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[−flo, flo] and seek to obtain a higher resolution estimate by extrapolating the spectrumup to a frequency fhi > flo. We show that as long as the sources are separated by 2/flo, solving asimple convex program produces a stable estimate in the sense that the approximation error between thehigher-resolution reconstruction and the truth is proportional to the noise level times the square of thesuper-resolution factor (SRF) fhi/flo.