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Geometry of the phase retrieval problem : = graveyard of algorithms /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Geometry of the phase retrieval problem :/ Alexander H. Barnett, Flatiron Institute, Charles L. Epstein, Flatiron Institute, Leslie Greengard, Courant Institute, Jeremy Magland, Flatiron Institute.
Reminder of title:	graveyard of algorithms /
Author:	Barnett, Alex,
other author:	Epstein, Charles L.,
Description:	1 online resource (xii, 307 pages) :digital, PDF file(s). :
Notes:	Title from publisher's bibliographic system (viewed on 07 Apr 2022).
Subject:	Geometry. -
Online resource:	https://doi.org/10.1017/9781009003919
ISBN:	9781009003919 (ebook)

Geometry of the phase retrieval problem : = graveyard of algorithms /
Barnett, Alex,1972 December 7-

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. - 1 online resource (xii, 307 pages) :digital, PDF file(s). - Cambridge monographs on applied and computational mathematics ;37. - Cambridge monographs on applied and computational mathematics ;16..

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.

ISBN: 9781009003919 (ebook)Subjects--Topical Terms:

579899
Geometry.

LC Class. No.: QC20.7.G44 / B36 2022

Dewey Class. No.: 530.15/6

Geometry of the phase retrieval problem : = graveyard of algorithms /
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500 $a Title from publisher's bibliographic system (viewed on 07 Apr 2022).
520 $a 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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