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Abstract: A fast algorithm is developed for the directional correlation of scalar band-limited signals and band-limited steerable filters on the sphere. The asymptotic complexity associated to it through simple quadrature is of order \(O(L^5)\), where \(2L\) stands for the square-root of the number of sampling points on the sphere, also setting a band limit L for the signals and filters considered.

Abstract: Wavelets on the sphere are reintroduced and further developed independently of the original group theoretic formalism, in an equivalent, but more straightforward approach. These developments are motivated by the interest of the scale-space analysis of the cosmic microwave background (CMB) anisotropies on the sky.

Abstract: In this paper we exploit the continuous wavelet transform (CWT) on the two-dimensional sphere S-2, introduced previously by two of us, to build associated discrete wavelet frames. We first explore half-continuous frames, i.

Abstract: The extreme ultraviolet imaging telescope (EIT) of SOHO offers a unique record of the solar atmosphere for its sampling in temperature, field of view, resolution, duration, and cadence. To investigate globally and locally its topology and evolution during the solar cycle, we consider a multi-scale approach, and more precisely we use the wavelet spectrum.

Abstract: The 2-D continuous wavelet transform has been applied to a number of problems in astrophysics. We survey quickly some of these, then focus on two new applications. The first one is the automatic detection and analysis of special objects from the solar corona in the data taken by the EIT instrument aboard the SoHO satellite.

Abstract: We continue the analysis of the continuous wavelet transform on the 2-sphere, introduced in a previous paper. After a brief review of the transform, we define and discuss the notion of directional spherical wavelet, i.

Abstract: We determine all (statistical) rotation-dilation symmetries of a planar quasiperiodic tiling with fivefold symmetry, with a two-dimensional continuous wavelet transform, using a modified Cauchy wavelet and the scale-angle measure. The tiling is constructed via an affine extension of the Coxeter group H-2 and its statistical symmetries were unknown.