86884
20190316233743.0
10.1016/S1063-5203(02)00507-9
doi
3474
DAR
000179980300001
ISI
ARTICLE
Wavelets on the sphere : Implementation and approximations
2002
2002
Journal Articles
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.
2-sphere;
Approximate
Continuous
Directional
identity
LTS2
spherical
transform;
wavelet
wavelet;
Antoine, J.
Demanet, L.
Jacques, L.
182131
243987
Vandergheynst, P.
120906
240428
177-200
3
Applied and Computational Harmonic Analysis
13
459529
n/a
http://infoscience.epfl.ch/record/86884/files/Antoine2002_22.pdf
LTS2
252392
U10380
oai:infoscience.tind.io:86884
article
STI
GLOBAL_SET
EPFL-ARTICLE-86884
Antoine2002_22/LTS
EPFL
PUBLISHED
REVIEWED
ARTICLE