Wavelet Bases on the Sphere Obtained by Radial Projection

Abstract

We present a method for constructing wavelet bases on the unit sphere S² of R³, using the radial projection and an inner product associated to a convex polyhedron having the origin inside. The main advantage of this method is the avoidance of singularities and distortions around poles, which occur in other approaches. Also, we can obtain spherical wavelets with small support, a fact which is crucial in working with large amounts of data, since the algorithms deal with sparse matrices.