Original scientific paper

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

Abstract

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.

Keywords

Image denoising; wavelet shrinkage; integrodifferential equations

Hrčak ID:

63486

URI

https://hrcak.srce.hr/63486

Publication date:

20.6.2010.

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