Overview
- Chapters written by leading researchers in compressed sensing
- Explores recent developments of compressed sensing, both in theory and practice
- With appeal to a broad audience with research areas
Part of the book series: Applied and Numerical Harmonic Analysis (ANHA)
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Table of contents (16 chapters)
Editors and Affiliations
About the editors
Gitta Kutyniok has received various awards for her research such as an award from the Universität Paderborn in 2003, the Research Prize
of the Justus-Liebig Universität Gießen and a Heisenberg-Fellowship in 2006, and the von Kaven Prize by the DFG in 2007. She was invited as the Noether Lecturer at the ÖMG-DMV Congress in 2013, the Hans Schneider ILAS Lecturer at IWOTA in 2016, a plenary lecturer at the 8th European Congress of Mathematics (8ECM) in 2021, and the lecturer of the London Mathematical Society (LMS) Invited Lecture Series in 2022. Moreover, she will give invited lectures at the International Congress of Mathematicians (ICM) 2022 and at the International Congress on Industrial and Applied Mathematics (ICIAM) 2023. She also became a member of the Berlin-Brandenburg Academy of Sciences and Humanities in 2017, a SIAM Fellow in 2019, and a Simons Fellow at the Isaac Newton Institute in 2021; she received an Einstein Chair at TU Berlin in 2008, a Francqui Chair of the Belgian Francqui Foundation in 2020, and holds the first Bavarian AI Chair at LMU from 2020 on. She was Chair of the SIAM Activity Group on Imaging Sciences from 2018-2019 and Vice Chair of the new SIAM Activity Group on Data Science in 2021, and currently serves as Vice President-at-Large of SIAM. She is also the main coordinator of the Long-Term Programme on "Mathematics of Deep Learning" at the Isaac Newton Institute in 2021 and of the Research Focus "Next Generation AI" at the Center for Advanced Studies at LMU from 2021 to 2023.
Gitta Kutyniok's research work covers, in particular, the areas of applied and computational harmonic analysis, approximation theory, artificial intelligence, compressed sensing, frame theory, imaging sciences, inverse problems, machine learning, numerical analysis of partial differential equations, and applications to life sciences and telecommunication. She is primarily interested in developing mathematical methodologies and associated theories to solve application motivated problems. The most significant of Gitta Kutyniok's contributions is perhaps the introduction of the directional multiscale system of shearlets (www.ShearLab.org) and a comprehensive theoretical approach to analyze sparse regularization
of inverse problems using harmonic analysis and microlocal analysis. In 2015, she entered the area of machine learning, aiming to develop a theoretical foundation for deep learning, also for its application within mathematics. In this direction, some of her most well-known contributions are the analysis and construction of memory-optimal deep neural networks by using classical approximation theory as well as a theoretical analysis of deep neural networks and parametric partial differential equations. Another focus of hers is on optimal combinations of model- and
data-based approaches, where she, for instance, developed a state-of-the-art algorithm for the limited-angle computed tomography problem using a combination of deep neural networks and sparse regularization by shearlets.
Prof. Dr. Holger Rauhut has studied mathematics at the Technical University of Munich from 1996 until 2001, where he also obtained his doctoral degree in mathematics in 2004 with a thesis related to time-frequency and wavelet analysis. After a short postdoc at the University of Wroclaw in 2005, he moved to the Numerical Harmonic Analysis Group at the University of Vienna, where he obtained his habilitation degree in mathematics in 2008. In the same year, he became temporary associate professor ("Bonn Junior Fellow") at the Hausdorff Center for Mathematics at the University of Bonn. Since 2013 he is full professor for Mathematics at RWTH Aachen University leading the Chair for Mathematics of Information Processing. From 2016 to 2018 he was the spokesperson of the Department of Mathematics of RWTH and since 2018 he is member of the Senate of RWTH. His research interests include compressive sensing, applied harmonic analysis, random matrices and mathematics of deep learning. Together with Prof. Simon Foucart he authored a monograph entitled "A Mathematical Introduction to Compressive Sensing", which appeared in 2013. Since 2018 he serves as co-spokesperson, jointly with Prof. Dr. Gitta Kutyniok, of the DFG priority program SPP1798 "Compressive Sensing in Information Processing".
Dr. Robert J. Kunsch has studied Mathematics at the Friedrich Schiller University Jena from 2009 until 2014. His doctoral degree in mathematics was obained in 2017, also in Jena, the thesis dealing with Monte Carlo methods for high-dimensional function approximation. Spending two years as a postdoctoral researcher in Osnabrück, from 2019 on he is member of the Chair for Mathematics of Information Processing lead by Prof. Dr. Holger Rauhut at the RWTH Aachen University. His research interests comprise Monte Carlo methods as well as mathematics of deep learning.
Bibliographic Information
Book Title: Compressed Sensing in Information Processing
Editors: Gitta Kutyniok, Holger Rauhut, Robert J. Kunsch
Series Title: Applied and Numerical Harmonic Analysis
DOI: https://doi.org/10.1007/978-3-031-09745-4
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022
Hardcover ISBN: 978-3-031-09744-7Published: 22 October 2022
Softcover ISBN: 978-3-031-09747-8Published: 22 October 2023
eBook ISBN: 978-3-031-09745-4Published: 20 October 2022
Series ISSN: 2296-5009
Series E-ISSN: 2296-5017
Edition Number: 1
Number of Pages: XVII, 542
Number of Illustrations: 26 b/w illustrations, 90 illustrations in colour
Topics: Abstract Harmonic Analysis, Computational Mathematics and Numerical Analysis, Signal, Image and Speech Processing, Computer Imaging, Vision, Pattern Recognition and Graphics