Multiple Input Single Output Phase Retrieval

  • Yina GuoEmail author
  • Tao Wang
  • Jianyu Li
  • Anhong Wang
  • Wenwu Wang


In this paper, we consider the problem of recovering the phase information of multiple sources from a mixed phaseless short-time Fourier transform measurement, which is called multiple input single output (MISO) phase retrieval problem. It is an inherently ill-posed problem due to the lack of the phase and mixing information, and the existing phase retrieval algorithms are not explicitly designed for this case. To address the MISO phase retrieval problem, a least-squares method coupled with an independent component analysis (ICA) algorithm is proposed for the case of sufficiently long window length. When these conditions are not met, an integrated algorithm is presented, which combines a gradient descent algorithm by minimizing a non-convex loss function with an ICA algorithm. Experimental evaluation has been conducted to show that under appropriate conditions the proposed algorithms can explicitly recover the signals, the phases of the signals, and the mixing matrix. In addition, the algorithm is robust to noise.


Multiple input single output (MISO) Phase retrieval Short-time Fourier transform (STFT) Non-convex optimization Independent component analysis (ICA) 



This work was supported by the National Natural Science Foundation of China under Grant 61301250, the Key Research and Development Project of Shanxi Province under Grant 201803D421035, the Outstanding young academic leaders of Higher Learning Institutions of Shanxi under Grant [2015]3 and the Outstanding Innovative Teams of Higher Learning Institutions of Shanxi under Grant 201705D131025. The work was conducted during Guo’s visit at the University of Surrey.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Electronics and Information EngineeringTaiyuan University of Science and TechnologyTaiyuanChina
  2. 2.Centre for Vision, Speech and Signal ProcessingUniversity of SurreyGuildfordUK

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