A partial differential equation for continuous nonlinear shrinkage filtering and its application for analyzing MMG data

Kristian Bredies; Dirk A. Lorenz; Peter Maass; Gerd Teschke

doi:10.1117/12.515945

27 February 2004 A partial differential equation for continuous nonlinear shrinkage filtering and its application for analyzing MMG data

Kristian Bredies, Dirk A. Lorenz, Peter Maass, Gerd Teschke

Author Affiliations +

Proceedings Volume 5266, Wavelet Applications in Industrial Processing; (2004) https://doi.org/10.1117/12.515945
Event: Photonics Technologies for Robotics, Automation, and Manufacturing, 2003, Providence, RI, United States

Abstract

The starting point for this paper is the well known equivalence between convolution filtering with a rescaled Gaussian and the solution of the heat equation. In the first sections we analyze the equivalence between multiscale convolution filtering, linear smoothing methods based on continuous wavelet transforms and the solutions of linear diffusion equations. I.e. we determine a wavelet ψ, resp. a convolution filter φ, which is associated with a given linear diffusion equation u_t = Pu and vice versa. This approach has an extension to non-linear smoothing techniques. The main result of this paper is the derivation of a differential equation, whose solution is equivalent to non-linear multi-scale smoothing based on soft shrinkage methods applied to Fourier or continuous wavelet transforms.

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Kristian Bredies, Dirk A. Lorenz, Peter Maass, and Gerd Teschke "A partial differential equation for continuous nonlinear shrinkage filtering and its application for analyzing MMG data", Proc. SPIE 5266, Wavelet Applications in Industrial Processing, (27 February 2004); https://doi.org/10.1117/12.515945

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