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Fourier Phase Retrieval Problem
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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 Geometry of the Phase Retrieval Problem by : Alexander H. Barnett
Download or read book Geometry of the Phase Retrieval Problem written by Alexander H. Barnett and published by Cambridge University Press. This book was released on 2022-05-05 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a theoretical foundation and conceptual framework for the problem of recovering the phase of the Fourier transform.
Book Synopsis Fourier Ptychographic Imaging by : Guoan Zheng
Download or read book Fourier Ptychographic Imaging written by Guoan Zheng and published by Morgan & Claypool Publishers. This book was released on 2016-06-30 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book demonstrates the concept of Fourier ptychography, a new imaging technique that bypasses the resolution limit of the employed optics. In particular, it transforms the general challenge of high-throughput, high-resolution imaging from one that is coupled to the physical limitations of the optics to one that is solvable through computation. Demonstrated in a tutorial form and providing many MATLAB® simulation examples for the reader, it also discusses the experimental implementation and recent developments of Fourier ptychography. This book will be of interest to researchers and engineers learning simulation techniques for Fourier optics and the Fourier ptychography concept.
Book Synopsis Music Through Fourier Space by : Emmanuel Amiot
Download or read book Music Through Fourier Space written by Emmanuel Amiot and published by Springer. This book was released on 2016-10-26 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explains the state of the art in the use of the discrete Fourier transform (DFT) of musical structures such as rhythms or scales. In particular the author explains the DFT of pitch-class distributions, homometry and the phase retrieval problem, nil Fourier coefficients and tilings, saliency, extrapolation to the continuous Fourier transform and continuous spaces, and the meaning of the phases of Fourier coefficients. This is the first textbook dedicated to this subject, and with supporting examples and exercises this is suitable for researchers and advanced undergraduate and graduate students of music, computer science and engineering. The author has made online supplementary material available, and the book is also suitable for practitioners who want to learn about techniques for understanding musical notions and who want to gain musical insights into mathematical problems.
Book Synopsis The Fractional Fourier Transform by : Haldun M. Ozaktas
Download or read book The Fractional Fourier Transform written by Haldun M. Ozaktas and published by John Wiley & Sons. This book was released on 2001-02-08 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt: The discovery of the Fractional Fourier Transform and its role in optics and data management provides an elegant mathematical framework within which to discuss diffraction and other fundamental aspects of optical systems. This book explains how the fractional Fourier transform has allowed the generalization of the Fourier transform and the notion of the frequency transform. It will serve as the standard reference on Fourier transforms for many years to come.
Book Synopsis Image Recovery: Theory and Application by : Henry Stark
Download or read book Image Recovery: Theory and Application written by Henry Stark and published by Elsevier. This book was released on 2013-04-25 with total page 565 pages. Available in PDF, EPUB and Kindle. Book excerpt: Image Recovery: Theory and Application focuses on signal recovery and synthesis problems. This book discusses the concepts of image recovery, including regularization, the projection theorem, and the pseudoinverse operator. Comprised of 13 chapters, this volume begins with a review of the basic properties of linear vector spaces and associated operators, followed by a discussion on the Gerchberg-Papoulis algorithm. It then explores image restoration and the basic mathematical theory in image restoration problems. The reader is also introduced to the problem of obtaining artifact-free computed tomographic reconstruction. Other chapters consider the importance of Bayesian approach in the context of medical imaging. In addition, the book discusses the linear programming method, which is particularly important for images with large number of pixels with zero value. Such images are usually found in medical imaging, microscopy, electron microscopy, and astronomy. This book can be a valuable resource to materials scientists, engineers, computed tomography technologists, and astronomers.
Book Synopsis Foundations of Time-Frequency Analysis by : Karlheinz Gröchenig
Download or read book Foundations of Time-Frequency Analysis written by Karlheinz Gröchenig and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: Time-frequency analysis is a modern branch of harmonic analysis. It com prises all those parts of mathematics and its applications that use the struc ture of translations and modulations (or time-frequency shifts) for the anal ysis of functions and operators. Time-frequency analysis is a form of local Fourier analysis that treats time and frequency simultaneously and sym metrically. My goal is a systematic exposition of the foundations of time-frequency analysis, whence the title of the book. The topics range from the elemen tary theory of the short-time Fourier transform and classical results about the Wigner distribution via the recent theory of Gabor frames to quantita tive methods in time-frequency analysis and the theory of pseudodifferential operators. This book is motivated by applications in signal analysis and quantum mechanics, but it is not about these applications. The main ori entation is toward the detailed mathematical investigation of the rich and elegant structures underlying time-frequency analysis. Time-frequency analysis originates in the early development of quantum mechanics by H. Weyl, E. Wigner, and J. von Neumann around 1930, and in the theoretical foundation of information theory and signal analysis by D.
Book Synopsis Fast Fourier Transform - Algorithms and Applications by : K.R. Rao
Download or read book Fast Fourier Transform - Algorithms and Applications written by K.R. Rao and published by Springer Science & Business Media. This book was released on 2011-02-21 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an introduction to the principles of the fast Fourier transform. This book covers FFTs, frequency domain filtering, and applications to video and audio signal processing. As fields like communications, speech and image processing, and related areas are rapidly developing, the FFT as one of essential parts in digital signal processing has been widely used. Thus there is a pressing need from instructors and students for a book dealing with the latest FFT topics. This book provides thorough and detailed explanation of important or up-to-date FFTs. It also has adopted modern approaches like MATLAB examples and projects for better understanding of diverse FFTs.
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 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 Attosecond Molecular Dynamics by : Marc J J Vrakking
Download or read book Attosecond Molecular Dynamics written by Marc J J Vrakking and published by Royal Society of Chemistry. This book was released on 2018-08-31 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: Attosecond science is a new and rapidly developing research area in which molecular dynamics are studied at the timescale of a few attoseconds. Within the past decade, attosecond pump–probe spectroscopy has emerged as a powerful experimental technique that permits electron dynamics to be followed on their natural timescales. With the development of this technology, physical chemists have been able to observe and control molecular dynamics on attosecond timescales. From these observations it has been suggested that attosecond to few-femtosecond timescale charge migration may induce what has been called “post-Born-Oppenheimer dynamics”, where the nuclei respond to rapidly time-dependent force fields resulting from transient localization of the electrons. These real-time observations have spurred exciting new advances in the theoretical work to both explain and predict these novel dynamics. This book presents an overview of current theoretical work relevant to attosecond science written by theoreticians who are presently at the forefront of its development. It is a valuable reference work for anyone working in the field of attosecond science as well as those studying the subject.
Book Synopsis Linear Canonical Transforms by : John J. Healy
Download or read book Linear Canonical Transforms written by John J. Healy and published by Springer. This book was released on 2015-11-26 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a clear and accessible introduction to the essential mathematical foundations of linear canonical transforms from a signals and systems perspective. Substantial attention is devoted to how these transforms relate to optical systems and wave propagation. There is extensive coverage of sampling theory and fast algorithms for numerically approximating the family of transforms. Chapters on topics ranging from digital holography to speckle metrology provide a window on the wide range of applications. This volume will serve as a reference for researchers in the fields of image and signal processing, wave propagation, optical information processing and holography, optical system design and modeling, and quantum optics. It will be of use to graduate students in physics and engineering, as well as for scientists in other areas seeking to learn more about this important yet relatively unfamiliar class of integral transformations.
Book Synopsis Feedback Control Theory by : John C. Doyle
Download or read book Feedback Control Theory written by John C. Doyle and published by Courier Corporation. This book was released on 2013-04-09 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: An excellent introduction to feedback control system design, this book offers a theoretical approach that captures the essential issues and can be applied to a wide range of practical problems. Its explorations of recent developments in the field emphasize the relationship of new procedures to classical control theory, with a focus on single input and output systems that keeps concepts accessible to students with limited backgrounds. The text is geared toward a single-semester senior course or a graduate-level class for students of electrical engineering. The opening chapters constitute a basic treatment of feedback design. Topics include a detailed formulation of the control design program, the fundamental issue of performance/stability robustness tradeoff, and the graphical design technique of loopshaping. Subsequent chapters extend the discussion of the loopshaping technique and connect it with notions of optimality. Concluding chapters examine controller design via optimization, offering a mathematical approach that is useful for multivariable systems.
Book Synopsis A Mathematical Introduction to Compressive Sensing by : Simon Foucart
Download or read book A Mathematical Introduction to Compressive Sensing written by Simon Foucart and published by Springer Science & Business Media. This book was released on 2013-08-13 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: At the intersection of mathematics, engineering, and computer science sits the thriving field of compressive sensing. Based on the premise that data acquisition and compression can be performed simultaneously, compressive sensing finds applications in imaging, signal processing, and many other domains. In the areas of applied mathematics, electrical engineering, and theoretical computer science, an explosion of research activity has already followed the theoretical results that highlighted the efficiency of the basic principles. The elegant ideas behind these principles are also of independent interest to pure mathematicians. A Mathematical Introduction to Compressive Sensing gives a detailed account of the core theory upon which the field is build. With only moderate prerequisites, it is an excellent textbook for graduate courses in mathematics, engineering, and computer science. It also serves as a reliable resource for practitioners and researchers in these disciplines who want to acquire a careful understanding of the subject. A Mathematical Introduction to Compressive Sensing uses a mathematical perspective to present the core of the theory underlying compressive sensing.
Book Synopsis Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses by : Rick Trebino
Download or read book Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses written by Rick Trebino and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Frequency-Resolved Optical-Gating (FROG) technique has revolutionized our ability to measure and understand ultrashort laser pulses. This book contains everything you need to know to measure even the shortest, weakest, or most complex ultrashort laser pulses. Whether you're an undergrad or an advanced researcher, you'll find easy-to-understand descriptions of all the key ideas behind all the FROG techniques, all the practical details of pulse measurement, and many new directions of research. This book is not like any other scientific book. It is a lively discussion of the basic concepts. It is an advanced treatment of research-level issues.
Book Synopsis Handbook of Mathematical Methods in Imaging by : Otmar Scherzer
Download or read book Handbook of Mathematical Methods in Imaging written by Otmar Scherzer and published by Springer Science & Business Media. This book was released on 2010-11-23 with total page 1626 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Mathematical Methods in Imaging provides a comprehensive treatment of the mathematical techniques used in imaging science. The material is grouped into two central themes, namely, Inverse Problems (Algorithmic Reconstruction) and Signal and Image Processing. Each section within the themes covers applications (modeling), mathematics, numerical methods (using a case example) and open questions. Written by experts in the area, the presentation is mathematically rigorous. The entries are cross-referenced for easy navigation through connected topics. Available in both print and electronic forms, the handbook is enhanced by more than 150 illustrations and an extended bibliography. It will benefit students, scientists and researchers in applied mathematics. Engineers and computer scientists working in imaging will also find this handbook useful.
Book Synopsis A First Course in Fourier Analysis by : David W. Kammler
Download or read book A First Course in Fourier Analysis written by David W. Kammler and published by Cambridge University Press. This book was released on 2008-01-17 with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a meaningful resource for applied mathematics through Fourier analysis. It develops a unified theory of discrete and continuous (univariate) Fourier analysis, the fast Fourier transform, and a powerful elementary theory of generalized functions and shows how these mathematical ideas can be used to study sampling theory, PDEs, probability, diffraction, musical tones, and wavelets. The book contains an unusually complete presentation of the Fourier transform calculus. It uses concepts from calculus to present an elementary theory of generalized functions. FT calculus and generalized functions are then used to study the wave equation, diffusion equation, and diffraction equation. Real-world applications of Fourier analysis are described in the chapter on musical tones. A valuable reference on Fourier analysis for a variety of students and scientific professionals, including mathematicians, physicists, chemists, geologists, electrical engineers, mechanical engineers, and others.
