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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: 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: 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: 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: Alex Barnett Publisher: ISBN: 9781009003919 Category : Algorithms Languages : en Pages :
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"--
Author: Publisher: Newnes ISBN: 0444536337 Category : Science Languages : en Pages : 4052
Book Description
Comprehensive Biomedical Physics, Ten Volume Set is a new reference work that provides the first point of entry to the literature for all scientists interested in biomedical physics. It is of particularly use for graduate and postgraduate students in the areas of medical biophysics. This Work is indispensable to all serious readers in this interdisciplinary area where physics is applied in medicine and biology. Written by leading scientists who have evaluated and summarized the most important methods, principles, technologies and data within the field, Comprehensive Biomedical Physics is a vital addition to the reference libraries of those working within the areas of medical imaging, radiation sources, detectors, biology, safety and therapy, physiology, and pharmacology as well as in the treatment of different clinical conditions and bioinformatics. This Work will be valuable to students working in all aspect of medical biophysics, including medical imaging and biomedical radiation science and therapy, physiology, pharmacology and treatment of clinical conditions and bioinformatics. The most comprehensive work on biomedical physics ever published Covers one of the fastest growing areas in the physical sciences, including interdisciplinary areas ranging from advanced nuclear physics and quantum mechanics through mathematics to molecular biology and medicine Contains 1800 illustrations, all in full color
Author: Marina Eckermann Publisher: Universitätsverlag Göttingen ISBN: 3863955285 Category : Languages : en Pages : 276
Book Description
To bring physiology and pathology of the human brain into better micro-anatomical and histological context, studies with different methodologies are required. Established techniques such as electron microscopy or histology show limitations in view of invasiveness, labor-intense and artifact-prone sample preparation, as well as an adequate ratio between resolution and volume throughput. For this reason, X-ray phase-contrast tomography (PC-CT) has been proposed as a three-dimensional non-destructive imaging technique, which requires less effort in sample preparation and can assess larger volumes. Furthermore, it offers quantitative electron density based contrast even for unstained tissue. Up to now, however, PC-CT studies fell short in number of samples, so that structural alterations caused by neurodegenerative diseases cannot be distinguished from physiological inter-subject variations. In this thesis, the scalability of PC-CT with respect to the required number of samples and resolution-to-volume-throughput is demonstrated, and the methodology is advanced with respect to data acquisition, processing and segmentation. In addition to the human cerebellum, cortex and hippocampus are studied. Concerning quantification and analysis of PC-CT data, this work introduces optimal transport analysis to obtain quantitative metrics of the cyto-architecture and to identify changes due to neurodegenerative diseases. For the case of Alzheimer’s disease, this workflow reveals a yet undescribed compactification of granular cells in the human hippocampus. This thesis also provides optimized configurations to study neural tissues with laboratory instrumentation, and – finally – provides new correlative imaging approaches, in particular with scanning electron microscopy.
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: Carolin Homann
Author: Tim Salditt
Author: David Paganin
Author: Frederic Weidling
Author: Alex Barnett
Author: 
Author: Marina Eckermann
Author: Andreas Maier
Author: Rolf Behling