Compressed Sensing and Its Applications

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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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.

• Compressed sensing
• Compressed sensing theory and applications
• Compressed sensing book
• Compressed sensing introduction
• Compressed sensing 2019
• Deep learning compressed sensing
• Deep learning book
• Machine learning
• Quantized compressed sensing
• Signal sensing book
• Generalization error machine learning
• MATHEON conference
• information and communication, circuits

• 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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