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

Abstract
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 to the existing methods, which shows its effectiveness in suppressing outlier interference.

Citation
Fu, N., Li, X., Zheng, P., & Qiao, L. (2023). A Weighted Convex Optimized Phase Retrieval Method for Short-Time Fourier Transform Measurement With Outliers. IEEE Transactions on Instrumentation and Measurement, 1–1. https://doi.org/10.1109/tim.2023.3317376

Acknowledgements
This work was supported in part by the National Natural Science Foundation of China (NSFC) under Grant 62071149 and Grant 61671177 and in part by the National Key Research and Development Program of China under Grant 2022YFB3304000.

Publisher
Institute of Electrical and Electronics Engineers (IEEE)

Journal
IEEE Transactions on Instrumentation and Measurement

DOI
10.1109/tim.2023.3317376

Additional Links
https://ieeexplore.ieee.org/document/10256049/

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