appears that the nonlocal means approach leads to very good qualitative results.
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