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A Geometric Construction of Multivariate Sinc Functions | IEEE Journals & Magazine | IEEE Xplore

A Geometric Construction of Multivariate Sinc Functions


Abstract:

We present a geometric framework for explicit derivation of multivariate sampling functions (sinc) on multidimensional lattices. The approach leads to a generalization of...Show More

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.
Published in: IEEE Transactions on Image Processing ( Volume: 21, Issue: 6, June 2012)
Page(s): 2969 - 2979
Date of Publication: 18 July 2011

ISSN Information:

PubMed ID: 21775264

References

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