Sparse phase retrieval from short-time fourier measurements

Yonina C. Eldar; Pavel Sidorenko; Dustin G. Mixon; Shaby Barel; Oren Cohen

doi:10.1109/LSP.2014.2364225

Sparse phase retrieval from short-time fourier measurements

Yonina C. Eldar^*, Pavel Sidorenko, Dustin G. Mixon, Shaby Barel, Oren Cohen

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

80 Scopus citations

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.

Original language	English
Article number	6932437
Pages (from-to)	638-642
Number of pages	5
Journal	IEEE Signal Processing Letters
Volume	22
Issue number	5
DOIs	https://doi.org/10.1109/LSP.2014.2364225
State	Published - 1 May 2015
Externally published	Yes

Keywords

GESPAR
phase retrieval
short-time Fourier transform
sparsity

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10.1109/LSP.2014.2364225

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title = "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.",

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AU - Eldar, Yonina C.

AU - Sidorenko, Pavel

AU - Mixon, Dustin G.

AU - Barel, Shaby

AU - Cohen, Oren

PY - 2015/5/1

Y1 - 2015/5/1

N2 - 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.

AB - 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.

KW - GESPAR

KW - phase retrieval

KW - short-time Fourier transform

KW - sparsity

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EP - 642

JO - IEEE Signal Processing Letters

JF - IEEE Signal Processing Letters

IS - 5

M1 - 6932437

ER -

Sparse phase retrieval from short-time fourier measurements

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Keywords

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