Super-Resolution from Noisy Data

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 the low-frequency band [-f (lo),f (lo)] and seek to obtain a higher resolution estimate by extrapolating the spectrum up to a frequency f (hi)> f (lo). We show that as long as the sources are separated by 2/f (lo), 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) f (hi)/f (lo).