A Mathematical Introduction to Compressive Sensing
Authors: Foucart, Simon, Rauhut, Holger
Free Preview- 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
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- About this Textbook
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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.
- Reviews
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From the book reviews:
“The book by S. Foucart and H. Rauhut is the first textbook on the subject of compressed sensing … Compressed sensing has provided an opportunity for electrical engineers to learn new mathematics, and it has given mathematicians some challenging new problems to consider. Foucart and Rauhut have written a comprehensive survey of the ideas and methods from this field. Their book will engage the interest of many researchers, both theoretical and applied.” (Joel A. Tropp, Bulletin of the American Mathematical Society, Vol. 54 (1), January, 2017)
“As a textbook it offers great flexibility for the instructor and can be used for both introductory and advanced courses in compressed sensing. … The book can be highly recommended for teaching purposes, and the homework problems are really excellent. As an encyclopedia the book is very comprehensive and offers detailed proofs and discussions. … It is expected that this book will become a classical reference source in the field.” (Anders C. Hansen, Mathematical Reviews, November, 2014)
- Table of contents (15 chapters)
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An Invitation to Compressive Sensing
Pages 1-39
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Sparse Solutions of Underdetermined Systems
Pages 41-59
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Basic Algorithms
Pages 61-75
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Basis Pursuit
Pages 77-110
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Coherence
Pages 111-131
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Table of contents (15 chapters)
- Download Preface 1 PDF (2.5 MB)
- Download Sample pages 1 PDF (2 MB)
- Download Table of contents PDF (3.2 MB)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- A Mathematical Introduction to Compressive Sensing
- Authors
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- Simon Foucart
- Holger Rauhut
- Series Title
- Applied and Numerical Harmonic Analysis
- Copyright
- 2013
- Publisher
- Birkhäuser Basel
- Copyright Holder
- Springer Science+Business Media New York
- eBook ISBN
- 978-0-8176-4948-7
- DOI
- 10.1007/978-0-8176-4948-7
- Hardcover ISBN
- 978-0-8176-4947-0
- Softcover ISBN
- 978-1-4939-0063-3
- Series ISSN
- 2296-5009
- Edition Number
- 1
- Number of Pages
- XVIII, 625
- Topics
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