STFT Phase Retrieval: Uniqueness Guarantees and Recovery Algorithms

TL;DR

This paper investigates the conditions for unique signal recovery from STFT magnitude and introduces a semidefinite relaxation algorithm with theoretical guarantees, supported by numerical simulations.

Contribution

It establishes conditions for almost sure uniqueness of STFT magnitude signals and proposes a novel recovery algorithm with proven guarantees.

Findings

Conditions for almost sure uniqueness of STFT magnitude signals

Development of the STliFT semidefinite relaxation algorithm

Numerical simulations validating theoretical results

Abstract

The problem of recovering a signal from its Fourier magnitude is of paramount importance in various fields of engineering and applied physics. Due to the absence of Fourier phase information, some form of additional information is required in order to be able to uniquely, efficiently and robustly identify the underlying signal. Inspired by practical methods in optical imaging, we consider the problem of signal reconstruction from the Short-Time Fourier Transform (STFT) magnitude. We first develop conditions under which the STFT magnitude is an almost surely unique signal representation. We then consider a semidefinite relaxation-based algorithm (STliFT) and provide recovery guarantees. Numerical simulations complement our theoretical analysis and provide directions for future work.