Discrete multiscale wavelet shrinkage and integrodifferential equations

S. Didas; G. Steidl; J. Weickert

doi:10.1117/12.782472

25 April 2008 Discrete multiscale wavelet shrinkage and integrodifferential equations

S. Didas, G. Steidl, J. Weickert

Author Affiliations +

Proceedings Volume 7000, Optical and Digital Image Processing; 70000S (2008) https://doi.org/10.1117/12.782472
Event: SPIE Photonics Europe, 2008, Strasbourg, France

Abstract

We investigate the relation between discrete wavelet shrinkage and integrodifferential equations in the context of simplification and denoising of one-dimensional signals. In the continuous setting, strong connections between these two approaches were discovered in 6 (see references). The key observation is that the wavelet transform can be understood as derivative operator after the convolution with a smoothing kernel. In this paper, we extend these ideas to the practically relevant discrete setting with both orthogonal and biorthogonal wavelets. In the discrete case, the behaviour of the smoothing kernels for different scales requires additional investigation. The results of discrete multiscale wavelet shrinkage and related discrete versions of integrodifferential equations are compared with respect to their denoising quality by numerical experiments.

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S. Didas, G. Steidl, and J. Weickert "Discrete multiscale wavelet shrinkage and integrodifferential equations", Proc. SPIE 7000, Optical and Digital Image Processing, 70000S (25 April 2008); https://doi.org/10.1117/12.782472

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