Locally supported orthogonal wavelet bases on the sphere via stereographic projection
given at strobl07 (21.06.07 16:15)
The stereographic projection determines a bijection between the two-sphere, minus the North Pole, and the tangent plane at the South Pole. This correspondence induces a unitary map between the corresponding $L^2$ spaces. As it is known, this map in turn leads to an equivalence between the continuous wavelet transform formalisms on the plane and on the sphere. More precisely, any plane wavelet may be lifted, by inverse stereographic projection, to a wavelet on the sphere. In this work, we apply this procedure to orthogonal bases
of locally supported wavelets in the plane and get similar bases on the sphere. Numerical examples are given and compared with the results obtained by other types of spherical wavelet frames.