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Compressed sensing (Telecommunication) --- Biosensing Techniques --- Medical innovations. --- Innovations, Medical --- Medicine --- Medical technology --- Technological innovations --- Compressive sensing (Telecommunication) --- Sensing, Compressed (Telecommunication) --- Sparse sampling (Telecommunication) --- Signal processing --- Innovations
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This first book on greedy approximation gives a systematic presentation of the fundamental results. It also contains an introduction to two hot topics in numerical mathematics: learning theory and compressed sensing. Nonlinear approximation is becoming increasingly important, especially since two types are frequently employed in applications: adaptive methods are used in PDE solvers, while m-term approximation is used in image/signal/data processing, as well as in the design of neural networks. The fundamental question of nonlinear approximation is how to devise good constructive methods (algorithms) and recent results have established that greedy type algorithms may be the solution. The author has drawn on his own teaching experience to write a book ideally suited to graduate courses. The reader does not require a broad background to understand the material. Important open problems are included to give students and professionals alike ideas for further research.
Approximation theory. --- Theory of approximation --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems --- Compressed sensing (Telecommunication) --- Compressive sensing (Telecommunication) --- Sensing, Compressed (Telecommunication) --- Sparse sampling (Telecommunication) --- Signal processing
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Compressed sensing is an exciting, rapidly growing field, attracting considerable attention in electrical engineering, applied mathematics, statistics and computer science. This book provides the first detailed introduction to the subject, highlighting recent theoretical advances and a range of applications, as well as outlining numerous remaining research challenges. After a thorough review of the basic theory, many cutting-edge techniques are presented, including advanced signal modeling, sub-Nyquist sampling of analog signals, non-asymptotic analysis of random matrices, adaptive sensing, greedy algorithms and use of graphical models. All chapters are written by leading researchers in the field, and consistent style and notation are utilized throughout. Key background information and clear definitions make this an ideal resource for researchers, graduate students and practitioners wanting to join this exciting research area. It can also serve as a supplementary textbook for courses on computer vision, coding theory, signal processing, image processing and algorithms for efficient data processing.
Signal processing. --- Wavelets (Mathematics). --- Signal processing --- Wavelets (Mathematics) --- Compressed sensing (Telecommunication) --- Compressive sensing (Telecommunication) --- Sensing, Compressed (Telecommunication) --- Sparse sampling (Telecommunication) --- Wavelet analysis --- Harmonic analysis --- Processing, Signal --- Information measurement --- Signal theory (Telecommunication) --- telecommunicatie
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Optical fiber communication --- Compressed sensing (Telecommunication) --- Quality control. --- Compressive sensing (Telecommunication) --- Sensing, Compressed (Telecommunication) --- Sparse sampling (Telecommunication) --- Signal processing --- Fiber-optic communication --- Fiber optic telecommunication --- Optical communications --- Fiber optics
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This book presents the state of the art in sparse and multiscale image and signal processing, covering linear multiscale transforms, such as wavelet, ridgelet, or curvelet transforms, and non-linear multiscale transforms based on the median and mathematical morphology operators. Recent concepts of sparsity and morphological diversity are described and exploited for various problems such as denoising, inverse problem regularization, sparse signal decomposition, blind source separation, and compressed sensing. This book weds theory and practice in examining applications in areas such as astronomy, biology, physics, digital media, and forensics. A final chapter explores a paradigm shift in signal processing, showing that previous limits to information sampling and extraction can be overcome in very significant ways. Matlab and IDL code accompany these methods and applications to reproduce the experiments and illustrate the reasoning and methodology of the research are available for download at the associated web site.
Transformations (Mathematics) --- Signal processing. --- Image processing. --- Sparse matrices. --- Wavelets (Mathematics) --- Wavelet analysis --- Harmonic analysis --- Spare matrix techniques --- Matrices --- Pictorial data processing --- Picture processing --- Processing, Image --- Imaging systems --- Optical data processing --- Processing, Signal --- Information measurement --- Signal theory (Telecommunication) --- Algorithms --- Differential invariants --- Geometry, Differential --- Compressed sensing (Telecommunication) --- Compressive sensing (Telecommunication) --- Sensing, Compressed (Telecommunication) --- Sparse sampling (Telecommunication) --- Signal processing
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This book describes algorithmic methods and hardware implementations that aim to help realize the promise of Compressed Sensing (CS), namely the ability to reconstruct high-dimensional signals from a properly chosen low-dimensional “portrait”. The authors describe a design flow and some low-resource physical realizations of sensing systems based on CS. They highlight the pros and cons of several design choices from a pragmatic point of view, and show how a lightweight and mild but effective form of adaptation to the target signals can be the key to consistent resource saving. The basic principle of the devised design flow can be applied to almost any CS-based sensing system, including analog-to-information converters, and has been proven to fit an extremely diverse set of applications. Many practical aspects required to put a CS-based sensing system to work are also addressed, including saturation, quantization, and leakage phenomena.
Engineering. --- Electronics. --- Microelectronics. --- Electronic circuits. --- Circuits and Systems. --- Signal, Image and Speech Processing. --- Electronics and Microelectronics, Instrumentation. --- Compressed sensing (Telecommunication) --- Compressive sensing (Telecommunication) --- Sensing, Compressed (Telecommunication) --- Sparse sampling (Telecommunication) --- Signal processing --- Systems engineering. --- Electrical engineering --- Physical sciences --- Engineering systems --- System engineering --- Engineering --- Industrial engineering --- System analysis --- Design and construction --- Signal processing. --- Image processing. --- Speech processing systems. --- Microminiature electronic equipment --- Microminiaturization (Electronics) --- Electronics --- Microtechnology --- Semiconductors --- Miniature electronic equipment --- Computational linguistics --- Electronic systems --- Information theory --- Modulation theory --- Oral communication --- Speech --- Telecommunication --- Singing voice synthesizers --- Pictorial data processing --- Picture processing --- Processing, Image --- Imaging systems --- Optical data processing --- Processing, Signal --- Information measurement --- Signal theory (Telecommunication) --- Electron-tube circuits --- Electric circuits --- Electron tubes
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The objective of this 5th edition of the book, as with the prior editions, is to teach through images a practical approach to magnetic resonance (MR) physics and image quality. Unlike other texts covering this topic, the focus is on clinical images rather than equations. A practical approach to MR physics is developed through images, emphasizing knowledge of fundamentals important to achieve high image quality. Pulse diagrams are also included, which many at first find difficult to understand. Readers are encouraged to glance at these as they go through the text. With time and repetition, as a reader progresses through the book, the value of these and the knowledge thus available will become evident (and the diagrams themselves easier to understand). The text is organized into concise chapters, each discussing an important point relevant to clinical MR and illustrated largely with images from routine patient exams. The topics covered encompass the breadth of the field, from imaging basics and pulse sequences to advanced topics including contrast-enhanced MR angiography, spectroscopy, perfusion and advanced parallel imaging/data sparsity techniques. Discussion of the latest hardware and software innovations, for example next generation low field MR, deep learning, MR-PET, 7 T, interventional MR, 4D flow, CAIPIRINHA, spiral techniques, radial acquisition, simultaneous multislice, compressed sensing and MR fingerprinting, is included because these topics are critical to current clinical practice as well as to future advances. Included in the fifth edition are a large number of new topics, keeping the text up to date in this increasingly complex field. The text has also been thoroughly revised to include additional relevant clinical images, to improve the clarity of descriptions, and to increase the depth of content. The book is highly recommended for radiologists, physicists, and technologists interested in the background of image acquisition used in standard as well as specialized clinical settings. .
Magnetic resonance imaging. --- Medical radiology. --- Compressed sensing (Telecommunication) --- Compressive sensing (Telecommunication) --- Sensing, Compressed (Telecommunication) --- Sparse sampling (Telecommunication) --- Signal processing --- Clinical radiology --- Radiology, Medical --- Radiology (Medicine) --- Medical physics --- Clinical magnetic resonance imaging --- Diagnostic magnetic resonance imaging --- Functional magnetic resonance imaging --- Imaging, Magnetic resonance --- Medical magnetic resonance imaging --- MR imaging --- MRI (Magnetic resonance imaging) --- NMR imaging --- Nuclear magnetic resonance --- Nuclear magnetic resonance imaging --- Cross-sectional imaging --- Diagnostic imaging --- Diagnostic use --- Radiology. --- Medical physics. --- Neurology. --- Nervous system --- Medical Physics. --- Neurosurgery. --- Surgery. --- Nerves --- Neurosurgery --- Medicine --- Neuropsychiatry --- Health physics --- Health radiation physics --- Medical radiation physics --- Radiotherapy physics --- Radiation therapy physics --- Biophysics --- Physics --- Radiological physics --- Radiation --- Surgery --- Diseases
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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. Key features include: · The first textbook completely devoted to the topic of compressive sensing · Comprehensive treatment of the subject, including background material from probability theory, detailed proofs of the main theorems, and an outline of possible applications · Numerous exercises designed to help students understand the material · An extensive bibliography with over 500 references that guide researchers through the literature With only moderate prerequisites, A Mathematical Introduction to Compressive Sensing 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.
Linear integrated circuits. --- Mathematics. --- Signal processing -- Digital techniques -- Mathematics. --- Signal processing -- Digital techniques. --- Signal processing --- Compressed sensing (Telecommunication) --- Mathematics --- Physical Sciences & Mathematics --- Mathematics - General --- Digital techniques --- Compressive sensing (Telecommunication) --- Sensing, Compressed (Telecommunication) --- Sparse sampling (Telecommunication) --- Computer science --- Functional analysis. --- Computer mathematics. --- Electrical engineering. --- Computational Science and Engineering. --- Signal, Image and Speech Processing. --- Math Applications in Computer Science. --- Communications Engineering, Networks. --- Functional Analysis. --- Electric engineering --- Engineering --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Math --- Science --- Computer science. --- Telecommunication. --- Electric communication --- Mass communication --- Telecom --- Telecommunication industry --- Telecommunications --- Communication --- Information theory --- Telecommuting --- Informatics --- Signal processing. --- Image processing. --- Speech processing systems. --- Computer science—Mathematics. --- Computational linguistics --- Electronic systems --- Modulation theory --- Oral communication --- Speech --- Telecommunication --- Singing voice synthesizers --- Processing, Signal --- Information measurement --- Signal theory (Telecommunication) --- Pictorial data processing --- Picture processing --- Processing, Image --- Imaging systems --- Optical data processing
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Reconstructing or approximating objects from seemingly incomplete information is a frequent challenge in mathematics, science, and engineering. A multitude of tools designed to recover hidden information are based on Shannon’s classical sampling theorem, a central pillar of Sampling Theory. The growing need to efficiently obtain precise and tailored digital representations of complex objects and phenomena requires the maturation of available tools in Sampling Theory as well as the development of complementary, novel mathematical theories. Today, research themes such as Compressed Sensing and Frame Theory re-energize the broad area of Sampling Theory. This volume illustrates the renaissance that the area of Sampling Theory is currently experiencing. It touches upon trendsetting areas such as Compressed Sensing, Finite Frames, Parametric Partial Differential Equations, Quantization, Finite Rate of Innovation, System Theory, as well as sampling in Geometry and Algebraic Topology.
Mathematical Theory --- Computer Science --- Engineering & Applied Sciences --- Mathematics --- Physical Sciences & Mathematics --- Mathematical statistics --- Compressed sensing (Telecommunication) --- Compressive sensing (Telecommunication) --- Sensing, Compressed (Telecommunication) --- Sparse sampling (Telecommunication) --- Mathematics. --- Approximation theory. --- Functions of complex variables. --- Information theory. --- Applied mathematics. --- Engineering mathematics. --- Information and Communication, Circuits. --- Signal, Image and Speech Processing. --- Approximations and Expansions. --- Appl.Mathematics/Computational Methods of Engineering. --- Functions of a Complex Variable. --- Signal processing --- Mathematical and Computational Engineering. --- Complex variables --- Elliptic functions --- Functions of real variables --- Engineering --- Engineering analysis --- Mathematical analysis --- Math --- Science --- Signal processing. --- Image processing. --- Speech processing systems. --- Theory of approximation --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems --- Computational linguistics --- Electronic systems --- Information theory --- Modulation theory --- Oral communication --- Speech --- Telecommunication --- Singing voice synthesizers --- Pictorial data processing --- Picture processing --- Processing, Image --- Imaging systems --- Optical data processing --- Processing, Signal --- Information measurement --- Signal theory (Telecommunication) --- Communication theory --- Communication --- Cybernetics
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