Generalized sampling expansion for functions on the sphere

Ilan Ben Hagai, Filippo Maria Fazi, Boaz Rafaely

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

Functions on the sphere appear in several applications, including geodesics, imaging and acoustics. Sampling of these functions may result in aliasing if the sampling condition is not met. The generalized sampling expansion introduced by Papoulis enables the reconstruction of a band-limited function sampled at a frequency lower than the Nyquist frequency using the outputs of several linear time-invariant systems. This paper formulates the generalized sampling expansion for functions on the sphere using spherical harmonics decomposition, facilitating sub-Nyquit sampling without aliasing error. An analysis of linear systems on the sphere and the aliasing phenomenon in the spherical harmonics domain is presented. Examples demonstrating the performance of the method and its limitations are studied.

Original languageEnglish
Article number6252066
Pages (from-to)5870-5879
Number of pages10
JournalIEEE Transactions on Signal Processing
Volume60
Issue number11
DOIs
StatePublished - 22 Oct 2012

Keywords

  • Aliasing
  • generalized sampling expansion
  • spherical harmonics

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