TY - EJOUR
DO - 10.1016/S1063-5203(02)00507-9
AB - 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.
T1 - Wavelets on the sphere : Implementation and approximations
IS - 3
DA - 2002
AU - Antoine, J.
AU - Demanet, L.
AU - Jacques, L.
AU - Vandergheynst, P.
JF - Applied and Computational Harmonic Analysis
SP - 177-200
VL - 13
EP - 177-200
ID - 86884
KW - 2-sphere;
KW - Approximate
KW - Continuous
KW - Directional
KW - identity
KW - LTS2
KW - spherical
KW - transform;
KW - wavelet
KW - wavelet;
UR - http://infoscience.epfl.ch/record/86884/files/Antoine2002_22.pdf
ER -