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Image Processing Using a Wavelet Algorithm for Nonlinear Diffusion

  • The edge enhancement property of a nonlinear diffusion equation with a suitable expression for the diffusivity is an important feature for image processing. We present an algorithm to solve this equation in a wavelet basis and discuss its one dimensional version in some detail. Sample calculations demonstrate principle effects and treat in particular the case of highly noise perturbed signals. The results are discussed with respect to performance, efficiency, choice of parameters and are illustrated by a large number of figures. Finally, a comparison with a Fourier method and a finite volume method is performed.

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Author:Joachim Weickert, Jochen Fröhlich
URN (permanent link):urn:nbn:de:hbz:386-kluedo-5019
Serie (Series number):Berichte der Arbeitsgruppe Technomathematik (AGTM Report) (104)
Document Type:Preprint
Language of publication:English
Year of Completion:1994
Year of Publication:1994
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):1994/01/01
Tag:Perona-Malik filter; finite volume methods; pseudospectral methods; wavelets
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
MSC-Classification (mathematics):35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Qxx Equations of mathematical physics and other areas of application [See also 35J05, 35J10, 35K05, 35L05] / 35Q80 PDEs in connection with classical thermodynamics and heat transfer
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011