# STFT Phase Retrieval: Uniqueness Guarantees and Recovery Algorithms

arXiv: https://arxiv.org/abs/1508.02820 · HTML: https://mlsanity.com/paper/1508.02820/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Aug 2015.

## Built on by (most cited first, 2 of 2)

- [RF-GPT: Teaching AI to See the Wireless World](https://mlsanity.com/paper/2602.14833/) (2026)
- [Single-shot Phase Retrieval from a Fractional Fourier Transform Perspective](https://mlsanity.com/paper/2311.10950/) (2023)

## Abstract (arXiv)

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.