Author: Carolin Homann Publisher: Göttingen University Press ISBN: 3863952103 Category : Languages : en Pages : 126
Book Description
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: ISBN: Category : Languages : de Pages : 126
Book Description
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 ISBN: 3030344134 Category : Science Languages : en Pages : 634
Book Description
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: Alexander H. Barnett Publisher: Cambridge University Press ISBN: 1316518876 Category : Mathematics Languages : en Pages : 321
Book Description
This book provides a theoretical foundation and conceptual framework for the problem of recovering the phase of the Fourier transform.
Author: David Paganin Publisher: Oxford University Press on Demand ISBN: 0198567286 Category : Medical Languages : en Pages : 424
Book Description
X-ray optics is undergoing a renaissance, which may be paralleled to that experienced by visible-light optics following the invention of the laser. The associated surge of activity in "coherent" x-ray optics has been documented in this monograph, the first of its type in the field.
Author: Jens Als-Nielsen Publisher: John Wiley & Sons ISBN: 9781119970156 Category : Science Languages : en Pages : 432
Book Description
Eagerly awaited, this second edition of a best-selling text comprehensively describes from a modern perspective the basics of x-ray physics as well as the completely new opportunities offered by synchrotron radiation. Written by internationally acclaimed authors, the style of the book is to develop the basic physical principles without obscuring them with excessive mathematics. The second edition differs substantially from the first edition, with over 30% new material, including: A new chapter on non-crystalline diffraction - designed to appeal to the large community who study the structure of liquids, glasses, and most importantly polymers and bio-molecules A new chapter on x-ray imaging - developed in close cooperation with many of the leading experts in the field Two new chapters covering non-crystalline diffraction and imaging Many important changes to various sections in the book have been made with a view to improving the exposition Four-colour representation throughout the text to clarify key concepts Extensive problems after each chapter There is also supplementary book material for this title available online (http://booksupport.wiley.com). Praise for the previous edition: “The publication of Jens Als-Nielsen and Des McMorrow’s Elements of Modern X-ray Physics is a defining moment in the field of synchrotron radiation... a welcome addition to the bookshelves of synchrotron–radiation professionals and students alike.... The text is now my personal choice for teaching x-ray physics...” – Physics Today, 2002
Author: Frederic Weidling Publisher: Göttingen University Press ISBN: 3863954114 Category : Languages : en Pages : 225
Book Description
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 ISBN: 0080569129 Category : Technology & Engineering Languages : en Pages : 281
Book Description
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 ISBN: 3319965204 Category : Computers Languages : en Pages : 263
Book Description
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 ISBN: 1000376133 Category : Technology & Engineering Languages : en Pages : 413
Book Description
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: Carolin Homann
Author: Carolin Homann
Author: Tim Salditt
Author: Alexander H. Barnett
Author: David Paganin
Author: Jens Als-Nielsen
Author: Frederic Weidling
Author: 
Author: Andreas Maier
Author: Rolf Behling