Phase Retrieval Using Feasible Point Pursuit: Algorithms and Cramér-Rao Bound

Cheng Qian, Nicholas D. Sidiropoulos, Kejun Huang, Lei Huang, Hing Cheung So

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

Abstract

Reconstructing a signal from squared linear (rank-1 quadratic) measurements is a challenging problem with important applications in optics and imaging, where it is known as phase retrieval. This paper proposes two new phase retrieval algorithms based on nonconvex quadratically constrained quadratic programming) formulations, and a recently proposed approximation technique dubbed feasible point pursuit (FPP). The first is designed for uniformly distributed bounded measurement errors, such as those arising from high-rate quantization (B-FPP). The second is designed for Gaussian measurement errors, using a least-squares criterion (LS-FPP). Their performance is measured against state-of-the-art algorithms and the Cramér-Rao bound (CRB), which is also derived here. Simulations show that LS-FPP outperforms the existing schemes and operates close to the CRB. Compact CRB expressions, properties, and insights are obtained by explicitly computing the CRB in various special cases - including when the signal of interest admits a sparse parametrization, using harmonic retrieval as an example.

Original languageEnglish (US)
Article number7517302
Pages (from-to)5282-5296
Number of pages15
JournalIEEE Transactions on Signal Processing
Volume64
Issue number20
DOIs
StatePublished - Oct 15 2016

Bibliographical note

Funding Information:
The work of N. Sidiropoulos was supported by NSF CIF-1525194. K. Huang was supported by a UMII dissertation fellowship. C. Qian is on leave from the Department of Electronics and Information Engineering, Harbin Institute of Technology, China, supported in part by the Natural Science Foundation of China (NSFC) under Grant No. 61171187 and the Chinese Scholarship Council.

Publisher Copyright:
© 2016 IEEE.

Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.

Keywords

  • Cramér-Rao bound (CRB)
  • feasible point pursuit (FPP)
  • phase retrieval
  • quadratically constrained quadratic programming (QCQP)
  • semidefinite programming (SDP)

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