Phase retrieval from power spectra of masked signals

TL;DR

This paper introduces a novel ensemble of masks for phase retrieval in diffraction imaging, leveraging the polarization method to achieve unique signal reconstruction efficiently and with stability comparable to existing algorithms.

Contribution

The paper constructs a new ensemble of masks using the polarization method that guarantees unique signal recovery and demonstrates its efficiency and stability through numerical simulations.

Findings

Polarization method provides faster reconstruction than PhaseLift.

The ensemble of masks ensures unique signal determination.

Numerical results confirm stability of the proposed approach.

Abstract

In diffraction imaging, one is tasked with reconstructing a signal from its power spectrum. To resolve the ambiguity in this inverse problem, one might invoke prior knowledge about the signal, but phase retrieval algorithms in this vein have found limited success. One alternative is to create redundancy in the measurement process by illuminating the signal multiple times, distorting the signal each time with a different mask. Despite several recent advances in phase retrieval, the community has yet to construct an ensemble of masks which uniquely determines all signals and admits an efficient reconstruction algorithm. In this paper, we leverage the recently proposed polarization method to construct such an ensemble. We also present numerical simulations to illustrate the stability of the polarization method in this setting. In comparison to a state-of-the-art phase retrieval algorithm known as PhaseLift, we find that polarization is much faster with comparable stability.