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Birkhäuser

Compressed Sensing and Its Applications

Third International MATHEON Conference 2017

  • Book
  • © 2019

Overview

Editors:
  1. Holger Boche

    1. Department of Electrical and Computer Engineering, Munich Center for Quantum Science and Technology (MCQST), Technical University of Munich, Munich, Germany

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  2. Giuseppe Caire

    1. Institute of Telecommunications Systems, Technical University of Berlin, Berlin, Germany

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  3. Robert Calderbank

    1. Department of Electrical and Computer Engineering, Duke University, Durham, USA

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  4. Gitta Kutyniok

    1. Department of Mathematics, Technical University of Berlin, Berlin, Germany

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  5. Rudolf Mathar

    1. Faculty of Electrical Engineering and Information Technology, RWTH Aachen University, Aachen, Germany

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  6. Philipp Petersen

    1. Mathematical Institute, University of Oxford, Oxford, UK

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  • Highlights state-of-the-art applications and methodologies of compressed sensing
  • Contains chapters written by leading experts in the fields of compressed sensing and deep learning
  • Includes a self-contained introduction to the theory and applications of compressed sensing

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

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xvii
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  2. An Introduction to Compressed Sensing

    • Niklas Koep, Arash Behboodi, Rudolf Mathar
    Pages 1-65

  3. Quantized Compressed Sensing: A Survey

    • Sjoerd Dirksen
    Pages 67-95

  4. On Reconstructing Functions from Binary Measurements

    • Robert Calderbank, Anders Hansen, Bogdan Roman, Laura Thesing
    Pages 97-128

  5. Classification Scheme for Binary Data with Extensions

    • Denali Molitor, Deanna Needell, Aaron Nelson, Rayan Saab, Palina Salanevich
    Pages 129-151

  6. Generalization Error in Deep Learning

    • Daniel Jakubovitz, Raja Giryes, Miguel R. D. Rodrigues
    Pages 153-193

  7. Deep Learning for Trivial Inverse Problems

    • Peter Maass
    Pages 195-209

  8. Oracle Inequalities for Local and Global Empirical Risk Minimizers

    • Andreas Elsener, Sara van de Geer
    Pages 211-236

  9. Median-Truncated Gradient Descent: A Robust and Scalable Nonconvex Approach for Signal Estimation

    • Yuejie Chi, Yuanxin Li, Huishuai Zhang, Yingbin Liang
    Pages 237-261

  10. Reconstruction Methods in THz Single-Pixel Imaging

    • Martin Burger, Lea Föcke, Lukas Nickel, Peter Jung, Sven Augustin
    Pages 263-290

  11. Back Matter

    Pages 291-295
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Keywords

About this book

The chapters in this volume highlight the state-of-the-art of compressed sensing and are based on talks given at the third international MATHEON conference on the same topic, held from December 4-8, 2017 at the Technical University in Berlin. In addition to methods in compressed sensing, chapters provide insights into cutting edge applications of deep learning in data science, highlighting the overlapping ideas and methods that connect the fields of compressed sensing and deep learning. Specific topics covered include:
  • Quantized compressed sensing
  • Classification
  • Machine learning
  • Oracle inequalities
  • Non-convex optimization
  • Image reconstruction
  • Statistical learning theory

This volume will be a valuable resource for graduate students and researchers in the areas of mathematics, computer science, and engineering, as well as other applied scientists exploring potential applications of compressed sensing.


Editors and Affiliations

  • Department of Electrical and Computer Engineering, Munich Center for Quantum Science and Technology (MCQST), Technical University of Munich, Munich, Germany

    Holger Boche

  • Institute of Telecommunications Systems, Technical University of Berlin, Berlin, Germany

    Giuseppe Caire

  • Department of Electrical and Computer Engineering, Duke University, Durham, USA

    Robert Calderbank

  • Department of Mathematics, Technical University of Berlin, Berlin, Germany

    Gitta Kutyniok

  • Faculty of Electrical Engineering and Information Technology, RWTH Aachen University, Aachen, Germany

    Rudolf Mathar

  • Mathematical Institute, University of Oxford, Oxford, UK

    Philipp Petersen

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