Sampling 2-D Signals on a Union of Lattices that Intersect on a Lattice

This paper presents new sufficient conditions under which a field (or image) can be perfectly reconstructed from its samples on a union of two lattices that share a common coarse lattice. In particular, if samples taken on the first lattice can be used to reconstruct a field bandlimited to some spectral support region, and likewise samples taken on the second lattice can reconstruct a field bandlimited to another spectral support region, then under certain conditions, a field bandlimited to the union of these two spectral regions can be reconstructed from its samples on the union of the two respective lattices. These results generalize a previous perfect reconstruction theorem for Manhattan sampling, where data is taken at high density along evenly spaced rows and columns of a rectangular grid. Additionally, a sufficient condition is given under which the Landau lower bound is achieved.


Published in:
Proceedings of the 39th IEEE International Conference on Acoustics, Speech, and Signal Processing
Presented at:
39th IEEE International Conference on Acoustics, Speech, and Signal Processing, Florence, Italy, May 4-9, 2014
Year:
2014
Publisher:
New York, Ieee
Keywords:
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 Record created 2014-03-05, last modified 2018-03-17

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