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Phase Retrieval And Zero Crossings
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Book Synopsis Phase Retrieval and Zero Crossings by : N.E. Hurt
Download or read book Phase Retrieval and Zero Crossings written by N.E. Hurt and published by Springer Science & Business Media. This book was released on 2001-11-30 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'Et moi, ... , si j'avait su comment en :revenir, One scrvice mathematics has rendered the je n'y scrais point alle.' human race. lt has put common sense back Jules Veme where it bdongs, on the topmost shelf next to the dusty canister labclled 'discarded non- The series is divergent; therefore we may be sense'. able to do something with it. Erle T. Bc1l 0. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'.All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.
Book Synopsis Phase Retrieval and Zero Crossings by : Norman Hurt
Download or read book Phase Retrieval and Zero Crossings written by Norman Hurt and published by . This book was released on 1989 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Pattern Recognition by : Carl Edward Rasmussen
Download or read book Pattern Recognition written by Carl Edward Rasmussen and published by Springer Science & Business Media. This book was released on 2004-08-23 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 26th Symposium of the German Association for Pattern Recognition, DAGM 2004, held in Tübingen, Germany in August/September 2004. The 22 revised papers and 48 revised poster papers presented were carefully reviewed and selected from 146 submissions. The papers are organized in topical sections on learning, Bayesian approaches, vision and faces, vision and motion, biologically motivated approaches, segmentation, object recognition, and object recognition and synthesis.
Book Synopsis Principles of Electron Optics, Volume 4 by : Peter W. Hawkes
Download or read book Principles of Electron Optics, Volume 4 written by Peter W. Hawkes and published by Academic Press. This book was released on 2022-05-10 with total page 665 pages. Available in PDF, EPUB and Kindle. Book excerpt: Principles of Electron Optics: Second Edition, Advanced Wave Optics provides a self-contained, modern account of electron optical phenomena with the Dirac or Schrödinger equation as a starting point. Knowledge of this branch of the subject is essential to understanding electron propagation in electron microscopes, electron holography and coherence. Sections in this new release include, Electron Interactions in Thin Specimens, Digital Image Processing, Acquisition, Sampling and Coding, Enhancement, Linear Restoration, Nonlinear Restoration – the Phase Problem, Three-dimensional Reconstruction, Image Analysis, Instrument Control, Vortex Beams, The Quantum Electron Microscope, and much more. Includes authoritative coverage of many recent developments in wave electron optics Describes the interaction of electrons with solids and the information that can be obtained from electron-beam techniques Includes new content on multislice optics, 3D reconstruction, Wigner optics, vortex beams and the quantum electron microscope
Book Synopsis Advances in Imaging and Electron Physics by :
Download or read book Advances in Imaging and Electron Physics written by and published by Academic Press. This book was released on 2018-06-15 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advances in Imaging and Electron Physics, Volume 206, merges two long-running serials, Advances in Electronics and Electron Physics and Advances in Optical and Electron Microscopy. The series features extended articles on the physics of electron devices (especially semiconductor devices), particle optics at high and low energies, microlithography, image science, digital image processing, electromagnetic wave propagation, electron microscopy, and the computing methods used in all these domains. Contains contributions from leading authorities on the subject matter Informs and updates on all the latest developments in the field of imaging and electron physics Provides practitioners interested in microscopy, optics, image processing, mathematical morphology, electromagnetic fields, electrons and ion emission with a valuable resource 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
Book Synopsis Utilization of Fourier Domain Real Zeros in the Phase Retrieval Problem by : Christopher C. Wackerman
Download or read book Utilization of Fourier Domain Real Zeros in the Phase Retrieval Problem written by Christopher C. Wackerman and published by . This book was released on 1993 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Harmonic Analysis and Convexity by : Alexander Koldobsky
Download or read book Harmonic Analysis and Convexity written by Alexander Koldobsky and published by Walter de Gruyter GmbH & Co KG. This book was released on 2023-07-24 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, the interaction between harmonic analysis and convex geometry has increased which has resulted in solutions to several long-standing problems. This collection is based on the topics discussed during the Research Semester on Harmonic Analysis and Convexity at the Institute for Computational and Experimental Research in Mathematics in Providence RI in Fall 2022. The volume brings together experts working in related fields to report on the status of major problems in the area including the isomorphic Busemann-Petty and slicing problems for arbitrary measures, extremal problems for Fourier extension and extremal problems for classical singular integrals of martingale type, among others.
Book Synopsis Formerly Advances in Electronics and Electron Physics by :
Download or read book Formerly Advances in Electronics and Electron Physics written by and published by Academic Press. This book was released on 1995-07-11 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: Academic Press is pleased to announce the creation of Advances in Imaging and Electron Physics. This serial publication results from the merger of two long running serials--Advances in Electronics and Electron Physics and Advances in Optical & Electron Microscopy. Advances in Imaging & Electron Physics will feature 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. Continuation order customers for either of the original Advances will receiveVolume 90, the first combined volume.
Book Synopsis Nanoscale Photonic Imaging by : Tim Salditt
Download or read book Nanoscale Photonic Imaging written by Tim Salditt and published by Springer Nature. This book was released on 2020-06-09 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Phase retrieval for object and probe in the optical near-field by : Anna-Lena Robisch
Download or read book Phase retrieval for object and probe in the optical near-field written by Anna-Lena Robisch and published by Göttingen University Press. This book was released on 2016 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lensless, holographic X-ray microscopy is a non-invasive imaging technique that provides resolution on the nanometer scale. Therefore, a divergent, coherent and especially clean wave front impinging on the sample is needed. Yet, focusing X-rays by even the most advanced X-ray mirrors causes so called figure errors of high spatial frequency content. The results are strongly deteriorated intensity profiles that are often even more pronounced than the holographic image of the sample itself. A common strategy to compensate these figure errors is to divide the hologram by the pure intensity profile of the beam (the so called flat field). However, this division is only valid in the limiting case of an illumination focused down to a point source. In reality, as a consequence of a fi nite spot size, one has to accept a loss in resolution when performing the flat field correction. An approach different from the described straightforward procedure is necessary. Here, the simultaneous reconstruction of object and probe is proposed using holograms which were not flat field corrected before phase retrieval. To this end, a method has been developed that allows simultaneously reconstructing object and probe in amplitude and phase from holographic intensity recordings. The experimental way of proceeding was mainly inspired by well-established holographic full-field X-ray imaging techniques that require holograms defocused to different degrees. Consequently, the conclusion seems reasonable that diversity in the optical near-field arises mainly from variation of the propagation distance of light. This so called longitudinal diversity is used to properly phase the transmission function of the sample of interest. The algorithmic strategy of simultaneous phase retrieval for object and probe draws on far-field ptychography where lateral translations of the sample create diverse diffraction patterns. In view of the need for longitudinal diversity realized by shifts of the sample along the optical axis, ptychography has been generalized and adapted for the optical near-field. Hence, translations of the sample in all three dimensions of space need to be exploited to collect enough information about object and probe such that both can be reconstructed simultaneously in amplitude and phase. Concepts have been put into practice by simulations as well as by experiments with coherent visible light and hard X-rays from synchrotron sources. The presented approach offers the opportunity to perform high resolution imaging, to be extended to tomography and to be adapted to super-resolution experiments.
Download or read book Wavelets written by John J. Benedetto and published by CRC Press. This book was released on 2021-07-29 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wavelets is a carefully organized and edited collection of extended survey papers addressing key topics in the mathematical foundations and applications of wavelet theory. The first part of the book is devoted to the fundamentals of wavelet analysis. The construction of wavelet bases and the fast computation of the wavelet transform in both continuous and discrete settings is covered. The theory of frames, dilation equations, and local Fourier bases are also presented. The second part of the book discusses applications in signal analysis, while the third part covers operator analysis and partial differential equations. Each chapter in these sections provides an up-to-date introduction to such topics as sampling theory, probability and statistics, compression, numerical analysis, turbulence, operator theory, and harmonic analysis. The book is ideal for a general scientific and engineering audience, yet it is mathematically precise. It will be an especially useful reference for harmonic analysts, partial differential equation researchers, signal processing engineers, numerical analysts, fluids researchers, and applied mathematicians.
Book Synopsis Inverse Problems in Medical Imaging and Nondestructive Testing by : Heinz W. Engl
Download or read book Inverse Problems in Medical Imaging and Nondestructive Testing written by Heinz W. Engl and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: 14 contributions present mathematical models for different imaging techniques in medicine and nondestructive testing. The underlying mathematical models are presented in a way that also newcomers in the field have a chance to understand the relation between the special applications and the mathematics needed for successfully treating these problems. The reader gets an insight into a modern field of scientific computing with applications formerly not presented in such form, leading from the basics to actual research activities.
Book Synopsis Advancing the Characterization of Neuronal Cyto-Architecture by X-ray Phase-Contrast Tomography by : Marina Eckermann
Download or read book Advancing the Characterization of Neuronal Cyto-Architecture by X-ray Phase-Contrast Tomography written by Marina Eckermann and published by Universitätsverlag Göttingen. This book was released on 2021 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Complex Motion written by Bernd Jähne and published by Springer Science & Business Media. This book was released on 2007-01-26 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-proceedings of the First International Workshop on Complex Motion, IWCM 2004, held in Schloss Reisensburg, Günzburg, Germany, in October 2004. The 17 full papers presented are fully revised to incorporate reviewers' comments and discussions at the workshop.
Book Synopsis Dynamic Systems on Measure Chains by : V. Lakshmikantham
Download or read book Dynamic Systems on Measure Chains written by V. Lakshmikantham and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: From a modelling point of view, it is more realistic to model a phenomenon by a dynamic system which incorporates both continuous and discrete times, namely, time as an arbitrary closed set of reals called time-scale or measure chain. It is therefore natural to ask whether it is possible to provide a framework which permits us to handle both dynamic systems simultaneously so that one can get some insight and a better understanding of the subtle differences of these two different systems. The answer is affirmative, and recently developed theory of dynamic systems on time scales offers the desired unified approach. In this monograph, we present the current state of development of the theory of dynamic systems on time scales from a qualitative point of view. It consists of four chapters. Chapter one develops systematically the necessary calculus of functions on time scales. In chapter two, we introduce dynamic systems on time scales and prove the basic properties of solutions of such dynamic systems. The theory of Lyapunov stability is discussed in chapter three in an appropriate setup. Chapter four is devoted to describing several different areas of investigations of dynamic systems on time scales which will provide an exciting prospect and impetus for further advances in this important area which is very new. Some important features of the monograph are as follows: It is the first book that is dedicated to a systematic development of the theory of dynamic systems on time scales which is of recent origin. It demonstrates the interplay of the two different theories, namely, the theory of continuous and discrete dynamic systems, when imbedded in one unified framework. It provides an impetus to investigate in the setup of time scales other important problems which might offer a better understanding of the intricacies of a unified study.£/LIST£ Audience: The readership of this book consists of applied mathematicians, engineering scientists, research workers in dynamic systems, chaotic theory and neural nets.
Book Synopsis Superanalysis by : Andrei Y. Khrennikov
Download or read book Superanalysis written by Andrei Y. Khrennikov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: defined as elements of Grassmann algebra (an algebra with anticom muting generators). The derivatives of these elements with respect to anticommuting generators were defined according to algebraic laws, and nothing like Newton's analysis arose when Martin's approach was used. Later, during the next twenty years, the algebraic apparatus de veloped by Martin was used in all mathematical works. We must point out here the considerable contribution made by F. A. Berezin, G 1. Kac, D. A. Leites, B. Kostant. In their works, they constructed a new division of mathematics which can naturally be called an algebraic superanalysis. Following the example of physicists, researchers called the investigations carried out with the use of commuting and anticom muting coordinates supermathematics; all mathematical objects that appeared in supermathematics were called superobjects, although, of course, there is nothing "super" in supermathematics. However, despite the great achievements in algebraic superanaly sis, this formalism could not be regarded as a generalization to the case of commuting and anticommuting variables from the ordinary Newton analysis. What is more, Schwinger's formalism was still used in practically all physical works, on an intuitive level, and physicists regarded functions of anticommuting variables as "real functions" == maps of sets and not as elements of Grassmann algebras. In 1974, Salam and Strathdee proposed a very apt name for a set of super points. They called this set a superspace.
Book Synopsis Boolean Valued Analysis by : A.G. Kusraev
Download or read book Boolean Valued Analysis written by A.G. Kusraev and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: Boolean valued analysis is a technique for studying properties of an arbitrary mathematical object by comparing its representations in two different set-theoretic models whose construction utilises principally distinct Boolean algebras. The use of two models for studying a single object is a characteristic of the so-called non-standard methods of analysis. Application of Boolean valued models to problems of analysis rests ultimately on the procedures of ascending and descending, the two natural functors acting between a new Boolean valued universe and the von Neumann universe. This book demonstrates the main advantages of Boolean valued analysis which provides the tools for transforming, for example, function spaces to subsets of the reals, operators to functionals, and vector-functions to numerical mappings. Boolean valued representations of algebraic systems, Banach spaces, and involutive algebras are examined thoroughly. Audience: This volume is intended for classical analysts seeking powerful new tools, and for model theorists in search of challenging applications of nonstandard models.
