A Weighted Convex Optimized Phase Retrieval Method for Short-Time Fourier Transform Measurement With Outliers

As a problem of reconstructing the original signal from phaseless short-time Fourier transform (STFT) measurement, STFT phase retrieval (PR) is widespread in many fields. The existing PR algorithms for STFT measurement can uniquely determine the original signal (up to a global phase); however, they...

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Bibliographic Details
Published inIEEE transactions on instrumentation and measurement Vol. 72; pp. 1 - 14
Main Authors Fu, Ning, Li, Xiaodong, Zheng, Pinjun, Qiao, Liyan
Format Journal Article
LanguageEnglish
Published New York IEEE 2023
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Algorithms
Antenna measurements
Convex functions
Convexity
Data analysis
Fourier transforms
Interference
Mathematical analysis
Noise measurement
Optimization
Outliers
Outliers (statistics)
Phase measurement
Phase retrieval
phase retrieval (PR)
Pollution measurement
short-time Fourier transform (STFT)
Signal processing algorithms
Time measurement
weight matrix
Weight measurement
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Summary:As a problem of reconstructing the original signal from phaseless short-time Fourier transform (STFT) measurement, STFT phase retrieval (PR) is widespread in many fields. The existing PR algorithms for STFT measurement can uniquely determine the original signal (up to a global phase); however, they are invalid when outlier interference exists. Aiming at this problem, we propose a weighted convex optimization PR method by introducing a weight matrix that can identify outliers. Meanwhile, a two-channel phaseless measurement structure based on the mask technique and the corresponding calculation algorithm are proposed to obtain the weight matrix. In particular, by accumulating the measurement results of all short-time segments, the support of outliers can be well-identified in the weight matrix calculation. Simulation and hardware experiments demonstrate the performance improvement of the proposed approach compared with the existing methods, which shows its effectiveness in suppressing outlier interference.
ISSN:0018-9456
1557-9662
DOI:10.1109/TIM.2023.3317376