a mathematical introduction to compressive sensing applied and numerical harmonic analysis

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A Mathematical Introduction To Compressive Sensing

Author : Simon Foucart
ISBN : 9780817649487
Genre : Computers
File Size : 35. 89 MB
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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 A Renaissance

Author : Götz E. Pfander
ISBN : 9783319197494
Genre : Mathematics
File Size : 88. 55 MB
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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.

Handbook Of Mathematical Methods In Imaging

Author : Otmar Scherzer
ISBN : 9780387929194
Genre : Mathematics
File Size : 45. 33 MB
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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.

Finite Frame Theory A Complete Introduction To Overcompleteness

Author : Kasso A. Okoudjou
ISBN : 9781470420192
Genre : Approximations and expansions
File Size : 68. 50 MB
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Frames are overcomplete sets of vectors that can be used to stably and faithfully decompose and reconstruct vectors in the underlying vector space. Frame theory stands at the intersection of many areas in mathematics such as functional and harmonic analysis, numerical analysis, matrix theory, numerical linear algebra, algebraic and differential geometry, probability, statistics, and convex geometry. At the same time its applications in engineering, medicine, computer science, and quantum computing are motivating new research problems in applied and pure mathematics. This volume is based on lectures delivered at the 2015 AMS Short Course “Finite Frame Theory: A Complete Introduction to Overcompleteness”, held January 8–9, 2015 in San Antonio, TX. Mostly written in a tutorial style, the seven chapters contained in this volume survey recent advances in the theory and applications of finite frames. In particular, it presents state-of-the-art results on foundational frame problems, and on the analysis and design of various frames, mostly motivated by specific applications. Carefully assembled, the volume quickly introduces the non-expert to the basic tools and techniques of frame theory. It then moves to develop many recent results in the area and presents some important applications. As such, the volume is designed for a diverse audience including researchers in applied and computational harmonic analysis, as well as engineers and graduate students.

New Trends In Applied Harmonic Analysis

Author : Akram Aldroubi
ISBN : 9783319278735
Genre : Mathematics
File Size : 34. 79 MB
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This volume is a selection of written notes corresponding to courses taught at the CIMPA School: "New Trends in Applied Harmonic Analysis: Sparse Representations, Compressed Sensing and Multifractal Analysis". New interactions between harmonic analysis and signal and image processing have seen striking development in the last 10 years, and several technological deadlocks have been solved through the resolution of deep theoretical problems in harmonic analysis. New Trends in Applied Harmonic Analysis focuses on two particularly active areas that are representative of such advances: multifractal analysis, and sparse representation and compressed sensing. The contributions are written by leaders in these areas, and cover both theoretical aspects and applications. This work should prove useful not only to PhD students and postdocs in mathematics and signal and image processing, but also to researchers working in related topics.

Compressed Sensing And Its Applications

Author : Holger Boche
ISBN : 9783319160429
Genre : Mathematics
File Size : 40. 72 MB
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Since publication of the initial papers in 2006, compressed sensing has captured the imagination of the international signal processing community, and the mathematical foundations are nowadays quite well understood. Parallel to the progress in mathematics, the potential applications of compressed sensing have been explored by many international groups of, in particular, engineers and applied mathematicians, achieving very promising advances in various areas such as communication theory, imaging sciences, optics, radar technology, sensor networks, or tomography. Since many applications have reached a mature state, the research center MATHEON in Berlin focusing on "Mathematics for Key Technologies", invited leading researchers on applications of compressed sensing from mathematics, computer science, and engineering to the "MATHEON Workshop 2013: Compressed Sensing and its Applications” in December 2013. It was the first workshop specifically focusing on the applications of compressed sensing. This book features contributions by the plenary and invited speakers of this workshop. To make this book accessible for those unfamiliar with compressed sensing, the book will not only contain chapters on various applications of compressed sensing written by plenary and invited speakers, but will also provide a general introduction into compressed sensing. The book is aimed at both graduate students and researchers in the areas of applied mathematics, computer science, and engineering as well as other applied scientists interested in the potential and applications of the novel methodology of compressed sensing. For those readers who are not already familiar with compressed sensing, an introduction to the basics of this theory will be included.

Einf Hrung In Die Numerische Mathematik

Author : Eduard L. Stiefel
ISBN : STANFORD:36105031205474
Genre : Numerical analysis
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Mathematik Der Digitalen Medien

Author : Martin Bossert
ISBN : 3800731371
Genre : Information theory
File Size : 36. 36 MB
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Theoretical Foundations And Numerical Methods For Sparse Recovery

Author : Massimo Fornasier
ISBN : 9783110226157
Genre : Mathematics
File Size : 55. 34 MB
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The present collection of four lecture notes is the very first contribution of this type in the field of sparse recovery. Compressed sensing is one of the important facets of the broader concept presented in the book, which by now has made connections with other branches such as mathematical imaging, inverse problems, numerical analysis and simulation. This unique collection will be of value for a broad community and may serve as a textbook for graduate courses.

Einf Hrung In Die Nachrichtentechnik

Author : Martin Bossert
ISBN : 9783486717440
Genre : Technology & Engineering
File Size : 70. 74 MB
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Dieses Buch bietet eine Einführung in die Nachrichtentechnik bis hin zu modernen Verfahren der Datenübertragung und Datensicherheit auf Basis der von Claude Shannon begründeten Informationstheorie. Shannons Informationstheorie löst sich von der Bedeutung der Daten und benutzt – vereinfacht ausgedrückt – ausschließlich deren statistische Eigenschaften. Damit macht sie eine mathematische Definition von Information erst möglich. Vor diesem Hintergrund führt der Autor in die Gebiete Quellen- und Kanalcodierung, Übertragungskanäle, Entscheidungstheorie, Modulationsverfahren sowie elementare Protokolle und Datensicherheit ein. Exemplarisch stellt er ausgewählte Modelle der Nachrichtentechnik, praktische Verfahren, Methoden und Algorithmen vor. Ein ausführlicher Anhang stellt Grundlagen der Wahrscheinlichkeitsrechnung, der Fourier-Analyse und der Signal- und Systemtheorie bereit. Die Einfachheit und Übersichtlichkeit der Inhalte sowie die klare Struktur des Lehrbuchs sorgen für eine ideale Prüfungsvorbereitung. Zahlreiche Beispiele und Übungsaufgaben inklusive Lösungen helfen bei der Überprüfung des Gelernten.

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