Please use this identifier to cite or link to this item: doi:10.22028/D291-26247
Title: On the equivalence of soft wavelet shrinkage, total variation diffusion, total variation regularization, and SIDEs
Author(s): Steidl, Gabriele
Weickert, Joachim
Brox, Thomas
Mrázek, Pavel
Welk, Martin
Language: English
Year of Publication: 2003
DDC notations: 510 Mathematics
Publikation type: Other
Abstract: 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 to this record: urn:nbn:de:bsz:291-scidok-44404
Series name: Preprint / Fachrichtung Mathematik, Universität des Saarlandes
Series volume: 94
Date of registration: 4-Jan-2012
Faculty: MI - Fakultät für Mathematik und Informatik
Department: MI - Mathematik
Collections:SciDok - Der Wissenschaftsserver der Universität des Saarlandes

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