PSWF-Radon approach to reconstruction from band-limited Hankel transform

We give new formulas for reconstructions from band-limited Hankel transform of integer or half-integer order. Our formulas rely on the PSWF-Radon approach to super-resolution in multidimensional Fourier analysis. This approach consists of combining the theory of classical one-dimensional prolate spheroidal wave functions with the Radon transform theory. We also use the relation between the Fourier and Hankel transforms and Cormack-type inversion of the Radon transform. As a result, we also establish new connections among the Fourier, Hankel, and Abel-type transforms. Finally, we investigate numerically the capabilities of our approach to super-resolution for band-limited Hankel inversion in relation to varying levels of noise.