Wavelets on the sphere: implementation and approximations

被引:81
作者
Antoine, JP [1 ]
Demanet, L
Jacques, L
Vandergheynst, P
机构
[1] Univ Catholique Louvain, Inst Theoret Phys, B-1348 Louvain, Belgium
[2] Ecole Polytech Fed Lausanne, Swiss Fed Inst Technol, Signal Proc Lab, CH-1015 Lausanne, Switzerland
关键词
continuous wavelet transform; 2-sphere; directional spherical wavelet; approximate identity;
D O I
10.1016/S1063-5203(02)00507-9
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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 g. This technique, which uses the FFT, is based on the invariance of g under discrete rotations around the z axis preserving the phi 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 L-p sense, for 1 less than or equal to p < infinity. 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. (C) 2002 Elsevier Science (USA). All rights reserved.
引用
收藏
页码:177 / 200
页数:24
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