[PDF] Phase Retrieval Problems In X Ray Physics eBook

Author : Carolin Homann
Publisher : Göttingen University Press
Page : 126 pages
File Size : 41,38 MB
Release : 2015
Category :
ISBN : 3863952103

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In phase retrieval problems that occur in imaging by coherent x-ray diffraction, one tries to reconstruct information about a sample of interest from possibly noisy intensity measurements of the wave fi eld traversing the sample. The mathematical formulation of these problems bases on some assumptions. Usually one of them is that the x-ray wave fi eld is generated by a point source. In order to address this very idealized assumption, it is common to perform a data preprocessing step, the so-called empty beam correction. Within this work, we study the validity of this approach by presenting a quantitative error estimate. Moreover, in order to solve these phase retrieval problems, we want to incorporate a priori knowledge about the structure of the noise and the solution into the reconstruction process. For this reason, the application of a problem adapted iteratively regularized Newton-type method becomes particularly attractive. This method includes the solution of a convex minimization problem in each iteration step. We present a method for solving general optimization problems of this form. Our method is a generalization of a commonly used algorithm which makes it efficiently applicable to a wide class of problems. We also proof convergence results and show the performance of our method by numerical examples.

Author : Carolin Homann
Publisher :
Page : 126 pages
File Size : 24,7 MB
Release : 2015
Category :
ISBN :

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In phase retrieval problems that occur in imaging by coherent x-ray diffraction, one tries to reconstruct information about a sample of interest from possibly noisy intensity measurements of the wave fi eld traversing the sample. The mathematical formulation of these problems bases on some assumptions. Usually one of them is that the x-ray wave fi eld is generated by a point source. In order to address this very idealized assumption, it is common to perform a data preprocessing step, the so-called empty beam correction. Within this work, we study the validity of this approach by presenting a quantitative error estimate. Moreover, in order to solve these phase retrieval problems, we want to incorporate a priori knowledge about the structure of the noise and the solution into the reconstruction process. For this reason, the application of a problem adapted iteratively regularized Newton-type method becomes particularly attractive. This method includes the solution of a convex minimization problem in each iteration step. We present a method for solving general optimization problems of this form. Our method is a generalization of a commonly used algorithm which makes it efficiently applicable to a wide class of problems. We also proof convergence results and show the performance of our method by numerical examples.

Author : Tim Salditt
Publisher : Springer Nature
Page : 634 pages
File Size : 18,50 MB
Release : 2020-06-09
Category : Science
ISBN : 3030344134

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This open access book, edited and authored by a team of world-leading researchers, provides a broad overview of advanced photonic methods for nanoscale visualization, as well as describing a range of fascinating in-depth studies. Introductory chapters cover the most relevant physics and basic methods that young researchers need to master in order to work effectively in the field of nanoscale photonic imaging, from physical first principles, to instrumentation, to mathematical foundations of imaging and data analysis. Subsequent chapters demonstrate how these cutting edge methods are applied to a variety of systems, including complex fluids and biomolecular systems, for visualizing their structure and dynamics, in space and on timescales extending over many orders of magnitude down to the femtosecond range. Progress in nanoscale photonic imaging in Göttingen has been the sum total of more than a decade of work by a wide range of scientists and mathematicians across disciplines, working together in a vibrant collaboration of a kind rarely matched. This volume presents the highlights of their research achievements and serves as a record of the unique and remarkable constellation of contributors, as well as looking ahead at the future prospects in this field. It will serve not only as a useful reference for experienced researchers but also as a valuable point of entry for newcomers.

Author : Alex Barnett
Publisher :
Page : pages
File Size : 43,57 MB
Release : 2022
Category : Algorithms
ISBN : 9781009003919

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"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"--

Author : Frederic Weidling
Publisher : Göttingen University Press
Page : 225 pages
File Size : 28,22 MB
Release : 2019
Category :
ISBN : 3863954114

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In inverse problems one wants to find some parameter of interest which is not directly observable by indirect measurement. These measurements are usually noisy while the mapping of measurement to parameter is typically illposed (that is unstable). Therefore one applies regularization techniques that balance these two factors to find a stable approximation of the sought for parameter. However, in order to bound the reconstruction error, one needs additional information on the true parameter, which is nowadays typically formulated in terms of variational source conditions. In this thesis, we develop a general strategy to verify these conditions based on smoothness of the true parameter and the illposedness of the problem; the latter will be characterized by exploiting structural similarities to stability estimates. Following this, we apply our strategy to verify variational source conditions for parameter identification problems, inverse scattering and electrical impedance tomography.

Author :
Publisher : Academic Press
Page : 281 pages
File Size : 16,35 MB
Release : 2011-09-06
Category : Technology & Engineering
ISBN : 0080569129

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Advances in Imaging and Electron Physics merges two long-running serials-Advances in Electronics and Electron Physics and Advances in Optical and Electron Microscopy. This series features extended articles on the physics of electron devices (especially semiconductor devices), particle optics at high and low energies, microlithography, image science and digital image processing, electromagnetic wave propagation, electron microscopy, and the computing methods used in all these domains. Publication of this 150th volume is an event to be celebrated and, to mark the occasion, the editor has brought together leaders of some of the main themes of past and hopefully of future volumes: electron microscopy, since Ladislaus Marton was one of the pioneers; mathematical morphology, which has often appeared in this series and also fills a supplement, so often cited that it usually appears just as “Academic Press, 1994 (H.J.A.M. Heijmans, Morphological Image Operators, Supplement 25, 1994) with no mention of the Advances; ptychography, a highly original approach to the phase problem, the latter also the subject of a much cited Supplement (W.O. Saxton, ‘Computer Techniques for Image Processing in Electron Microscopy’, Supplement 10, 1978); and wavelets, which have become a subject in their own right, not just a tool in image processing. Updated with contributions from leading international scholars and industry experts Discusses hot topic areas and presents current and future research trends Invaluable reference and guide for physicists, engineers and mathematicians

Author : Andreas Maier
Publisher : Springer
Page : 263 pages
File Size : 30,4 MB
Release : 2018-08-02
Category : Computers
ISBN : 3319965204

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This open access book gives a complete and comprehensive introduction to the fields of medical imaging systems, as designed for a broad range of applications. The authors of the book first explain the foundations of system theory and image processing, before highlighting several modalities in a dedicated chapter. The initial focus is on modalities that are closely related to traditional camera systems such as endoscopy and microscopy. This is followed by more complex image formation processes: magnetic resonance imaging, X-ray projection imaging, computed tomography, X-ray phase-contrast imaging, nuclear imaging, ultrasound, and optical coherence tomography.

Author : Rolf Behling
Publisher : CRC Press
Page : 413 pages
File Size : 21,78 MB
Release : 2021-04-18
Category : Technology & Engineering
ISBN : 1000376133

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Gives an up-to-date summary of X-ray source design for applications in modern diagnostic medical imaging. Lays a sound groundwork for education and advanced training in the physics of X-ray production and X-ray interactions with matter. Includes a historical overview of X-ray tube and generator development, including key achievements leading up to the current technological and economic state of the field.

Author : Paolo Russo
Publisher : CRC Press
Page : 2606 pages
File Size : 43,2 MB
Release : 2017-12-14
Category : Medical
ISBN : 149874155X

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Containing chapter contributions from over 130 experts, this unique publication is the first handbook dedicated to the physics and technology of X-ray imaging, offering extensive coverage of the field. This highly comprehensive work is edited by one of the world’s leading experts in X-ray imaging physics and technology and has been created with guidance from a Scientific Board containing respected and renowned scientists from around the world. The book's scope includes 2D and 3D X-ray imaging techniques from soft-X-ray to megavoltage energies, including computed tomography, fluoroscopy, dental imaging and small animal imaging, with several chapters dedicated to breast imaging techniques. 2D and 3D industrial imaging is incorporated, including imaging of artworks. Specific attention is dedicated to techniques of phase contrast X-ray imaging. The approach undertaken is one that illustrates the theory as well as the techniques and the devices routinely used in the various fields. Computational aspects are fully covered, including 3D reconstruction algorithms, hard/software phantoms, and computer-aided diagnosis. Theories of image quality are fully illustrated. Historical, radioprotection, radiation dosimetry, quality assurance and educational aspects are also covered. This handbook will be suitable for a very broad audience, including graduate students in medical physics and biomedical engineering; medical physics residents; radiographers; physicists and engineers in the field of imaging and non-destructive industrial testing using X-rays; and scientists interested in understanding and using X-ray imaging techniques. The handbook's editor, Dr. Paolo Russo, has over 30 years’ experience in the academic teaching of medical physics and X-ray imaging research. He has authored several book chapters in the field of X-ray imaging, is Editor-in-Chief of an international scientific journal in medical physics, and has responsibilities in the publication committees of international scientific organizations in medical physics. Features: Comprehensive coverage of the use of X-rays both in medical radiology and industrial testing The first handbook published to be dedicated to the physics and technology of X-rays Handbook edited by world authority, with contributions from experts in each field

Author : Alexander H. Barnett
Publisher : Cambridge University Press
Page : 321 pages
File Size : 33,56 MB
Release : 2022-05-05
Category : Mathematics
ISBN : 1316518876

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This book provides a theoretical foundation and conceptual framework for the problem of recovering the phase of the Fourier transform.