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Hybrid projection-reflection method for phase retrieval.

Heinz H Bauschke1, Patrick L Combettes, D Russell Luke

  • 1Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario N1G 2W1, Canada. hbauschk@uoguelph.ca

Journal of the Optical Society of America. A, Optics, Image Science, and Vision
|June 13, 2003
PubMed
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A new hybrid projection-reflection (HPR) algorithm effectively solves phase retrieval problems with nonnegativity constraints. A novel error measure provides a reliable stopping criterion for this robust algorithm.

Area of Science:

  • Applied Physics
  • Engineering
  • Computational Science

Background:

  • The phase retrieval problem is crucial in applied physics and engineering.
  • Existing methods like Fienup's algorithms and convex projection methods have limitations.
  • Connections between convex optimization and phase retrieval warrant further exploration.

Purpose of the Study:

  • Introduce a novel projection-based method for phase retrieval with nonnegativity constraints.
  • Develop a reliable and easily implementable stopping criterion for phase retrieval algorithms.
  • Evaluate the performance of the new algorithm against existing methods.

Main Methods:

  • Developed the hybrid projection-reflection (HPR) algorithm for phase retrieval.
  • Incorporated nonnegativity constraints in the object domain.

Related Experiment Videos

  • Utilized a previously underutilized error measure for a stopping criterion.

    • Main Results:

    • The HPR algorithm demonstrated competitive performance compared to the hybrid input-output (HIO) algorithm.
    • The proposed error measure proved to be a reliable and robust stopping criterion.
    • Numerical experiments validated the effectiveness of the HPR algorithm.

    Conclusions:

    • The HPR algorithm is a viable alternative for solving phase retrieval problems with nonnegativity constraints.
    • The recommended error measure offers a practical stopping criterion for phase retrieval.
    • This work highlights the potential of projection-based methods in phase retrieval.