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Digital Implementation of Ridgelet Packets A.G. Flesia, H. Hel-Or

Summary: Digital Implementation of Ridgelet Packets
A.G. Flesia, H. Hel-Or
A. Averbuch, E.J. Cand`es
R.R. Coifman, D.L. Donoho
Abstract. The Ridgelet Packets library provides a large family of or-
thonormal bases for functions f(x, y) in L2
(dxdy) which includes or-
thonormal ridgelets as well as bases deriving from tilings reminiscent from
the theory of wavelets and the study of oscillatory Fourier integrals. An
intuitively appealing feature: many of these bases have elements whose
envelope is strongly aligned along specified `ridges' while displaying oscil-
latory components across the main `ridge'.
There are two approaches to constructing ridgelet packets; the most
direct is a frequency-domain viewpoint. We take a recursive dyadic par-
tition of the polar Fourier domain into a collection of rectangular tiles
of various widths and lengths. Focusing attention on each tile in turn,
we take a tensor basis, using windowed sinusoids in times windowed
sinusoids in r. There is also a Radon-domain approach to constructing
ridgelet packets, which involves applying the Radon isometry and then,
in the Radon plane, using wavelets in times wavelet packets in t, with


Source: Averbuch, Amir - School of Computer Science, Tel Aviv University
Candes, Emmanuel J. - Department of Statistics, Stanford University
Donoho, David - Department of Statistics, Stanford University


Collections: Computer Technologies and Information Sciences; Engineering; Mathematics