TY - EJOUR
DO - 10.1109/TSP.2011.2166394
AB - We 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.
T1 - A novel sampling theorem on the sphere
DA - 2011
AU - McEwen, Jason
AU - Wiaux, Yves
JF - IEEE Transactions on Signal Processing
SP - 5876
VL - 59
EP - 5876
PB - Institute of Electrical and Electronics Engineers
ID - 165214
KW - Harmonic analysis
KW - sampling methods
KW - spheres
KW - Harmonics
KW - Transforms
KW - Rotation
KW - Ffts
KW - Computation
KW - Algorithm
KW - Anomalies
KW - Framework
KW - 2-Sphere
KW - Surface
KW - LTS5
KW - CIBM-SP
SN - 1053-587X
UR - http://infoscience.epfl.ch/record/165214/files/fssht_v3.pdf
ER -