The minimal measurement number problem in phase retrieval: a review of recent developments

TL;DR

This paper reviews recent progress on the fundamental problem of determining the minimal number of measurements needed for phase retrieval, highlighting key developments and open questions in the field.

Contribution

It provides a comprehensive review of recent advances in understanding the minimal measurement number in phase retrieval, and discusses open research questions.

Findings

Summarizes recent bounds on measurement numbers for phase retrieval

Identifies key open problems in minimal measurement theory

Highlights interdisciplinary approaches to phase retrieval challenges

Abstract

Phase retrieval is to recover the signals from phaseless measurements which is raised in many areas. A fundamental problem in phase retrieval is to determine the minimal measurement number $m$ so that one can recover $d$-dimensional signals from $m$ phaseless measurements. This problem attracts much attention of experts from different areas. In this paper, we review the recent development on the minimal measurement number and also raise many interesting open questions.