@inproceedings{f9eeaa334f4e40cfb8d7a4117109ce71,
title = "Finding optimal integral sampling lattices for a given frequency support in multidimensions",
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.",
keywords = "Critical sampling, Densest sampling, Maximal decimation, Packing, Tiling",
author = "Lu, {Yue M.} and Do, {Minh N.}",
year = "2007",
doi = "10.1109/ICIP.2007.4379118",
language = "English (US)",
isbn = "1424414377",
series = "Proceedings - International Conference on Image Processing, ICIP",
pages = "II165--II168",
booktitle = "2007 IEEE International Conference on Image Processing, ICIP 2007 Proceedings",
note = "14th IEEE International Conference on Image Processing, ICIP 2007 ; Conference date: 16-09-2007 Through 19-09-2007",
}