A sampling theorem for Manhattan grids

Sampling 2-D signals on a union of lattices that intersect on a lattice

“…The result of sampling on the union of two rectangular lattices considered in [8] follows immediately from the above result.…”

“…The answer to (2) was answered previously in [8] for rectangular Manhattan grids when Ω1 and Ω2 were the rectangular Nyquist regions centered at the origin, corresponding to lattices L1 and L2, respectively. Although it was not explicitly stated in the previous work, it can be shown that the Landau bound is achieved in this case.…”

“…Recently, a sampling theorem for Manhattan grids showed that a field can be recovered from its Manhattan grid samples when its spectrum is supported on the union of rectangular Nyquist regions corresponding to the spacing of the two rectangular lattices [8]. An example of such a cross-shaped region is shown in Figure 2 of Nyquist regions is exactly the sampling density of the Manhattan sampling set [9].…”

“…In this work, we generalize the result of [8] to slanted Manhattan grids, which is the union of two lattices that share a common coarse lattice, as shown in Fig.1. We find new sufficient conditions under which a two-dimensional field can be perfectly reconstructed from its samples on a slanted Manhattan grid.…”

Energy efficient source localization on a Manhattan grid wireless sensor network

“…Previously, Manhattan grid sampling has been used in bilevel image coding and reconstruction [6,7,8], as well as grayscale image reconstruction [9,10]. A sampling theorem for Manhattan grids has also been derived [11]. The problem of RSS source localization is similar to these image processing problems in that we are given noisy samples of an RSS "image" on the Manhattan grid and we would like to reconstruct properties of that image (in this case, the source location).…”