Finding optimal integral sampling lattices for a given frequency support in multidimensions

Yue M. Lu, Minh N. Do

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The search for alias-free sampling lattices for a given frequency support, in particular those lattices achieving minimum sampling densities, is a fundamental issue in various applications of signal and image processing. In this paper, we propose an efficient computational procedure to find all alias-free integral sampling lattices for a given frequency support with minimum sampling density. Central to this algorithm is a novel condition linking the alias-free sampling with the Fourier transform of the indicator function defined on the frequency support. We study the computation of these Fourier transforms based on the divergence theorem, and propose a simple closed-form formula for a fairly general class of support regions consisting of arbitrary N-dimensional polytopes, with polygons in 2-D and polyhedra in 3-D as special cases. The proposed algorithm can be useful in a variety of applications involving the design of efficient acquisition schemes for multidimensional bandlimited signals.

Original languageEnglish (US)
Title of host publication2007 IEEE International Conference on Image Processing, ICIP 2007 Proceedings
PagesII165-II168
DOIs
StatePublished - Dec 1 2007
Event14th IEEE International Conference on Image Processing, ICIP 2007 - San Antonio, TX, United States
Duration: Sep 16 2007Sep 19 2007

Publication series

NameProceedings - International Conference on Image Processing, ICIP
Volume2
ISSN (Print)1522-4880

Other

Other14th IEEE International Conference on Image Processing, ICIP 2007
CountryUnited States
CitySan Antonio, TX
Period9/16/079/19/07

Keywords

  • Critical sampling
  • Densest sampling
  • Maximal decimation
  • Packing
  • Tiling

ASJC Scopus subject areas

  • Engineering(all)

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  • Cite this

    Lu, Y. M., & Do, M. N. (2007). Finding optimal integral sampling lattices for a given frequency support in multidimensions. In 2007 IEEE International Conference on Image Processing, ICIP 2007 Proceedings (pp. II165-II168). [4379118] (Proceedings - International Conference on Image Processing, ICIP; Vol. 2). https://doi.org/10.1109/ICIP.2007.4379118