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 hdl:20.500.11880/26303 http://dx.doi.org/10.22028/D291-26247 |
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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preprint_94_03.pdf | 479,86 kB | Adobe PDF | View/Open |
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