Super-resolution of positive spikes by Toeplitz low-rank approximation

Super-resolution consists in recovering the fine details of a signal from low-resolution measurements. Here we con sider the estimation of Dirac pulses with positive amplitudes at arbitrary locations, from noisy lowpass-filtered samples. Maximum-likelihood estimation of the unknown parameters amounts to a difficult nonconvex matrix problem of structured low rank approximation. To solve it, we propose a new heuristic iterative algorithm, yielding state-of-the-art results.