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Interpreting translation-invariant wavelet shrinkage as a new image smoothing scale space

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2 Author(s)
Chambolle, A. ; CNRS, Univ. de Paris, Dauphine, France ; Lucier, B.J.

Coifman and Donoho (1995) suggested translation-invariant wavelet shrinkage as a way to remove noise from images. Basically, their technique applies wavelet shrinkage to a two-dimensional (2-D) version of the semi-discrete wavelet representation of Mallat and Zhong (1992), Coifman and Donoho also showed how the method could be implemented in O(Nlog N) operations, where there are N pixels. In this paper, we provide a mathematical framework for iterated translation-invariant wavelet shrinkage, and show, using a theorem of Kato and Masuda (1978), that with orthogonal wavelets it is equivalent to gradient descent in L 2(I) along the semi-norm for the Besov space B1 1(L1(I)), which, in turn, can be interpreted as a new nonlinear wavelet-based image smoothing scale space. Unlike many other scale spaces, the characterization is not in terms of a nonlinear partial differential equation

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Image Processing, IEEE Transactions on  (Volume:10 ,  Issue: 7 )