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  3. Geometry of the Phase Retrieval Problem
  • Cited by 5
Publisher:
Cambridge University Press
Online publication date:
April 2022
Print publication year:
2022
Online ISBN:
9781009003919
DOI:
https://doi.org/10.1017/9781009003919
Subjects:
Mathematics, Computational Science, Communications and Signal Processing, Engineering, Numerical Analysis and Computational Science
Series:
Cambridge Monographs on Applied and Computational Mathematics (39)
Information

Book description

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.

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