000086884 001__ 86884
000086884 005__ 20190316233743.0
000086884 0247_ $$2doi$$a10.1016/S1063-5203(02)00507-9
000086884 02470 $$2DAR$$a3474
000086884 02470 $$2ISI$$a000179980300001
000086884 037__ $$aARTICLE
000086884 245__ $$aWavelets on the sphere : Implementation and approximations
000086884 269__ $$a2002
000086884 260__ $$c2002
000086884 336__ $$aJournal Articles
000086884 520__ $$aWe 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.
000086884 6531_ $$a2-sphere;
000086884 6531_ $$aApproximate
000086884 6531_ $$aContinuous
000086884 6531_ $$aDirectional
000086884 6531_ $$aidentity
000086884 6531_ $$aLTS2
000086884 6531_ $$aspherical
000086884 6531_ $$atransform;
000086884 6531_ $$awavelet
000086884 6531_ $$awavelet;
000086884 700__ $$aAntoine, J.
000086884 700__ $$aDemanet, L.
000086884 700__ $$0243987$$g182131$$aJacques, L.
000086884 700__ $$aVandergheynst, P.$$g120906$$0240428
000086884 773__ $$j13$$tApplied and Computational Harmonic Analysis$$k3$$q177-200
000086884 8564_ $$uhttps://infoscience.epfl.ch/record/86884/files/Antoine2002_22.pdf$$zn/a$$s459529
000086884 909C0 $$xU10380$$0252392$$pLTS2
000086884 909CO $$qGLOBAL_SET$$pSTI$$ooai:infoscience.tind.io:86884$$particle
000086884 937__ $$aEPFL-ARTICLE-86884
000086884 970__ $$aAntoine2002_22/LTS
000086884 973__ $$rREVIEWED$$sPUBLISHED$$aEPFL
000086884 980__ $$aARTICLE