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.


Sampling Theory

Sampling Theory

Author: Yonina C. Eldar

Publisher: Cambridge University Press

Published: 2015-04-09

Total Pages: 837

ISBN-13: 1107003393

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A comprehensive guide to sampling for engineers, covering the fundamental mathematical underpinnings together with practical engineering principles and applications.


Image Mosaicing and Super-resolution

Image Mosaicing and Super-resolution

Author: David Capel

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 233

ISBN-13: 0857293842

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This book investigates sets of images consisting of many overlapping viewsofa scene, and how the information contained within them may be combined to produce single images of superior quality. The generic name for such techniques is frame fusion. Using frame fusion, it is possible to extend the fieldof view beyond that ofany single image, to reduce noise, to restore high-frequency content, and even to increase spatial resolution and dynamic range. The aim in this book is to develop efficient, robust and automated frame fusion algorithms which may be applied to real image sequences. An essential step required to enable frame fusion is image registration: computing the point-to-point mapping between images in their overlapping region. This sub problem is considered in detail, and a robust and efficient solution is proposed and its accuracy evaluated. Two forms of frame fusion are then considered: image mosaic ing and super-resolution. Image mosaicing is the alignment of multiple images into a large composition which represents part of a 3D scene. Super-resolution is a more sophisticated technique which aims to restore poor-quality video sequences by mod elling and removing the degradations inherent in the imaging process, such as noise, blur and spatial-sampling. A key element in this book is the assumption of a completely uncalibrated cam era. No prior knowledge of the camera parameters, its motion, optics or photometric characteristics is assumed. The power of the methods is illustrated with many real image sequence examples.


Statistical Parametric Mapping: The Analysis of Functional Brain Images

Statistical Parametric Mapping: The Analysis of Functional Brain Images

Author: William D. Penny

Publisher: Elsevier

Published: 2011-04-28

Total Pages: 689

ISBN-13: 0080466508

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In an age where the amount of data collected from brain imaging is increasing constantly, it is of critical importance to analyse those data within an accepted framework to ensure proper integration and comparison of the information collected. This book describes the ideas and procedures that underlie the analysis of signals produced by the brain. The aim is to understand how the brain works, in terms of its functional architecture and dynamics. This book provides the background and methodology for the analysis of all types of brain imaging data, from functional magnetic resonance imaging to magnetoencephalography. Critically, Statistical Parametric Mapping provides a widely accepted conceptual framework which allows treatment of all these different modalities. This rests on an understanding of the brain's functional anatomy and the way that measured signals are caused experimentally. The book takes the reader from the basic concepts underlying the analysis of neuroimaging data to cutting edge approaches that would be difficult to find in any other source. Critically, the material is presented in an incremental way so that the reader can understand the precedents for each new development. This book will be particularly useful to neuroscientists engaged in any form of brain mapping; who have to contend with the real-world problems of data analysis and understanding the techniques they are using. It is primarily a scientific treatment and a didactic introduction to the analysis of brain imaging data. It can be used as both a textbook for students and scientists starting to use the techniques, as well as a reference for practicing neuroscientists. The book also serves as a companion to the software packages that have been developed for brain imaging data analysis. - An essential reference and companion for users of the SPM software - Provides a complete description of the concepts and procedures entailed by the analysis of brain images - Offers full didactic treatment of the basic mathematics behind the analysis of brain imaging data - Stands as a compendium of all the advances in neuroimaging data analysis over the past decade - Adopts an easy to understand and incremental approach that takes the reader from basic statistics to state of the art approaches such as Variational Bayes - Structured treatment of data analysis issues that links different modalities and models - Includes a series of appendices and tutorial-style chapters that makes even the most sophisticated approaches accessible


Fast Fourier Transform - Algorithms and Applications

Fast Fourier Transform - Algorithms and Applications

Author: K.R. Rao

Publisher: Springer Science & Business Media

Published: 2011-02-21

Total Pages: 437

ISBN-13: 1402066295

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This book presents an introduction to the principles of the fast Fourier transform. This book covers FFTs, frequency domain filtering, and applications to video and audio signal processing. As fields like communications, speech and image processing, and related areas are rapidly developing, the FFT as one of essential parts in digital signal processing has been widely used. Thus there is a pressing need from instructors and students for a book dealing with the latest FFT topics. This book provides thorough and detailed explanation of important or up-to-date FFTs. It also has adopted modern approaches like MATLAB examples and projects for better understanding of diverse FFTs.


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.


Sparse Representations for Radar with MATLAB® Examples

Sparse Representations for Radar with MATLAB® Examples

Author: Peter Knee

Publisher: Morgan & Claypool Publishers

Published: 2012

Total Pages: 88

ISBN-13: 1627050345

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Although the field of sparse representations is relatively new, research activities in academic and industrial research labs are already producing encouraging results. The sparse signal or parameter model motivated several researchers and practitioners to explore high complexity/wide bandwidth applications such as Digital TV, MRI processing, and certain defense applications. The potential signal processing advancements in this area may influence radar technologies. This book presents the basic mathematical concepts along with a number of useful MATLAB(R) examples to emphasize the practical implementations both inside and outside the radar field.


Speech Coding Algorithms

Speech Coding Algorithms

Author: Wai C. Chu

Publisher: John Wiley & Sons

Published: 2004-03-04

Total Pages: 584

ISBN-13: 0471668877

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Speech coding is a highly mature branch of signal processing deployed in products such as cellular phones, communication devices, and more recently, voice over internet protocol This book collects many of the techniques used in speech coding and presents them in an accessible fashion Emphasizes the foundation and evolution of standardized speech coders, covering standards from 1984 to the present The theory behind the applications is thoroughly analyzed and proved


Exponential Data Fitting and Its Applications

Exponential Data Fitting and Its Applications

Author: Victor Pereyra

Publisher: Bentham Science Publishers

Published: 2010

Total Pages: 206

ISBN-13: 1608050483

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"Real and complex exponential data fitting is an important activity in many different areas of science and engineering, ranging from Nuclear Magnetic Resonance Spectroscopy and Lattice Quantum Chromodynamics to Electrical and Chemical Engineering, Vision a"