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Orthogonal quincunx wavelets with fractional orders
Conference proceeding

Orthogonal quincunx wavelets with fractional orders

Manuela Feilner, Mathews Jacob and Michael Unser
2001 INTERNATIONAL CONFERENCE ON IMAGE PROCESSING, VOL I, PROCEEDINGS, pp.606-609
2001
DOI: 10.1109/ICIP.2001.959118
url
http://infoscience.epfl.ch/record/211281View
Open Access

Abstract

We present a new family of 2D orthogonal wavelets which uses quincunx sampling. The orthogonal refinement filters have a simple analytical expression in the Fourier domain as a function of the order alpha, which may be non-integer. The wavelets have good isotropy properties. We can also prove that they yield wavelet bases of L-2 (R-2) for any alpha > 0. The wavelets are fractional in the sense that the approximation error at a given scale a decays like 0(a(alpha)); they also essentially behave like fractional derivative operators. To make our construction practical, we propose an FFT-based implementation that turns out to be surprisingly fast. In fact, our method is almost as efficient as the standard Mallat algorithm for separable wavelets.

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