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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)
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)
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)