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From Tensor-Driven Diffusion to Anisotropic Wavelet Shrinkage

  • Martin Welk
  • Joachim Weickert
  • Gabriele Steidl
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3951)

Abstract

Diffusion processes driven by anisotropic diffusion tensors are known to be well-suited for structure-preserving denoising. However, numerical implementations based on finite differences introduce unwanted blurring artifacts that deteriorate these favourable filtering properties. In this paper we introduce a novel discretisation of a fairly general class of anisotropic diffusion processes on a 2-D grid. It leads to a locally semi-analytic scheme (LSAS) that is absolutely stable, simple to implement and offers an outstanding sharpness of filtered images. By showing that this scheme can be translated into a 2-D Haar wavelet shrinkage procedure, we establish a connection between tensor-driven diffusion and anisotropic wavelet shrinkage for the first time. This result leads to coupled shrinkage rules that allow to perform highly anisotropic filtering even with the simplest wavelets.

Keywords

Diffusion Tensor Anisotropic Diffusion Structure Tensor Rotation Invariance Haar Wavelet 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Martin Welk
    • 1
  • Joachim Weickert
    • 1
  • Gabriele Steidl
    • 2
  1. 1.Mathematical Image Analysis Group, Faculty of Mathematics and Computer ScienceSaarland UniversitySaarbrückenGermany
  2. 2.Faculty of Mathematics and Computer ScienceUniversity of MannheimMannheimGermany

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