Geometry of the Phase Retrieval Problem
Graveyard of Algorithms
Published on 20. April 2022
322 pages
978-1-009-00855-6 (ISBN)
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.
More details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
College/higher education
Illustrations
Worked examples or Exercises
File size
11,72 MB
ISBN-13
978-1-009-00855-6 (9781009008556)
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Schweitzer Classification
Other editions
Additional editions
Alexander H. Barnett | Charles L. Epstein | Leslie Greengard
Geometry of the Phase Retrieval Problem
Graveyard of Algorithms
Book
05/2022
Cambridge University Press
€159.60
Shipment within 15-20 days
Content
Part I. Theoretical Foundations: 1. The geometry near an intersection; 2. Well posedness; 3. Uniqueness and the non-negativity constraint; 4. Some preliminary conclusions; Part II. Analysis of Algorithms for Phase Retrieval: 6. Introduction to Part II; 7. Algorithms for Phase Retrieval; 8. Discrete classical phase retrieval; 9. The non-negativity constraint; 10. Asymptotics of hybrid iterative maps; Part III. Further Properties of Hybrid Iterative Algorithms and Suggestions for Improvement: 11. Introduction to Part III; 12. Statistics of algorithms; 13. Suggestions for improvements; 14. Concluding Remarks; 15. Notational conventions.
