  In this paper, we address the problem of recovering point sources from two
dimensional low-pass measurements, which is known as super-resolution problem.
This is the fundamental concern of many applications such as electronic
imaging, optics, microscopy, and line spectral estimation. We assume that the
point sources are located in the square $[0,1]^2$ with unknown locations and
complex amplitudes. The only available information is low-pass Fourier
measurements band-limited to integer square $[-f_c,f_c]^2$. The signal is
estimated by minimizing Total Variation $(\mathrm{TV})$ norm, which leads to a
convex optimization problem. It is shown that if the sources are separated by
at least $1.68/f_c$, there exist a dual certificate that is sufficient for
exact recovery.
