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. © Springer-Verlag Berlin Heidelberg 2006.
CITATION STYLE
Welk, M., Weickert, J., & Steidl, G. (2006). From tensor-driven diffusion to anisotropic wavelet shrinkage. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 3951 LNCS, pp. 391–403). https://doi.org/10.1007/11744023_31
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