Sampling and approximation of bandlimited volumetric data

Rami Katz, Yoel Shkolnisky

Research output: Contribution to journalLetterpeer-review

Abstract

We present an approximation scheme for functions in three dimensions, that requires only their samples on the Cartesian grid, under the assumption that the functions are sufficiently concentrated in both space and frequency. The scheme is based on expanding the given function in the basis of generalized prolate spheroidal wavefunctions, with the expansion coefficients given by weighted dot products between the samples of the function and the samples of the basis functions. As numerical implementations require all expansions to be finite, we present a truncation rule for the expansions. Finally, we derive a bound on the overall approximation error in terms of the assumed space/frequency concentration.

Original languageEnglish
Pages (from-to)235-247
Number of pages13
JournalApplied and Computational Harmonic Analysis
Volume47
Issue number1
DOIs
StatePublished - Jul 2019

Keywords

  • Bandlimited approximation
  • Bandlimited functions
  • Prolate spheroidal wave functions

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