Fast Phase Retrieval: A Robust and Efficient Multidimensional Phase Retrieval Algorithm
We present the first phase retrieval algorithm with a set of deterministic recovery guarantees. We show that for a class of objects known as "Schwarz Objects", the algorithm is guaranteed to reconstruct the object given only the magnitudes of its discrete Fourier transform. We present nume...
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| Format: | Thesis |
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Massachusetts Institute of Technology
2024
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| Online Access: | https://hdl.handle.net/1721.1/153788 |
| _version_ | 1826206442450845696 |
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| author | Brabec, Cole |
| author2 | Englund, Dirk R. |
| author_facet | Englund, Dirk R. Brabec, Cole |
| author_sort | Brabec, Cole |
| collection | MIT |
| description | We present the first phase retrieval algorithm with a set of deterministic recovery guarantees. We show that for a class of objects known as "Schwarz Objects", the algorithm is guaranteed to reconstruct the object given only the magnitudes of its discrete Fourier transform. We present numerical evidence that the algorithm additionally succeeds quite often for non-Schwarz objects. We also present a set of measurement matrices for which the algorithm is guaranteed to recover any object. We derive the algorithm by converting instances of the phase-retrieval problem to the Schwarz problem and refine the solution with local optimization. The result is an algorithm that is fast, universal and robust against noise. |
| first_indexed | 2024-09-23T13:29:21Z |
| format | Thesis |
| id | mit-1721.1/153788 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T13:29:21Z |
| publishDate | 2024 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/1537882024-03-16T03:30:49Z Fast Phase Retrieval: A Robust and Efficient Multidimensional Phase Retrieval Algorithm Brabec, Cole Englund, Dirk R. Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science We present the first phase retrieval algorithm with a set of deterministic recovery guarantees. We show that for a class of objects known as "Schwarz Objects", the algorithm is guaranteed to reconstruct the object given only the magnitudes of its discrete Fourier transform. We present numerical evidence that the algorithm additionally succeeds quite often for non-Schwarz objects. We also present a set of measurement matrices for which the algorithm is guaranteed to recover any object. We derive the algorithm by converting instances of the phase-retrieval problem to the Schwarz problem and refine the solution with local optimization. The result is an algorithm that is fast, universal and robust against noise. S.M. 2024-03-15T19:24:07Z 2024-03-15T19:24:07Z 2024-02 2024-02-21T17:10:01.104Z Thesis https://hdl.handle.net/1721.1/153788 In Copyright - Educational Use Permitted Copyright retained by author(s) https://rightsstatements.org/page/InC-EDU/1.0/ application/pdf Massachusetts Institute of Technology |
| spellingShingle | Brabec, Cole Fast Phase Retrieval: A Robust and Efficient Multidimensional Phase Retrieval Algorithm |
| title | Fast Phase Retrieval: A Robust and Efficient Multidimensional Phase Retrieval Algorithm |
| title_full | Fast Phase Retrieval: A Robust and Efficient Multidimensional Phase Retrieval Algorithm |
| title_fullStr | Fast Phase Retrieval: A Robust and Efficient Multidimensional Phase Retrieval Algorithm |
| title_full_unstemmed | Fast Phase Retrieval: A Robust and Efficient Multidimensional Phase Retrieval Algorithm |
| title_short | Fast Phase Retrieval: A Robust and Efficient Multidimensional Phase Retrieval Algorithm |
| title_sort | fast phase retrieval a robust and efficient multidimensional phase retrieval algorithm |
| url | https://hdl.handle.net/1721.1/153788 |
| work_keys_str_mv | AT brabeccole fastphaseretrievalarobustandefficientmultidimensionalphaseretrievalalgorithm |