Phase retrieval from multiple-window short-time Fourier measurements

TL;DR

This paper establishes graph-theoretic conditions for phase retrieval from multiple-window short-time Fourier measurements, introduces an algebraic reconstruction algorithm, and analyzes its robustness to noise.

Contribution

It introduces novel graph-based conditions for phase retrieval and proposes an algebraic reconstruction method with error estimates under noisy measurements.

Findings

Graph connectivity conditions are necessary and sufficient for phase retrieval.

The proposed algorithm effectively reconstructs signals from noisy measurements.

Error bounds are provided for the reconstruction algorithm under noise.

Abstract

In this paper, we introduce two symmetric directed graphs depending on supports of signals and windows, and we show that the connectivity of those graphs provides either necessary and sufficient conditions to phase retrieval of a signal from magnitude measurements of its multiple-window short-time Fourier transform. Also we propose an algebraic reconstruction algorithm, and provide an error estimate to our algorithm when magnitude measurements are corrupted by deterministic/random noises.