Regridding and data interpolation of projection domain and Radon domain for super-resolution tomograpic reconstruction

Radon domain can be filled by the Fourier transforms for projection images in a polar gridding format (radial lines for parallel projections, radon arcs for fan-beam projections). The Radon-based tomographic reconstruction requires regridding a polar radon domain into a rectilinear lattice before inverse Fourier transform. Since the radon domain is irregularly sampled by Fourier-transformed projections, i.e, oversampled around the central regions and undersampled at the peripheral regions, the polar-to-Cartesian coordinate grid conversion involves rebinning for oversampled central region, interpolation for undersampled peripheral region, and extrapolation for extending the peripheral boundary. In this paper, we propose a general data rebinning/interpolation/extrapolation scheme to deal with the radon domain regridding, which is a local convex combination with weights determined by a function of inverse distances. For filling the unavailable entries at peripheral regions, we propose to calculate the corresponding entries in the projection domain, rather than in the radon domain, by interpolations and extrapolations. The interpolation for peripheral region allows us investigate the angular sampling for computed tomography scanning. The extrapolation leads to super-resolution tomographic reconstruction. We find that data interpolation in projection domain may produce better results than in radon domain. This finding may be justified by the fact that the data distribution is more continuous in projection domain than in Fourier domain.