Abstract
We present the convergence analysis of convex combination of the alternating projection and Douglas–Rachford operators for solving the phase retrieval problem. New convergence criteria for iterations generated by the algorithm are established by applying various schemes of numerical analysis and exploring both physical and mathematical characteristics of the phase retrieval problem. Numerical results demonstrate the advantages of the algorithm over the other widely known projection methods in practically relevant simulations.
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Acknowledgements
The authors would like to thank the two anonymous referees for their helpful and constructive comments on the first manuscript of the paper.
Funding
This project has received funding from the ECSEL Joint Undertaking (JU) under grant agreement no. 826589. The JU receives support from the European Union’s Horizon 2020 research and innovation programme and Netherlands, Belgium, Germany, France, Italy, Austria, Hungary, Romania, Sweden, and Israel.
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Communicated by: Leslie Greengard
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Thao, N.H., Soloviev, O. & Verhaegen, M. Convex combination of alternating projection and Douglas–Rachford operators for phase retrieval. Adv Comput Math 47, 33 (2021). https://doi.org/10.1007/s10444-021-09861-y
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DOI: https://doi.org/10.1007/s10444-021-09861-y
Keywords
- Nonconvex feasibility
- Projection method
- Prox-regularity
- Transversality
- Linear convergence
- Phase retrieval
- Fourier transform