Relations between Soft Wavelet Shrinkage and Total Variation Denoising

Authors:
Gabriele Steidl;Joachim Weickert
Affiliations:
-;-
Venue:
Proceedings of the 24th DAGM Symposium on Pattern Recognition
Year:
2002

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Abstract

Soft wavelet shrinkage and total variation (TV) denoising are two frequently used techniques for denoising signals and images, while preserving their discontinuities. In this paper we show that - under specific circumstances - both methods are equivalent. First we prove that 1-D Haar wavelet shrinkage on a single scale is equivalent to a single step of TV diffusion or regularisation of two-pixel pairs. Afterwards we show that wavelet shrinkage on multiple scales can be regarded as a single step diffusion filtering or regularisation of the Laplacian pyramid of the signal.