Symmetric masks for In-fill pixel interpolation on discrete p:q lattices

A 2D p:q lattice contains image intensity entries at pixels located at regular, staggered intervals that are spaced p rows and q columns apart. Zero values appear at all other intermediate grid locations. We consider here the construction, for any given p:q, of convolution masks to smoothly and uniformly interpolate values across all of the intermediate grid positions. The conventional pixel-filling approach is to allocate intensities proportional to the fractional area that each grid pixel occupies inside the boundaries formed by the p:q lines. However these area-based masks have asymmetric boundaries, flat interior values and may be odd or even in size. We ask here if smoother, symmetric versions of such convolution masks exist and, if so, is their structure unique for each p:q lattice? The answer appears to be yes on both counts. The coefficients of the masks constructed here have simple integer values whose distribution is derived purely from symmetry considerations. We have application for these symmetric interpolation masks as part of a precise image rotation algorithm, as well as to smooth back-projected values when performing discrete tomographic image reconstruction.