Geometrical properties and accelerated gradient solvers of non-convex phase retrieval

Yi Zhou, Huishuai Zhang, Yingbin Liang

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Scopus citations

Abstract

We consider recovering a signal x n from the magnitudes of Gaussian measurements by minimizing a second order yet non-smooth loss function. By exploiting existing concentration results of the loss function, we show that the non-convex loss function satisfies several quadratic geometrical properties. Based on these geometrical properties, we characterize the linear convergence of the sequence of function graph generated by the gradient flow on minimizing the loss function. Furthermore, we propose an accelerated version of the gradient flow, and establish an in-exact linear convergence of the generated sequence of function graph by exploiting the quadratic geometries of the loss function. Then, we verify the numerical advantages of the proposed algorithms over other state-of-art algorithms.

Original languageEnglish (US)
Title of host publication54th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2016
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages331-335
Number of pages5
ISBN (Electronic)9781509045495
DOIs
StatePublished - Feb 10 2017
Event54th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2016 - Monticello, United States
Duration: Sep 27 2016Sep 30 2016

Other

Other54th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2016
CountryUnited States
CityMonticello
Period9/27/169/30/16

ASJC Scopus subject areas

  • Artificial Intelligence
  • Computational Theory and Mathematics
  • Computer Networks and Communications
  • Hardware and Architecture
  • Control and Optimization

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    Zhou, Y., Zhang, H., & Liang, Y. (2017). Geometrical properties and accelerated gradient solvers of non-convex phase retrieval. In 54th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2016 (pp. 331-335). [7852249] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ALLERTON.2016.7852249