Sampling Theory, a Renaissance

Compressive Sensing and Other Developments

  • Götz E. Pfander

Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Random Measurements of High Dimensional Data

    1. Front Matter
      Pages 1-1
    2. Samuel Vaiter, Gabriel Peyré, Jalal Fadili
      Pages 103-153
  3. Finite and Structured Frames

    1. Front Matter
      Pages 155-155
    2. Evan Chou, C. Sinan Güntürk, Felix Krahmer, Rayan Saab, Özgür Yılmaz
      Pages 157-184
    3. John J. Benedetto, Matthew J. Begué
      Pages 185-215
    4. Peter G. Casazza, Lindsey M. Woodland
      Pages 217-266
  4. Bandlimitation and Generalizations

    1. Front Matter
      Pages 267-267
    2. Stephen D. Casey, Jens Gerlach Christensen
      Pages 331-359
    3. Michael Robinson
      Pages 361-399
  5. Sampling and Parametric Partial Differential Equations

    1. Front Matter
      Pages 401-401
    2. Wolfgang Dahmen
      Pages 403-435
  6. Data Acquisition

About this book

Introduction

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.

Keywords

Compressive Sensing Fourier Analysis Frame Theory Random Measurements Sampling Theory Sparsity

Editors and affiliations

  • Götz E. Pfander
    • 1
  1. 1.School of Engineering and ScienceJacobs University BremenBremenGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-19749-4
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-19748-7
  • Online ISBN 978-3-319-19749-4
  • Series Print ISSN 2296-5009
  • Series Online ISSN 2296-5017
  • About this book
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