Phase retrieval with polarization

TL;DR

This paper introduces a new measurement design inspired by interferometry and expander graphs for phase retrieval, providing an efficient algorithm with stability guarantees comparable to existing methods, supported by numerical simulations.

Contribution

It presents a novel measurement scheme and an efficient phase retrieval algorithm with stability guarantees, advancing the theoretical and practical aspects of phase retrieval.

Findings

Stable performance guarantee comparable to PhaseLift

Efficient phase retrieval procedure demonstrated

Numerical simulations show competitive accuracy and runtime

Abstract

In many areas of imaging science, it is difficult to measure the phase of linear measurements. As such, one often wishes to reconstruct a signal from intensity measurements, that is, perform phase retrieval. In this paper, we provide a novel measurement design which is inspired by interferometry and exploits certain properties of expander graphs. We also give an efficient phase retrieval procedure, and use recent results in spectral graph theory to produce a stable performance guarantee which rivals the guarantee for PhaseLift in [Candes et al. 2011]. We use numerical simulations to illustrate the performance of our phase retrieval procedure, and we compare reconstruction error and runtime with a common alternating-projections-type procedure.