One-Bit Phase Retrieval: More Samples Means Less Complexity?

TL;DR

This paper explores one-bit phase retrieval, showing that increasing sample size simplifies the convex formulation by making complex constraints redundant, and demonstrates the effectiveness through numerical results.

Contribution

It introduces a one-bit phase retrieval approach where larger sample sizes eliminate the need for complex constraints, simplifying the problem.

Findings

Matrix semi-definiteness constraints become redundant with more samples.

Rank constraints are unnecessary as sample size increases.

Numerical results validate the proposed methodology.

Abstract

The classical problem of phase retrieval has found a wide array of applications in optics, imaging and signal processing. In this paper, we consider the phase retrieval problem in a one-bit setting, where the signals are sampled using one-bit analog-to-digital converters (ADCs). A significant advantage of deploying one-bit ADCs in signal processing systems is their superior sampling rates as compared to their high-resolution counterparts. This leads to an enormous amount of one-bit samples gathered at the output of the ADC in a short period of time. We demonstrate that this advantage pays extraordinary dividends when it comes to convex phase retrieval formulations, namely that the often encountered matrix semi-definiteness constraints as well as rank constraints (that are computationally prohibitive to enforce), become redundant for phase retrieval in the face of a growing sample size. Several numerical results are presented to illustrate the effectiveness of the proposed methodologies.