@article{Antoine:86884,
title = {Wavelets on the sphere : Implementation and approximations},
author = {Antoine, J. and Demanet, L. and Jacques, L. and Vandergheynst, P.},
journal = {Applied and Computational Harmonic Analysis},
number = {3},
volume = {13},
pages = {177-200},
year = {2002},
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.e., wavelets on the sphere that are sensitive to directions. Then we present a calculation method for data given on a regular spherical grid . This technique, which uses the FFT, is based on the invariance of under discrete rotations around the z axis preserving the sampling. Next, a numerical criterion is given for controlling the scale interval where the spherical wavelet transform makes sense, and examples are given, both academic and realistic. In a second part, we establish conditions under which the reconstruction formula holds in strong Lp sense, for 1p<. This opens the door to techniques for approximating functions on the sphere, by use of an approximate identity, obtained by a suitable dilation of the mother wavelet.},
url = {http://infoscience.epfl.ch/record/86884},
doi = {10.1016/S1063-5203(02)00507-9},
}