  We explore a fundamental problem of super-resolving a signal of interest from
a few measurements of its low-pass magnitudes. We propose a 2-stage tractable
algorithm that, in the absence of noise, admits perfect super-resolution of an
$r$-sparse signal from $2r^2-2r+2$ low-pass magnitude measurements. The spike
locations of the signal can assume any value over a continuous disk, without
increasing the required sample size. The proposed algorithm first employs a
conventional super-resolution algorithm (e.g. the matrix pencil approach) to
recover unlabeled sets of signal correlation coefficients, and then applies a
simple sorting algorithm to disentangle and retrieve the true parameters in a
deterministic manner. Our approach can be adapted to multi-dimensional spike
models and random Fourier sampling by replacing its first step with other
harmonic retrieval algorithms.
