Sparse Phase Retrieval from Short-Time Fourier Measurements

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 ST...

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Bibliographic Details
Published in:IEEE signal processing letters 2015-05, Vol.22 (5), p.638-642
Main Authors: Eldar, Yonina C., Sidorenko, Pavel, Mixon, Dustin G., Barel, Shaby, Cohen, Oren
Format: Article
Language:English
Subjects:
Adaptation
Algorithms
Computer simulation
Discrete Fourier transforms
Fourier analysis
Fourier transforms
GESPAR
Phase measurement
Phase retrieval
Recovery
Redundancy
short-time Fourier transform
Signal processing
Signal processing algorithms
Sparse matrices
sparsity
Vectors
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Summary: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.
ISSN:1070-9908
1558-2361
DOI:10.1109/LSP.2014.2364225