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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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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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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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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. Contents Phase-Shift-Based Time-of-Flight Imaging Systems Fundamentals of Compressive Sensing High Resolution Characterization of PMD Pixels Compressive Sensing in Spatial and Time-Frequency Domains CS-PMD: A Compressive Sensing ToF Camera based on the Photonic Mixer Device Target Groups< Lecturers and students of computer science, electronic engineering and robotics Researchers and trainees working in application areas where depth sensing is required The Author Dr. Miguel Heredia Conde studied industrial engineering with specialization in automation and electronics at the University of Vigo, Spain. He defended his PhD thesis in engineering at the University of Siegen, Faculty of Science and Technology, Germany. There, he is currently head of the research group on compressive sensing for time-of-flight sensors at the Center for Sensor Systems (ZESS).

Computer science. --- Data structures (Computer science). --- Computer graphics. --- Applied mathematics. --- Engineering mathematics. --- Computer Science. --- Computer Imaging, Vision, Pattern Recognition and Graphics. --- Data Structures, Cryptology and Information Theory. --- Appl.Mathematics/Computational Methods of Engineering. --- Compressed sensing (Telecommunication) --- Compressive sensing (Telecommunication) --- Sensing, Compressed (Telecommunication) --- Sparse sampling (Telecommunication) --- Signal processing --- Computer vision. --- Data structures (Computer scienc. --- Data Structures and Information Theory. --- Mathematical and Computational Engineering. --- Data structures (Computer science) --- Information structures (Computer science) --- Structures, Data (Computer science) --- Structures, Information (Computer science) --- Electronic data processing --- File organization (Computer science) --- Abstract data types (Computer science) --- Engineering --- Engineering analysis --- Mathematical analysis --- Machine vision --- Vision, Computer --- Artificial intelligence --- Image processing --- Pattern recognition systems --- Mathematics --- Optical data processing. --- Optical computing --- Visual data processing --- Bionics --- Integrated optics --- Photonics --- Computers --- Optical equipment

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This thesis reports on sparsity-based multipath exploitation methods for through-the-wall radar imaging. Multipath creates ambiguities in the measurements provoking unwanted ghost targets in the image. This book describes sparse reconstruction methods that are not only suppressing the ghost targets, but using multipath to one’s advantage. With adopting the compressive sensing principle, fewer measurements are required for image reconstruction as compared to conventional techniques. The book describes the development of a comprehensive signal model and some associated reconstruction methods that can deal with many relevant scenarios, such as clutter from building structures, secondary reflections from interior walls, as well as stationary and moving targets, in urban radar imaging. The described methods are evaluated here using simulated as well as measured data from semi-controlled laboratory experiments.

Compressed sensing (Telecommunication) --- Engineering. --- Image processing. --- Remote sensing. --- Signal, Image and Speech Processing. --- Optics, Lasers, Photonics, Optical Devices. --- Remote Sensing/Photogrammetry. --- Image Processing and Computer Vision. --- Computer vision. --- Machine vision --- Vision, Computer --- Artificial intelligence --- Image processing --- Pattern recognition systems --- Signal processing. --- Speech processing systems. --- Lasers. --- Photonics. --- Optical data processing. --- Optical computing --- Visual data processing --- Bionics --- Electronic data processing --- Integrated optics --- Photonics --- Computers --- Remote-sensing imagery --- Remote sensing systems --- Remote terrain sensing --- Sensing, Remote --- Terrain sensing, Remote --- Aerial photogrammetry --- Aerospace telemetry --- Detectors --- Space optics --- New optics --- Optics --- Light amplification by stimulated emission of radiation --- Masers, Optical --- Optical masers --- Light amplifiers --- Light sources --- Optoelectronic devices --- Nonlinear optics --- Optical parametric oscillators --- 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) --- Optical equipment --- Compressive sensing (Telecommunication) --- Sensing, Compressed (Telecommunication) --- Sparse sampling (Telecommunication) --- Signal processing