  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.
