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Author : Christopher C. Wackerman
Publisher :
ISBN 13 :
Total Pages : 332 pages
Book Rating : 4.3/5 (91 download)
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:
Author : Tim Salditt
Publisher : Springer Nature
ISBN 13 : 3030344134
Total Pages : 634 pages
Book Rating : 4.0/5 (33 download)
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.
Author : Rolando III. Perez
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (126 download)
Download or read book Applications of Complex Analysis to the Phase Retrieval Problem written by Rolando III. Perez and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of phase retrieval involves the recovery of a function f in some functionspace from given data about the magnitude of |f| (phaseless information) and other assumptions on f, where these other assumptions can be in terms of some transform of f. Phase retrieval problems are widely studied because of their physical applications in fields of science and engineering.In this thesis, our central objective is to apply complex analytic tools to determine the solutions and investigate the stability of certain phase retrieval problems. Firstly, we solve the phase retrieval problem for wide-band signals, which are functions with mildly decreasing Fourier transforms. To do so, we first translate the problem to functions in the Hardy spaces on the disc via a conformal bijection, and take advantage of the inner-outer factorization. We also consider the same problem coupled with additional magnitude constraints, and determine if these constraints force uniqueness of the solution. Secondly, we extend some uniqueness results on the phase retrieval problem on the Hardy space on the disc to more general situations. More precisely, we show that certain holomorphic functions are uniquely determined by their moduli on two intersecting segments or on two concentric circles. Finally, we investigate the effect of zero-flipping on the stability of the phase retrieval problem for functions in the Paley-Wiener class, where zero-flipping refers to the replacement of zeros by their complex conjugates. We represent zero-flipping as an operator, and use its Fourier analytic properties to show our stability results.
Author :
Publisher :
ISBN 13 :
Total Pages : 672 pages
Book Rating : 4.:/5 (318 download)
Download or read book Journal of the Optical Society of America written by and published by . This book was released on 2004 with total page 672 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : David Aaron Barmherzig
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (11 download)
Download or read book The Phase Retrieval Problem written by David Aaron Barmherzig and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The phase retrieval problem is an inverse problem which consists of recovering a signal from a set of squared magnitude measurements. One version of this problem, often known as Fourier phase retrieval, arises ubiquitously in scientific imaging fields (such as diffraction imaging, crystallography, and optics, etc.) where one seeks to recover an image or signal from squared magnitude measurements of its Fourier transform. Another version, known as Gaussian phase retrieval, is manifested as the study of solving random systems of quadratic equations, and constitutes an important problem in the field of nonconvex optimization. The first part of this thesis introduces a general mathematical framework for the holographic phase retrieval problem. In this problem, which arises in holographic coherent diffraction imaging, a "reference" portion of the signal to be recovered via (Fourier) phase retrieval is a priori known from experimental design. A general formula is also derived for the expected recovery error when the measurement data is corrupted by Poisson shot noise. This facilitates an optimization perspective towards reference design and analysis, which is then employed towards quantifying the performance of various known reference choices. Based on insights gained from these results, a new "dual-reference" design is proposed which consists of two reference portions - being "block" and "pinhole" shaped regions - adjacent to the imaging specimen. Expected error analysis on data following a Poisson shot noise model shows that the dual-reference scheme produces uniformly superior performance over the leading single-reference schemes. Numerical experiments on simulated data corroborate these theoretical results, and demonstrate the advantage of the dual-reference design. Based on this work, a prototype experiment for holographic coherent diffraction imaging using a dual-reference has been designed at the SLAC National Accelerator Laboratory. The second part studies the one-dimensional Fourier phase retrieval problem, as well as the closely related spectral factorization problem. In its first chapter, a comprehensive exposition of the problem theory is provided. This includes a full characterization of its general nonuniqueness, as well as the special cases for which unique solutions exists. In the second chapter, a semidefinite programming formulation is derived for the Fourier phase retrieval problem. It is shown that this approach provides guaranteed recovery whenever there exists a unique phase retrieval solution. A correspondence is also established between solutions of the phase retrieval SDP, and sum-of-squares decompositions of Laurent and trigonometric polynomials. In the third chapter, a least-squares formulation is presented for the one-dimensional Fourier phase retrieval and spectral factorization problems. This formulation allows for the successful implementation of numerous first- and second-order optimization methods. In the third part, a biconvex formulation of the Gaussian phase retrieval problem is introduced. This allows for alternating-projection algorithms, such as ADMM and block coordinate descent, to be successfully applied to Gaussian phase retrieval. Both theoretical guarantees and numerical simulations demonstrate the success of these methods.
Author : N.E. Hurt
Publisher : Springer Science & Business Media
ISBN 13 : 9781402003370
Total Pages : 328 pages
Book Rating : 4.0/5 (33 download)
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.
Author :
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ISBN 13 :
Total Pages : 776 pages
Book Rating : 4.F/5 ( download)
Download or read book Dissertation Abstracts International written by and published by . This book was released on 1995 with total page 776 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Yaocheng Tian
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (141 download)
Download or read book Fourier Phase Retrieval Problem written by Yaocheng Tian and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher : Academic Press
ISBN 13 : 0080577598
Total Pages : 353 pages
Book Rating : 4.0/5 (85 download)
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 353 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.
Author : Peter Ebenfelt
Publisher :
ISBN 13 :
Total Pages : 48 pages
Book Rating : 4.:/5 (186 download)
Download or read book Aspects of the Phase Retrieval Problem of Fourier Analysis written by Peter Ebenfelt and published by . This book was released on 1990 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Karlheinz Gröchenig
Publisher : Springer Science & Business Media
ISBN 13 : 1461200032
Total Pages : 367 pages
Book Rating : 4.4/5 (612 download)
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.
Author : Michael A Fiddy
Publisher : CRC Press
ISBN 13 : 146656959X
Total Pages : 242 pages
Book Rating : 4.4/5 (665 download)
Download or read book Introduction to Imaging from Scattered Fields written by Michael A Fiddy and published by CRC Press. This book was released on 2014-11-10 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Obtain the Best Estimate of a Strongly Scattering Object from Limited Scattered Field DataIntroduction to Imaging from Scattered Fields presents an overview of the challenging problem of determining information about an object from measurements of the field scattered from that object. It covers widely used approaches to recover information about th
Author : Diling Zhu
Publisher : Stanford University
ISBN 13 :
Total Pages : 124 pages
Book Rating : 4.F/5 ( download)
Download or read book Lensless Holography Methods for Soft X-ray Resonant Coherent Imaging written by Diling Zhu and published by Stanford University. This book was released on 2010 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: The ability to interpret and inverse x-ray diffraction patterns from crystals has largely shaped our understanding of the structure of matter. However, structure determination of noncrystalline objects from their diffraction patterns is a much more difficult task. The dramatic increase in available coherent x-ray photon flux over the past decade has made possible a technique known as lensless coherent diffractive imaging (CDI), that addresses exactly this problem. The central question around CDI is the so-called phase problem: upon detection of the diffraction intensity, the phase information of the diffracted wave is inevitably lost. Generally, the phase problem is approached using iterative phase retrieval algorithms. Holographic methods, through interference with reference diffractions, encode the phase information directly inside the measured x-ray holograms, and are therefore able to avoid the stagnation and uniqueness problems commonly encountered by the iterative algorithms. This dissertation discusses two novel holographic methods for coherent lensless imaging using resonant soft x-rays. The first part focuses on generalizing the multiple-wavelength anomalous diffraction technique, a highly successful method for solving the crystal structures of biomacromolecules, into a multiple-wavelength holography technique for nanoscale resonant x-ray imaging. Using this method I show element specific reconstructions of nanoparticles and magnetization distribution in magnetic thin films with sub 50 nm resolution. The second part discusses progress in X-ray Fourier holography, an ultrafast lensless imaging platform that can be used with the upcoming x-ray free electron lasers. In particular, I will present experiments using two novel types of extended reference structures that bring the resolution beyond the precision of reference fabrication, previously regarded as the resolution limit for x-ray Fourier transform holography. Finally, future applications of holographic methods, especially experimental considerations for time-resolved studies of nanostructures using X-FELs, will be discussed.
Author : Joachim Frank
Publisher : Springer Science & Business Media
ISBN 13 : 1475721633
Total Pages : 398 pages
Book Rating : 4.4/5 (757 download)
Download or read book Electron Tomography written by Joachim Frank and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique resource details the theory, working methods, and applications of electron tomographic techniques for imaging asymmetric, noncrystalline biological specimens.
Author : Andrea Vedaldi
Publisher : Springer Nature
ISBN 13 : 3030585778
Total Pages : 501 pages
Book Rating : 4.0/5 (35 download)
Download or read book Computer Vision – ECCV 2020 written by Andrea Vedaldi and published by Springer Nature. This book was released on 2020-09-23 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 30-volume set, comprising the LNCS books 12346 until 12375, constitutes the refereed proceedings of the 16th European Conference on Computer Vision, ECCV 2020, which was planned to be held in Glasgow, UK, during August 23-28, 2020. The conference was held virtually due to the COVID-19 pandemic. The 1360 revised papers presented in these proceedings were carefully reviewed and selected from a total of 5025 submissions. The papers deal with topics such as computer vision; machine learning; deep neural networks; reinforcement learning; object recognition; image classification; image processing; object detection; semantic segmentation; human pose estimation; 3d reconstruction; stereo vision; computational photography; neural networks; image coding; image reconstruction; object recognition; motion estimation.
Author : Haldun M. Ozaktas
Publisher : John Wiley & Sons
ISBN 13 :
Total Pages : 546 pages
Book Rating : 4.F/5 ( download)
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.
Author : Jinghua Guo
Publisher : John Wiley & Sons
ISBN 13 : 3527632301
Total Pages : 279 pages
Book Rating : 4.5/5 (276 download)
Download or read book X-Rays in Nanoscience written by Jinghua Guo and published by John Wiley & Sons. This book was released on 2011-09-22 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: An up-to-date overview of the different x-ray based methods in the hot fields of nanoscience and nanotechnology, including methods for imaging nanomaterials, as well as for probing the electronic structure of nanostructured materials in order to investigate their different properties. Written by authors at one of the world's top facilities working with these methods, this monograph presents and discusses techniques and applications in the fields of x-ray scattering, spectroscopy and microscope imaging. The resulting systematic collection of these advanced tools will benefit graduate students, postdocs as well as professional researchers.
