The Algebraic Approach to Phase Retrieval and Explicit Inversion at the Identifiability Threshold

Understand

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.