Sparse Phase Retrieval from Short-Time Fourier Measurements
Abstract
We consider the classical 1D phase retrieval problem. In order to overcome the difficulties associated with phase retrieval from measurements of the Fourier magnitude, we treat recovery from the magnitude of the short-time Fourier transform (STFT). We first show that the redundancy offered by the STFT enables unique recovery for arbitrary nonvanishing inputs, under mild conditions. An efficient algorithm for recovery of a sparse input from the STFT magnitude is then suggested, based on an adaptation of the recently proposed GESPAR algorithm. We demonstrate through simulations that using the STFT leads to improved performance over recovery from the oversampled Fourier magnitude with the same number of measurements.
Cite
@article{arxiv.1411.1380,
title = {Sparse Phase Retrieval from Short-Time Fourier Measurements},
author = {Yonina C. Eldar and Pavel Sidorenko and Dustin G. Mixon and Shaby Barel and Oren Cohen},
journal= {arXiv preprint arXiv:1411.1380},
year = {2015}
}
Comments
To appear in IEEE Signal Processing Letters