  This paper studies the recovery of a superposition of point sources from
noisy bandlimited data. In the fewest possible words, we only have information
about the spectrum of an object in a low-frequency band bounded by a certain
cut-off frequency and seek to obtain a higher resolution estimate by
extrapolating the spectrum up to a higher frequency. We show that as long as
the sources are separated by twice the inverse of the cut-off frequency,
solving a simple convex program produces a stable estimate in the sense that
the approximation error between the higher-resolution reconstruction and the
truth is proportional to the noise level times the square of the
super-resolution factor (SRF), which is the ratio between the desired high
frequency and the cut-off frequency of the data.
