title: Interpreting translation-invariant wavelet shrinkage as a new image smoothing scale space.
abstract: 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 B(1) (1)(L(1)(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.
authors.affiliation: CEREMADE (CNRS UMR 7534), Université de Paris-Dauphine, 75775 Paris CEDEX 16, France. Antonin.Chambolle@ceremade.dauphine.fr
authors.forename: A
authors.initials: A
authors.lastname: Chambolle
authors.forename: B J
authors.initials: BJ
authors.lastname: Lucier