Please use this identifier to cite or link to this item: doi:10.22028/D291-26497
Title: Integrodifferential equations for multiscale wavelet shrinkage : the discrete case
Author(s): Didas, Stephan
Steidl, Gabriele
Weickert, Joachim
Language: English
Year of Publication: 2008
Free key words: image denoising
wavelet shrinkage
integrodifferential equations
DDC notations: 510 Mathematics
Publikation type: Other
Abstract: We investigate the relations between wavelet shrinkage and integrodifferential equations for image simplification and denoising in the discrete case. Previous investigations in the continuous one-dimensional setting are transferred to the discrete multidimentional case. The key observation is that a wavelet transform can be understood as derivative operator in connection with convolution with a smoothing kernel. In this paper, we extend these ideas to the practically relevant discrete formulation with both orthogonal and biorthogonal wavelets. In the discrete setting, the behaviour of the smoothing kernels for different scales is more complicated than in the continuous setting and of special interest for the understanding of the filters. With the help of tensor product wavelets and special shrinkage rules, the approach is extended to more than one spatial dimension. The results of wavelet shrinkage and related integrodifferential equations are compared in terms of quality by numerical experiments.
Link to this record: urn:nbn:de:bsz:291-scidok-47447
Series name: Preprint / Fachrichtung Mathematik, Universität des Saarlandes
Series volume: 214
Date of registration: 5-Jun-2013
Faculty: MI - Fakultät für Mathematik und Informatik
Department: MI - Mathematik
Collections:SciDok - Der Wissenschaftsserver der Universität des Saarlandes

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