Sparse Phase Retrieval from Short-Time Fourier Measurements
- Resource Type
- Periodical
- Authors
- Eldar, Y. C.; Sidorenko, P.; Mixon, D. G.; Barel, S.; Cohen, O.
- Source
- IEEE Signal Processing Letters IEEE Signal Process. Lett. Signal Processing Letters, IEEE. 22(5):638-642 May, 2015
- Subject
- Signal Processing and Analysis
Computing and Processing
Communication, Networking and Broadcast Technologies
Discrete Fourier transforms
Signal processing algorithms
Vectors
Phase measurement
Redundancy
Sparse matrices
GESPAR
phase retrieval
short-time Fourier transform
sparsity
- Language
- ISSN
- 1070-9908
1558-2361
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.