Greed is Super: A Fast Algorithm for Super-Resolution

We present a fast two-phase algorithm for super-resolution with strong theoretical guaran-tees. Given the low-frequency part of the spectrum of a sequence of impulses, Phase I consistsof a greedy algorithm that roughly estimates the impulse positions. These estimates are thenrefined by local optimization in Phase II.In contrast to the convex relaxation proposed by Candès et al., our approach has a lowcomputational complexity but requires the impulses to be separated by an additional logarithmicfactor to succeed. The backbone of our work is the fundamental work of Slepian et al. involvingdiscrete prolate spheroidal wave functions and their unique properties. Keywords— Super-resolution, Parameter estimation, Greedy algorithms, Local optimization, Dis-crete prolate spheroidal wave functions, Slepian functionsAMS Subject Classifications— 94A12, 94A15, 42A99