Download or read book Compressive Phase Retrieval written by Lei Tian (Ph. D.) and published by . This book was released on 2013 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recovering a full description of a wave from limited intensity measurements remains a central problem in optics. Optical waves oscillate too fast for detectors to measure anything but time{averaged intensities. This is unfortunate since the phase can reveal important information about the object. When the light is partially coherent, a complete description of the phase requires knowledge about the statistical correlations for each pair of points in space. Recovery of the correlation function is a much more challenging problem since the number of pairs grows much more rapidly than the number of points. In this thesis, quantitative phase imaging techniques that works for partially coherent illuminations are investigated. In order to recover the phase information with few measurements, the sparsity in each underly problem and ecient inversion methods are explored under the framework of compressed sensing. In each phase retrieval technique under study, diffraction during spatial propagation is exploited as an effective and convenient mechanism to uniformly distribute the information about the unknown signal into the measurement space. Holography is useful to record the scattered field from a sparse distribution of particles; the ability of localizing each particles using compressive reconstruction method is studied. When a thin sample is illuminated with partially coherent waves, the transport of intensity phase retrieval method is shown to be eective to recover the optical path length of the sample and remove the eect of the illumination. This technique is particularly suitable for X-ray phase imaging since it does not require a coherent source or any optical components. Compressive tomographic reconstruction, which makes full use of the priors that the sample consists of piecewise constant refractive indices, are demonstrated to make up missing data. The third technique, known as the phase space tomography (PST), addresses the correlation function recovery problem. Implementing the PST involves measuring many intensity images under spatial propagation. Experimental demonstration of a compressive reconstruction method, which finds the sparse solution by decomposing the correlation function into a few mutually uncorrelated coherent modes, is presented to produce accurate reconstruction even when the measurement suers from the 'missing cone' problem in the Fourier domain.
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.
Download or read book Evaluation of Phase Retrieval in a Compressive Computational Ghost Imaging Setup written by Juan Andrés Urrea Niño and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Ghost imaging has been developed into different setups to use the correlation properties of light to obtain the image of an object. Its computational version has been combined with Compressive Sensing algorithms to recover images with far less data than the Nyquist limit dictates. However, the retrieval in the image of certain properties of the object, such as its Fourier phase spectrum, has not been studied using ghost imaging setups. This monograph precisely presents this type of studies. Specifically, a new compressive computational ghost imaging setup is introduced, and implemented in the optical table, obtaining high quality images. Additionally, a procedure to indirectly measure and quantify the phase retrieval is proposed, explained and implemented. This procedure allows to confirm the successful recovery of phase spectrum information through compressive sensing methods in computational ghost imaging.
Download or read book Compressed Sensing and its Applications written by Holger Boche and published by Birkhäuser. This book was released on 2018-01-17 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: This contributed volume contains articles written by the plenary and invited speakers from the second international MATHEON Workshop 2015 that focus on applications of compressed sensing. Article authors address their techniques for solving the problems of compressed sensing, as well as connections to related areas like detecting community-like structures in graphs, curbatures on Grassmanians, and randomized tensor train singular value decompositions. Some of the novel applications covered include dimensionality reduction, information theory, random matrices, sparse approximation, and sparse recovery. This book is aimed at both graduate students and researchers in the areas of applied mathematics, computer science, and engineering, as well as other applied scientists exploring the potential applications for the novel methodology of compressed sensing. An introduction to the subject of compressed sensing is also provided for researchers interested in the field who are not as familiar with it.
Download or read book Optical Compressive Imaging written by Adrian Stern and published by CRC Press. This book was released on 2016-11-17 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dedicated overview of optical compressive imaging addresses implementation aspects of the revolutionary theory of compressive sensing (CS) in the field of optical imaging and sensing. It overviews the technological opportunities and challenges involved in optical design and implementation, from basic theory to optical architectures and systems for compressive imaging in various spectral regimes, spectral and hyperspectral imaging, polarimetric sensing, three-dimensional imaging, super-resolution imaging, lens-free, on-chip microscopy, and phase sensing and retrieval. The reader will gain a complete introduction to theory, experiment, and practical use for reducing hardware, shortening image scanning time, and improving image resolution as well as other performance parameters. Optics practitioners and optical system designers, electrical and optical engineers, mathematicians, and signal processing professionals will all find the book a unique trove of information and practical guidance. Delivers the first book on compressed sensing dealing with system development for a wide variety of optical imaging and sensing applications. Covers the fundamentals of CS theory, including noise and algorithms, as well as basic design approaches for data acquisition in optics. Addresses the challenges of implementing compressed sensing theory in the context of different optical imaging designs, from 3D imaging to tomography and microscopy. Provides an essential resource for the design of new and improved devices with improved image quality and shorter acquisition times. Adrian Stern, PhD, is associate professor and head of the Electro-Optical Engineering Unit at Ben-Gurion University of the Negev, Israel. He is an elected Fellow of SPIE.
Download or read book Grid independent Compressive Imaging and Fourier Phase Retrieval written by Wenjing Liao and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation is composed of two parts. In the first part techniques of band exclusion(BE) and local optimization(LO) are proposed to solve linear continuum inverse problems independently of the grid spacing. The second part is devoted to the Fourier phase retrieval problem.Many situations in optics, medical imaging and signal processing call for solutions of linear continuum inverse problems. Spectral estimation is an example among those. A commonly used method is to seek a discrete, approximate solution for the continuum problem by discretizing the problem on a finite grid, but meanwhile, a gridding error, roughly proportional to the grid spacing, arises in the discretization process. When the grid spacing is above the Rayleigh length, the gridding error can be as large as the data themselves, creating an unfavorable signal to noise ratio. To reduce the gridding error, one has to refine the grid. However, when the grid spacing is reduced below the Rayleigh length, sensing matrices become underdetermined and highly coherent, resulting in the failure of many existing compressive sensing(CS) algorithms. In order to fill the gap, we propose the techniques of BE and LO to deal with coherent sensing matrices on a fine grid. These techniques are embedded in the existing CS algorithms, such as Orthogonal Matching Pursuit(OMP) and Basis Pursuit(BP), and give rise to the modified algorithms, such as BLO-based OMP (also called BLOOMP) and BLO-based BP (also called BP-BLOT) respectively. We have proved that, under certain conditions, BLO-based OMP is capable of reconstructing sparse, widely separated objects within one Rayleigh length in bottleneck distance independent of the grid spacing. Detailed numerical comparisons with other algorithms designed for the same purpose, such as the Spectral Iterative Hard Thresholding (SIHT) and the analysis-based BP, demonstrate the superiority of BLO-based algorithms.The second part of this dissertation is mainly concerned with the Fourier phase retrieval problem: reconstructing an unknown image from its Fourier magnitude measurements. This problem arises frequently in a number of different imaging modalities including X-ray crystallography, coherent light microscopy, astronomy, etc. It is well known that traditional phasing methods have stagnation problems of outputting an image that is not fully reconstructed, due to non-convexity as well as non-absolute-uniqueness, with absolute uniqueness being referred to as uniqueness up to a constant global phase. In the phasing literature a lot of emphasis has been put on the algorithm designs or the utilization of a priori information in order to avoid stagnation. Instead, we attack the Fourier phase retrieval problem using well-designed illuminations. Specifically we explore a phasing method based on a random phase mask(RPM) that randomly modifies the phases of the original image. We demonstrate that the use of RPM in Fourier phasing not only results in an absolute uniqueness but also leads to superior numerical performances, including rapid convergence, much reduced data and noise stability. More importantly, Fourier phasing with RPM does not rely on accurate information of the phase mask. We show that nearly perfect recovery can be achieved in the case of phase-uncertain mask where one's estimates on the mask phases differ from the true mask phases within certain level. Absolute uniqueness results are generalized to the case of phase-uncertain mask, stating that under certain conditions both the image and the mask within the image support are uniquely determined up to a constant global phase with high probability. A numerical scheme alternating between the image update and the mask update is proposed to recover the image and the mask simultaneously. Our numerical simulations demonstrate that nearly perfect recovery can be achieved by RPM with high uncertainty in mask phases.
Download or read book Compressive Sensing Based Algorithms for Electronic Defence written by Amit Kumar Mishra and published by Springer. This book was released on 2016-12-22 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book details some of the major developments in the implementation of compressive sensing in radio applications for electronic defense and warfare communication use. It provides a comprehensive background to the subject and at the same time describes some novel algorithms. It also investigates application value and performance-related parameters of compressive sensing in scenarios such as direction finding, spectrum monitoring, detection, and classification.
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.
Download or read book Excursions in Harmonic Analysis Volume 4 written by Radu Balan and published by Birkhäuser. This book was released on 2015-10-20 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of contributions spanning a wide spectrum of harmonic analysis and its applications written by speakers at the February Fourier Talks from 2002 – 2013. Containing cutting-edge results by an impressive array of mathematicians, engineers and scientists in academia, industry and government, it will be an excellent reference for graduate students, researchers and professionals in pure and applied mathematics, physics and engineering. Topics covered include: Special Topics in Harmonic Analysis Applications and Algorithms in the Physical Sciences Gabor Theory RADAR and Communications: Design, Theory, and Applications The February Fourier Talks are held annually at the Norbert Wiener Center for Harmonic Analysis and Applications. Located at the University of Maryland, College Park, the Norbert Wiener Center provides a state-of- the-art research venue for the broad emerging area of mathematical engineering.
Download or read book Compressive Imaging Structure Sampling Learning written by Ben Adcock and published by Cambridge University Press. This book was released on 2021-09-16 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: Accurate, robust and fast image reconstruction is a critical task in many scientific, industrial and medical applications. Over the last decade, image reconstruction has been revolutionized by the rise of compressive imaging. It has fundamentally changed the way modern image reconstruction is performed. This in-depth treatment of the subject commences with a practical introduction to compressive imaging, supplemented with examples and downloadable code, intended for readers without extensive background in the subject. Next, it introduces core topics in compressive imaging – including compressed sensing, wavelets and optimization – in a concise yet rigorous way, before providing a detailed treatment of the mathematics of compressive imaging. The final part is devoted to recent trends in compressive imaging: deep learning and neural networks. With an eye to the next decade of imaging research, and using both empirical and mathematical insights, it examines the potential benefits and the pitfalls of these latest approaches.
Download or read book Sampling Theory written by Yonina C. Eldar and published by Cambridge University Press. This book was released on 2015-04-09 with total page 837 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive guide to sampling for engineers, covering the fundamental mathematical underpinnings together with practical engineering principles and applications.
Download or read book Information Theoretic Methods in Data Science written by Miguel R. D. Rodrigues and published by Cambridge University Press. This book was released on 2021-04-08 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first unified treatment of the interface between information theory and emerging topics in data science, written in a clear, tutorial style. Covering topics such as data acquisition, representation, analysis, and communication, it is ideal for graduate students and researchers in information theory, signal processing, and machine learning.
Download or read book Regularization Optimization Kernels and Support Vector Machines written by Johan A.K. Suykens and published by CRC Press. This book was released on 2014-10-23 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: Regularization, Optimization, Kernels, and Support Vector Machines offers a snapshot of the current state of the art of large-scale machine learning, providing a single multidisciplinary source for the latest research and advances in regularization, sparsity, compressed sensing, convex and large-scale optimization, kernel methods, and support vecto
Download or read book Compressive Sensing for the Photonic Mixer Device written by Miguel Heredia Conde and published by Springer. This book was released on 2017-04-18 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: Miguel Heredia Conde aims at finding novel ways to fit the valuable mathematical results of the Compressive Sensing (CS) theory to the specific case of the Photonic Mixer Device (PMD).To this end, methods are presented that take profit of the sparsity of the signals gathered by PMD sensors. In his research, the author reveals that CS enables outstanding tradeoffs between sensing effort and depth error reduction or resolution enhancement.
Download or read book Compressed Sensing in Information Processing written by Gitta Kutyniok and published by Springer Nature. This book was released on 2022-10-20 with total page 549 pages. Available in PDF, EPUB and Kindle. Book excerpt: This contributed volume showcases the most significant results obtained from the DFG Priority Program on Compressed Sensing in Information Processing. Topics considered revolve around timely aspects of compressed sensing with a special focus on applications, including compressed sensing-like approaches to deep learning; bilinear compressed sensing - efficiency, structure, and robustness; structured compressive sensing via neural network learning; compressed sensing for massive MIMO; and security of future communication and compressive sensing.
Download or read book Phase Retrieval in the High dimensional Regime written by Milad Bakhshizadeh and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose an iterative recovery method that can take advantage of any prior knowledge about the signal that is given as a compression code to efficiently solve the problem. We rigorously analyze the performance of our proposed method and provide extensive simulations to demonstrate its state-of-the-art performance.
Download or read book Compressive Sensing of Earth Observations written by C.H. Chen and published by CRC Press. This book was released on 2017-05-25 with total page 727 pages. Available in PDF, EPUB and Kindle. Book excerpt: Future remote sensing systems will make extensive use of Compressive Sensing (CS) as it becomes more integrated into the system design with increased high resolution sensor developments and the rising earth observation data generated each year. Written by leading experts in the field Compressive Sensing of Earth Observations provides a comprehensive and balanced coverage of the theory and applications of CS in all aspects of earth observations. This work covers a myriad of practical aspects such as the use of CS in detection of human vital signs in a cluttered environment and the corresponding modeling of rib-cage breathing. Readers are also presented with three different applications of CS to the ISAR imaging problem, which includes image reconstruction from compressed data, resolution enhancement, and image reconstruction from incomplete data.
