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The two-dimensional continuous wavelet transform (CWT), derived from a square in-tegrable representation of the similitude group of IR 2 , is characterized by a rotation parameter, in addition to the usual translations and dilations. This enables it to detect edges and directions in images, provided a directional wavelet is used. First we review the general… (More)

Many techniques have been devised these last ten years to add an appropriate direc-tionality concept in decompositions of images from the specific transformations of a small set of atomic functions. Let us mention for instance works on directional wavelets, steer-able filters, dual-tree wavelet transform, curvelets, wave atoms, ridgelet packets,. .. In… (More)

- J D Mcewen, P Vielva, Y Wiaux, R B Barreiro, L Cayón, M P Hobson +4 others
- 2008

The cosmic microwave background (CMB) is a relic radiation of the Big Bang and as such it contains a wealth of cosmological information. Statistical analyses of the CMB, in conjunction with other cosmological observables, represent some of the most powerful techniques available to cosmologists for placing strong constraints on the cosmological parameters… (More)

- Y Wiaux, J D Mcewen, P Vielva, Jean-Pierre Antoine
- 2008

In the general context of complex data processing, this paper reviews a recent practical approach to the continuous wavelet formalism on the sphere. This formalism notably yields a correspondence principle which relates wavelets on the plane and on the sphere. Two fast algorithms are also presented for the analysis of signals on the sphere with steerable… (More)

Received (Day Month Year) Revised (Day Month Year) Communicated by (xxxxxxxxxx) We review the coherent state or group-theoretical construction of the continuous wavelet transform (CWT) on the two-sphere. Next we describe the construction of a CWT on the upper sheet of a two-sheeted hyperboloid, emphasizing the similarities between the two cases.. Finally we… (More)

In this paper we exploit the Continuous Wavelet Transform (CWT) on the sphere introduced in [1, 2] to build the associated Discrete Wavelet Frames. We first explore half-continuous frames, i.e, frames where the position remains a continuous variable, and then move on to a fully discrete theory. This forces us to introduce the notion of controlled frames… (More)