A Sampling Theorem for Deconvolution in Two Dimensions

Abstract

This work studies the problem of estimating a two-dimensional superposition of point sources or spikes from samples of their convolution with a Gaussian kernel. Our results show that minimizing a continuous counterpart of the ${\ell }_1$ norm exactly recovers the true spikes if they are sufficiently separated, and the samples are sufficiently dense. In addition, we provide numerical evidence that our results extend to non-Gaussian kernels relevant to microscopy and telescopy.

41 pages, 18 figures; added references and additional comments and description throughout for clarity