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A geometric construction of multivariate sinc functions.

Authors
  • Ye, Wenxing
  • Entezari, Alireza
Type
Published Article
Journal
IEEE Transactions on Image Processing
Publisher
Institute of Electrical and Electronics Engineers
Publication Date
Jun 01, 2012
Volume
21
Issue
6
Pages
2969–2979
Identifiers
DOI: 10.1109/TIP.2011.2162421
PMID: 21775264
Source
Medline
License
Unknown

Abstract

We present a geometric framework for explicit derivation of multivariate sampling functions (sinc) on multidimensional lattices. The approach leads to a generalization of the link between sinc functions and the Lagrange interpolation in the multivariate setting. Our geometric approach also provides a frequency partition of the spectrum that leads to a nonseparable extension of the 1-D Shannon (sinc) wavelets to the multivariate setting. Moreover, we propose a generalization of the Lanczos window function that provides a practical and unbiased approach for signal reconstruction on sampling lattices. While this framework is general for lattices of any dimension, we specifically characterize all 2-D and 3-D lattices and show the detailed derivations for 2-D hexagonal body-centered cubic (BCC) and face-centered cubic (FCC) lattices. Both visual and numerical comparisons validate the theoretical expectations about superiority of the BCC and FCC lattices over the commonly used Cartesian lattice.

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