The Algebraic Approach to Phase Retrieval and Explicit Inversion at the Identifiability Threshold
Functional Analysis
2014-02-18 v1 Computer Vision and Pattern Recognition
Information Theory
Algebraic Geometry
math.IT
Machine Learning
Abstract
We study phase retrieval from magnitude measurements of an unknown signal as an algebraic estimation problem. Indeed, phase retrieval from rank-one and more general linear measurements can be treated in an algebraic way. It is verified that a certain number of generic rank-one or generic linear measurements are sufficient to enable signal reconstruction for generic signals, and slightly more generic measurements yield reconstructability for all signals. Our results solve a few open problems stated in the recent literature. Furthermore, we show how the algebraic estimation problem can be solved by a closed-form algebraic estimation technique, termed ideal regression, providing non-asymptotic success guarantees.
Cite
@article{arxiv.1402.4053,
title = {The Algebraic Approach to Phase Retrieval and Explicit Inversion at the Identifiability Threshold},
author = {Franz J Király and Martin Ehler},
journal= {arXiv preprint arXiv:1402.4053},
year = {2014}
}