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Titel: On the equivalence of soft wavelet shrinkage, total variation diffusion, total variation regularization, and SIDEs
Verfasser: Steidl, Gabriele
Weickert, Joachim
Brox, Thomas
Mrázek, Pavel
Welk, Martin
Sprache: Englisch
Erscheinungsjahr: 2003
DDC-Sachgruppe: 510 Mathematik
Dokumentart : Preprint (Vorabdruck)
Kurzfassung: Soft wavelet shrinkage, total variation (TV) diffusion, total variation regularization, and a dynamical system called SIDEs are four useful techniques for discontinuity preserving denoising of signals and images. In this paper we investigate under which circumstances these methods are equivalent in the 1-D case. First we prove that Haar wavelet shrinkage on a single scale is equivalent to a single step of space-discrete TV diffusion or regularization of two-pixel pairs. In the translationally invariant case we show that applying cycle spinning to Haar wavelet shrinkage on a single scale can be regarded as an absolutely stable explicit discretization of TV diffusion. We prove that space-discrete TV difusion and TV regularization are identical, and that they are also equivalent to the SIDEs system when a specific force function is chosen. Afterwards we show that wavelet shrinkage on multiple scales can be regarded as a single step diffusion filtering or regularization of the Laplacian pyramid of the signal. We analyse possibilities to avoid Gibbs-like artifacts for multiscale Haar wavelet shrinkage by scaling the thesholds. Finally we present experiments where hybrid methods are designed that combine the advantages of wavelets and PDE / variational approaches. These methods are based on iterated shift-invariant wavelet shrinkage at multiple scales with scaled thresholds.
Link zu diesem Datensatz: urn:nbn:de:bsz:291-scidok-44404
hdl:20.500.11880/26303
http://dx.doi.org/10.22028/D291-26247
Schriftenreihe: Preprint / Fachrichtung Mathematik, Universität des Saarlandes
Band: 94
SciDok-Publikation: 4-Jan-2012
Fakultät: Fakultät 6 - Naturwissenschaftlich-Technische Fakultät I
Fachrichtung: MI - Mathematik
Fakultät / Institution:MI - Fakultät für Mathematik und Informatik

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