000165214 001__ 165214
000165214 005__ 20190316235102.0
000165214 0247_ $$2doi$$a10.1109/TSP.2011.2166394
000165214 022__ $$a1053-587X
000165214 02470 $$2ISI$$a000297115500017
000165214 037__ $$aARTICLE
000165214 245__ $$aA novel sampling theorem on the sphere
000165214 269__ $$a2011
000165214 260__ $$bInstitute of Electrical and Electronics Engineers$$c2011
000165214 336__ $$aJournal Articles
000165214 520__ $$aWe develop a novel sampling theorem on the sphere and corresponding fast algorithms by associating the sphere with the torus through a periodic extension. The fundamental property of any sampling theorem is the number of samples required to represent a band-limited signal. To represent exactly a signal on the sphere band-limited at L, all sampling theorems on the sphere require O(L2) samples. However, our sampling theorem requires less than half the number of samples of other equiangular sampling theorems on the sphere and an asymptotically identical, but smaller, number of samples than the Gauss-Legendre sampling theorem. The complexity of our algorithms scale as O(L3), however, the continual use of fast Fourier transforms reduces the constant prefactor associated with the asymptotic scaling considerably, resulting in algorithms that are fast. Furthermore, we do not require any precomputation and our algorithms apply to both scalar and spin functions on the sphere without any change in computational complexity or computation time. We make our implementation of these algorithms available publicly and perform numerical experiments demonstrating their speed and accuracy up to very high band-limits. Finally, we highlight the advantages of our sampling theorem in the context of potential applications, notably in the field of compressive sampling.
000165214 6531_ $$aHarmonic analysis
000165214 6531_ $$asampling methods
000165214 6531_ $$aspheres
000165214 6531_ $$aHarmonics
000165214 6531_ $$aTransforms
000165214 6531_ $$aRotation
000165214 6531_ $$aFfts
000165214 6531_ $$aComputation
000165214 6531_ $$aAlgorithm
000165214 6531_ $$aAnomalies
000165214 6531_ $$aFramework
000165214 6531_ $$a2-Sphere
000165214 6531_ $$aSurface
000165214 6531_ $$aLTS5
000165214 6531_ $$aCIBM-SP
000165214 700__ $$0242931$$g201873$$aMcEwen, Jason
000165214 700__ $$aWiaux, Yves$$g163268$$0240427
000165214 773__ $$j59$$tIEEE Transactions on Signal Processing$$q5876
000165214 8564_ $$uhttps://infoscience.epfl.ch/record/165214/files/fssht_v3.pdf$$zPreprint$$s627822$$yPreprint
000165214 909C0 $$xU10954$$0252394$$pLTS5
000165214 909C0 $$0252392$$pLTS2$$xU10380
000165214 909C0 $$xU12623$$0252477$$pCIBM
000165214 909CO $$qGLOBAL_SET$$pSB$$pSTI$$particle$$ooai:infoscience.tind.io:165214
000165214 917Z8 $$x201873
000165214 917Z8 $$x201873
000165214 917Z8 $$x201873
000165214 917Z8 $$x163268
000165214 917Z8 $$x163268
000165214 917Z8 $$x163268
000165214 917Z8 $$x163268
000165214 917Z8 $$x161735
000165214 937__ $$aEPFL-ARTICLE-165214
000165214 973__ $$rREVIEWED$$sPUBLISHED$$aEPFL
000165214 980__ $$aARTICLE