Phase retrieval from low-rate samples
Information Theory
2014-07-21 v4 math.IT
Abstract
The paper considers the phase retrieval problem in N-dimensional complex vector spaces. It provides two sets of deterministic measurement vectors which guarantee signal recovery for all signals, excluding only a specific subspace and a union of subspaces, respectively. A stable analytic reconstruction procedure of low complexity is given. Additionally it is proven that signal recovery from these measurements can be solved exactly via a semidefinite program. A practical implementation with 4 deterministic diffraction patterns is provided and some numerical experiments with noisy measurements complement the analytic approach.
Cite
@article{arxiv.1311.7045,
title = {Phase retrieval from low-rate samples},
author = {Volker Pohl and Fanny Yang and Holger Boche},
journal= {arXiv preprint arXiv:1311.7045},
year = {2014}
}
Comments
Preprint accepted for publication in Sampling Theory in Signal and Image Processing -- Special issue on SampTa 2013