Compressed Sensing and Its Applications: Third International MATHEON Conference 2017

✍ Scribed by Holger Boche, Giuseppe Caire, Robert Calderbank, Gitta Kutyniok, Rudolf Mathar, Philipp Petersen

• Publisher: Springer International Publishing;Birkhäuser
• Year: 2019
• Tongue: English
• Leaves: 305
• Series: Applied and Numerical Harmonic Analysis
• Edition: 1st ed. 2019
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter ....Pages i-xvii
An Introduction to Compressed Sensing (Niklas Koep, Arash Behboodi, Rudolf Mathar)....Pages 1-65
Quantized Compressed Sensing: A Survey (Sjoerd Dirksen)....Pages 67-95
On Reconstructing Functions from Binary Measurements (Robert Calderbank, Anders Hansen, Bogdan Roman, Laura Thesing)....Pages 97-128
Classification Scheme for Binary Data with Extensions (Denali Molitor, Deanna Needell, Aaron Nelson, Rayan Saab, Palina Salanevich)....Pages 129-151
Generalization Error in Deep Learning (Daniel Jakubovitz, Raja Giryes, Miguel R. D. Rodrigues)....Pages 153-193
Deep Learning for Trivial Inverse Problems (Peter Maass)....Pages 195-209
Oracle Inequalities for Local and Global Empirical Risk Minimizers (Andreas Elsener, Sara van de Geer)....Pages 211-236
Median-Truncated Gradient Descent: A Robust and Scalable Nonconvex Approach for Signal Estimation (Yuejie Chi, Yuanxin Li, Huishuai Zhang, Yingbin Liang)....Pages 237-261
Reconstruction Methods in THz Single-Pixel Imaging (Martin Burger, Janic Föcke, Lukas Nickel, Peter Jung, Sven Augustin)....Pages 263-290
Back Matter ....Pages 291-295

✦ Subjects

Mathematics; Information and Communication, Circuits; Fourier Analysis; Mathematical Applications in Computer Science; Signal, Image and Speech Processing