Antoine, J.
Demanet, L.
Jacques, L.
Vandergheynst, P.
Wavelets on the sphere : Implementation and approximations
Applied and Computational Harmonic Analysis
Applied and Computational Harmonic Analysis
Applied and Computational Harmonic Analysis
Applied and Computational Harmonic Analysis
13
3
2-sphere;
Approximate
Continuous
Directional
identity
LTS2
spherical
transform;
wavelet
wavelet;
2002
2002
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.
Applied and Computational Harmonic Analysis
Journal Articles
10.1016/S1063-5203(02)00507-9