Abstract
We study the connections between discrete one-dimensional schemes for nonlinear diffusion and shift-invariant Haar wavelet shrinkage. We show that one step of (stabilised) explicit discretisation of nonlinear diffusion can be expressed in terms of wavelet shrinkage on a single spatial level. This equivalence allows a fruitful exchange of ideas between the two fields. In this paper we derive new wavelet shrinkage functions from existing diffusivity functions, and identify some previously used shrinkage functions as corresponding to well known diffusivities. We demonstrate experimentally that some of the diffusion-inspired shrinkage functions are among the best for translation-invariant multiscale wavelet shrinkage denoising.
This joint research was supported by the project Relations between nonlinear filters in digital image processing within the DFG-Schwerpunktprogramm 1114: Mathematical methods for time series analysis and digital image processing. This is gratefully acknowledged.
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Mrázek, P., Weickert, J., Steidl, G. (2003). Correspondences between Wavelet Shrinkage and Nonlinear Diffusion. In: Griffin, L.D., Lillholm, M. (eds) Scale Space Methods in Computer Vision. Scale-Space 2003. Lecture Notes in Computer Science, vol 2695. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44935-3_8
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DOI: https://doi.org/10.1007/3-540-44935-3_8
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