Geometry of the phase retrieval problem: graveyard of algorithms
Recovering the phase of the Fourier transform is a ubiquitous problem in imaging applications from astronomy to nanoscale X-ray diffraction imaging. Despite the efforts of a multitude of scientists, from astronomers to mathematicians, there is, as yet, no satisfactory theoretical or algorithmic solu...
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| Hauptverfasser: | , , , |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2022
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| Schriftenreihe: | Cambridge monographs on applied and computational mathematics
37 |
| Schlagworte: | |
| Online-Zugang: | BSB01 BTU01 FHN01 Volltext |
| Zusammenfassung: | Recovering the phase of the Fourier transform is a ubiquitous problem in imaging applications from astronomy to nanoscale X-ray diffraction imaging. Despite the efforts of a multitude of scientists, from astronomers to mathematicians, there is, as yet, no satisfactory theoretical or algorithmic solution to this class of problems. Written for mathematicians, physicists and engineers working in image analysis and reconstruction, this book introduces a conceptual, geometric framework for the analysis of these problems, leading to a deeper understanding of the essential, algorithmically independent, difficulty of their solutions. Using this framework, the book studies standard algorithms and a range of theoretical issues in phase retrieval and provides several new algorithms and approaches to this problem with the potential to improve the reconstructed images. The book is lavishly illustrated with the results of numerous numerical experiments that motivate the theoretical development and place it in the context of practical applications |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 07 Apr 2022) |
| Beschreibung: | 1 Online-Ressource (xii, 307 Seiten) |
| ISBN: | 9781009003919 |
| DOI: | 10.1017/9781009003919 |
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| author | Barnett, Alex H. 1972- Epstein, Charles L. 1957- Greengard, Leslie 1958- Magland, Jeremy ca. 20./21. Jh |
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| index_date | 2024-07-03T19:54:15Z |
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| isbn | 9781009003919 |
| language | English |
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| spelling | Barnett, Alex H. 1972- (DE-588)1031119000 aut Geometry of the phase retrieval problem graveyard of algorithms Alexander H. Barnett, Flatiron Institute, Charles L. Epstein, Flatiron Institute, Leslie Greengard, Courant Institute, Jeremy Magland, Flatiron Institute Cambridge Cambridge University Press 2022 1 Online-Ressource (xii, 307 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge monographs on applied and computational mathematics 37 Title from publisher's bibliographic system (viewed on 07 Apr 2022) Recovering the phase of the Fourier transform is a ubiquitous problem in imaging applications from astronomy to nanoscale X-ray diffraction imaging. Despite the efforts of a multitude of scientists, from astronomers to mathematicians, there is, as yet, no satisfactory theoretical or algorithmic solution to this class of problems. Written for mathematicians, physicists and engineers working in image analysis and reconstruction, this book introduces a conceptual, geometric framework for the analysis of these problems, leading to a deeper understanding of the essential, algorithmically independent, difficulty of their solutions. Using this framework, the book studies standard algorithms and a range of theoretical issues in phase retrieval and provides several new algorithms and approaches to this problem with the potential to improve the reconstructed images. The book is lavishly illustrated with the results of numerous numerical experiments that motivate the theoretical development and place it in the context of practical applications Geometry Algorithms Epstein, Charles L. 1957- (DE-588)133727807 aut Greengard, Leslie 1958- (DE-588)1258302926 aut Magland, Jeremy ca. 20./21. Jh. (DE-588)125830693X aut Erscheint auch als Druck-Ausgabe 978-1-31-651887-8 https://doi.org/10.1017/9781009003919 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Barnett, Alex H. 1972- Epstein, Charles L. 1957- Greengard, Leslie 1958- Magland, Jeremy ca. 20./21. Jh Geometry of the phase retrieval problem graveyard of algorithms Geometry Algorithms |
| title | Geometry of the phase retrieval problem graveyard of algorithms |
| title_auth | Geometry of the phase retrieval problem graveyard of algorithms |
| title_exact_search | Geometry of the phase retrieval problem graveyard of algorithms |
| title_exact_search_txtP | Geometry of the phase retrieval problem graveyard of algorithms |
| title_full | Geometry of the phase retrieval problem graveyard of algorithms Alexander H. Barnett, Flatiron Institute, Charles L. Epstein, Flatiron Institute, Leslie Greengard, Courant Institute, Jeremy Magland, Flatiron Institute |
| title_fullStr | Geometry of the phase retrieval problem graveyard of algorithms Alexander H. Barnett, Flatiron Institute, Charles L. Epstein, Flatiron Institute, Leslie Greengard, Courant Institute, Jeremy Magland, Flatiron Institute |
| title_full_unstemmed | Geometry of the phase retrieval problem graveyard of algorithms Alexander H. Barnett, Flatiron Institute, Charles L. Epstein, Flatiron Institute, Leslie Greengard, Courant Institute, Jeremy Magland, Flatiron Institute |
| title_short | Geometry of the phase retrieval problem |
| title_sort | geometry of the phase retrieval problem graveyard of algorithms |
| title_sub | graveyard of algorithms |
| topic | Geometry Algorithms |
| topic_facet | Geometry Algorithms |
| url | https://doi.org/10.1017/9781009003919 |
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