Please use this identifier to cite or link to this item:
doi:10.22028/D291-26249
Title: | Diffusion-inspired shrinkage functions and stability results for wavelet denoising |
Author(s): | Mrázek, Pavel Weickert, Joachim Steidl, Gabriele |
Language: | English |
Year of Publication: | 2003 |
Free key words: | image denoising wavelet shrinkage diffusion filtering |
DDC notations: | 510 Mathematics |
Publikation type: | Other |
Abstract: | We study the connections between discrete 1-D schemes for non-linear diffusion and shift-invariant Haar wavelet shrinkage. We show that one step of a (stabilised) explicit discretisation of nonlinear diffusion can be expressed in terms of wavelet shrinkage on a single spatial level. This equivalence allows a fruitful exchange of ideas between the two fields. In this paper we derive new wavelet shrinkage functions from existing diffusivity functions, and identify some previously used shrinkage functions as corresponding to well known diffusivities. We demonstrate experimentally that some of the diffusion-inspired shrinkage functions are among the best for translation-invariant multiscale wavelet denoising. Moreover, by transferring stability notions from diffusion filtering to wavelet shrinkage, we derive conditions on the shrinkage function that ensure that shift invariant single-level Haar wavelet shrinkage is maximum-minimum stable, monotonicity preserving, and variation diminishing. |
Link to this record: | urn:nbn:de:bsz:291-scidok-44427 hdl:20.500.11880/26305 http://dx.doi.org/10.22028/D291-26249 |
Series name: | Preprint / Fachrichtung Mathematik, Universität des Saarlandes |
Series volume: | 96 |
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_96_03.pdf | 832,43 kB | Adobe PDF | View/Open |
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