A sampling theorem for Manhattan grids

This paper presents a sampling theorem for Manhattan-grid sampling, which is a sampling scheme in which data is taken along evenly spaced rows and columns. Given the spacing between the rows, the columns, and the samples along the rows and columns, the theorem shows that an image can be perfectly reconstructed from Manhattan-grid sampling if its spectrum is bandlimited to a cross-shaped region whose arm lengths and widths are determined by the aforementioned sample spacings. The nature of such cross-bandlimited images is demonstrated by filtering an image with a cross-bandlimiting filter for several choices of sampling parameters.