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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
Summary
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.
- 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.