We prove by means of elementary methods that phase retrieval of complex polynomials p of degree less than N is possible with 4N-4 phaseless Fourier measurements of p and p'. In addition, we provide an associated algorithm and prove that it recovers p up to global phase.
Cite
@article{arxiv.1403.4769,
title = {Phase Retrieval from 4N-4 Measurements},
author = {Friedrich Philipp},
journal= {arXiv preprint arXiv:1403.4769},
year = {2014}
}