A Mathematical Introduction to Compressive Sensing
A Mathematical Introduction to Compressive Sensing

Author: Simon Foucart

Publisher: Springer Science & Business Media

Published: 2013-08-13

Total Pages: 634

ISBN-13: 0817649484

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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. 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.

An Introduction to Compressed Sensing
An Introduction to Compressed Sensing

Author: M. Vidyasagar

Publisher: SIAM

Published: 2019-12-03

Total Pages: 354

ISBN-13: 161197612X

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Compressed sensing is a relatively recent area of research that refers to the recovery of high-dimensional but low-complexity objects from a limited number of measurements. The topic has applications to signal/image processing and computer algorithms, and it draws from a variety of mathematical techniques such as graph theory, probability theory, linear algebra, and optimization. The author presents significant concepts never before discussed as well as new advances in the theory, providing an in-depth initiation to the field of compressed sensing. An Introduction to Compressed Sensing contains substantial material on graph theory and the design of binary measurement matrices, which is missing in recent texts despite being poised to play a key role in the future of compressed sensing theory. It also covers several new developments in the field and is the only book to thoroughly study the problem of matrix recovery. The book supplies relevant results alongside their proofs in a compact and streamlined presentation that is easy to navigate. The core audience for this book is engineers, computer scientists, and statisticians who are interested in compressed sensing. Professionals working in image processing, speech processing, or seismic signal processing will also find the book of interest.

Data-Driven Science and Engineering
Data-Driven Science and Engineering

Author: Steven L. Brunton

Publisher: Cambridge University Press

Published: 2022-05-05

Total Pages: 615

ISBN-13: 1009098489

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A textbook covering data-science and machine learning methods for modelling and control in engineering and science, with Python and MATLAB®.

Compressed Sensing & Sparse Filtering
Compressed Sensing & Sparse Filtering

Author: Avishy Y. Carmi

Publisher: Springer Science & Business Media

Published: 2013-09-13

Total Pages: 505

ISBN-13: 364238398X

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This book is aimed at presenting concepts, methods and algorithms ableto cope with undersampled and limited data. One such trend that recently gained popularity and to some extent revolutionised signal processing is compressed sensing. Compressed sensing builds upon the observation that many signals in nature are nearly sparse (or compressible, as they are normally referred to) in some domain, and consequently they can be reconstructed to within high accuracy from far fewer observations than traditionally held to be necessary. Apart from compressed sensing this book contains other related approaches. Each methodology has its own formalities for dealing with such problems. As an example, in the Bayesian approach, sparseness promoting priors such as Laplace and Cauchy are normally used for penalising improbable model variables, thus promoting low complexity solutions. Compressed sensing techniques and homotopy-type solutions, such as the LASSO, utilise l1-norm penalties for obtaining sparse solutions using fewer observations than conventionally needed. The book emphasizes on the role of sparsity as a machinery for promoting low complexity representations and likewise its connections to variable selection and dimensionality reduction in various engineering problems. This book is intended for researchers, academics and practitioners with interest in various aspects and applications of sparse signal processing.

Handbook of Mathematical Methods in Imaging
Handbook of Mathematical Methods in Imaging

Author: Otmar Scherzer

Publisher: Springer Science & Business Media

Published: 2010-11-23

Total Pages: 1626

ISBN-13: 0387929193

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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.

Compressed Sensing
Compressed Sensing

Author: Yonina C. Eldar

Publisher: Cambridge University Press

Published: 2012-05-17

Total Pages: 557

ISBN-13: 1107394392

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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 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.

Compressed Sensing in Radar Signal Processing
Compressed Sensing in Radar Signal Processing

Author: Antonio De Maio

Publisher: Cambridge University Press

Published: 2019-10-17

Total Pages: 381

ISBN-13: 110857694X

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Learn about the most recent theoretical and practical advances in radar signal processing using tools and techniques from compressive sensing. Providing a broad perspective that fully demonstrates the impact of these tools, the accessible and tutorial-like chapters cover topics such as clutter rejection, CFAR detection, adaptive beamforming, random arrays for radar, space-time adaptive processing, and MIMO radar. Each chapter includes coverage of theoretical principles, a detailed review of current knowledge, and discussion of key applications, and also highlights the potential benefits of using compressed sensing algorithms. A unified notation and numerous cross-references between chapters make it easy to explore different topics side by side. Written by leading experts from both academia and industry, this is the ideal text for researchers, graduate students and industry professionals working in signal processing and radar.

Compressed Sensing Magnetic Resonance Image Reconstruction Algorithms
Compressed Sensing Magnetic Resonance Image Reconstruction Algorithms

Author: Bhabesh Deka

Publisher: Springer

Published: 2018-12-29

Total Pages: 133

ISBN-13: 9811335974

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This book presents a comprehensive review of the recent developments in fast L1-norm regularization-based compressed sensing (CS) magnetic resonance image reconstruction algorithms. Compressed sensing magnetic resonance imaging (CS-MRI) is able to reduce the scan time of MRI considerably as it is possible to reconstruct MR images from only a few measurements in the k-space; far below the requirements of the Nyquist sampling rate. L1-norm-based regularization problems can be solved efficiently using the state-of-the-art convex optimization techniques, which in general outperform the greedy techniques in terms of quality of reconstructions. Recently, fast convex optimization based reconstruction algorithms have been developed which are also able to achieve the benchmarks for the use of CS-MRI in clinical practice. This book enables graduate students, researchers, and medical practitioners working in the field of medical image processing, particularly in MRI to understand the need for the CS in MRI, and thereby how it could revolutionize the soft tissue imaging to benefit healthcare technology without making major changes in the existing scanner hardware. It would be particularly useful for researchers who have just entered into the exciting field of CS-MRI and would like to quickly go through the developments to date without diving into the detailed mathematical analysis. Finally, it also discusses recent trends and future research directions for implementation of CS-MRI in clinical practice, particularly in Bio- and Neuro-informatics applications.

Compressive Imaging: Structure, Sampling, Learning
Compressive Imaging: Structure, Sampling, Learning

Author: Ben Adcock

Publisher: Cambridge University Press

Published: 2021-08-31

Total Pages: 300

ISBN-13: 9781108421614

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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.

Compressed Sensing for Engineers
Compressed Sensing for Engineers

Author: Angshul Majumdar

Publisher: CRC Press

Published: 2018-12-07

Total Pages: 225

ISBN-13: 1351261347

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Compressed Sensing (CS) in theory deals with the problem of recovering a sparse signal from an under-determined system of linear equations. The topic is of immense practical significance since all naturally occurring signals can be sparsely represented in some domain. In recent years, CS has helped reduce scan time in Magnetic Resonance Imaging (making scans more feasible for pediatric and geriatric subjects) and has also helped reduce the health hazard in X-Ray Computed CT. This book is a valuable resource suitable for an engineering student in signal processing and requires a basic understanding of signal processing and linear algebra. Covers fundamental concepts of compressed sensing Makes subject matter accessible for engineers of various levels Focuses on algorithms including group-sparsity and row-sparsity, as well as applications to computational imaging, medical imaging, biomedical signal processing, and machine learning Includes MATLAB examples for further development