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Integrodifferential Equations for Multiscale Wavelet Shrinkage: The Discrete Case

Stephan Didas ; Fraunhofer-Institut für Techno- und Wirtschaftsmathematik (ITWM)
Gabriele Steidl ; Faculty of Mathematics and Computer Science University of Mannheim, D-68131 Mannheim, Germany
Joachim Weickert ; Mathematical Image Analysis Group, Department of Mathematics and Computer Science Saarland University, D-66041 Saarbrücken, Germany

Puni tekst: engleski, pdf (4 MB) str. 1-17 preuzimanja: 296* citiraj
APA 6th Edition
Didas, S., Steidl, G. i Weickert, J. (2010). Integrodifferential Equations for Multiscale Wavelet Shrinkage: The Discrete Case. International journal of electrical and computer engineering systems, 1 (1), 1-17. Preuzeto s https://hrcak.srce.hr/63486
MLA 8th Edition
Didas, Stephan, et al. "Integrodifferential Equations for Multiscale Wavelet Shrinkage: The Discrete Case." International journal of electrical and computer engineering systems, vol. 1, br. 1, 2010, str. 1-17. https://hrcak.srce.hr/63486. Citirano 03.06.2020.
Chicago 17th Edition
Didas, Stephan, Gabriele Steidl i Joachim Weickert. "Integrodifferential Equations for Multiscale Wavelet Shrinkage: The Discrete Case." International journal of electrical and computer engineering systems 1, br. 1 (2010): 1-17. https://hrcak.srce.hr/63486
Harvard
Didas, S., Steidl, G., i Weickert, J. (2010). 'Integrodifferential Equations for Multiscale Wavelet Shrinkage: The Discrete Case', International journal of electrical and computer engineering systems, 1(1), str. 1-17. Preuzeto s: https://hrcak.srce.hr/63486 (Datum pristupa: 03.06.2020.)
Vancouver
Didas S, Steidl G, Weickert J. Integrodifferential Equations for Multiscale Wavelet Shrinkage: The Discrete Case. International journal of electrical and computer engineering systems [Internet]. 2010 [pristupljeno 03.06.2020.];1(1):1-17. Dostupno na: https://hrcak.srce.hr/63486
IEEE
S. Didas, G. Steidl i J. Weickert, "Integrodifferential Equations for Multiscale Wavelet Shrinkage: The Discrete Case", International journal of electrical and computer engineering systems, vol.1, br. 1, str. 1-17, 2010. [Online]. Dostupno na: https://hrcak.srce.hr/63486. [Citirano: 03.06.2020.]

Sažetak
We investigate the relations between wavelet shrinkage and integrodifferential equations for image simplification
and denoising in the discrete case. Previous investigations in the continuous one-dimensional setting are transferred to the discrete
multidimentional case. The key observation is that a wavelet transform can be understood as a derivative operator in connection
with convolution with a smoothing kernel. In this paper, we extend these ideas to a practically relevant discrete formulation with
both orthogonal and biorthogonal wavelets. In the discrete setting, the behaviour of smoothing kernels for different scales is more
complicated than in the continuous setting and of special interest for the understanding of the filters. With the help of tensor product
wavelets and special shrinkage rules, the approach is extended to more than one spatial dimension. The results of wavelet shrinkage
and related integrodifferential equations are compared in terms of quality by numerical experiments.

Ključne riječi
Image denoising; wavelet shrinkage; integrodifferential equations

Hrčak ID: 63486

URI
https://hrcak.srce.hr/63486

Posjeta: 491 *