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Geometry of the Phase Retrieval Problem : Graveyard of Algorithms.
・ISBN 978-1-316-51887-8 hard GB£ 104.00
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電子版あり 大学・学術機関向け電子ブック（eBook）ISBN 978-1-009-00391-9
| 著者・編者 | Barnett, Alexander H. / Epstein, Charles L. / Greengard, Leslie / Magland, Jeremy, |
|---|---|
| シリーズ | Cambridge Monographs on Applied and Computational Mathematics |
| 出版社 | (Cambridge University Press, UK) |
| 出版年月 | 2022 |
| ページ数 | 350 pp. |
| 言語 | ENG |
| ニュース番号 | ＜M25-16018＞ |
解説
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.