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Harmonic and Applied Analysis

From Radon Transforms to Machine Learning

  • Book
  • © 2021

Overview

Editors:
  1. Filippo De Mari

    1. Dipartimento di Matematica, Università di Genova, Genova, Italy

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  2. Ernesto De Vito

    1. Dipartimento di Matematica, Università di Genova, Genova, Italy

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    You can also search for this editor in PubMed   Google Scholar

  • Explores mathematical connections between harmonic analysis and machine learning, data analysis, and imaging science
  • Offers a current and accessible entrance into cutting-edge research in the data sciences
  • Features contributions from the 2017 and 2019 Summer Schools on Applied Harmonic Analysis at the University of Genova

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

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-xv
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  2. Unitarization of the Horocyclic Radon Transform on Symmetric Spaces

    • Francesca Bartolucci, Filippo De Mari, Matteo Monti
    Pages 1-54

  3. Entropy and Concentration

    • Andreas Maurer
    Pages 55-100

  4. Ill-Posed Problems: From Linear to Nonlinear and Beyond

    • Rima Alaifari
    Pages 101-148

  5. Proximal Gradient Methods for Machine Learning and Imaging

    • Saverio Salzo, Silvia Villa
    Pages 149-244

  6. Regularization: From Inverse Problems to Large-Scale Machine Learning

    • Ernesto De Vito, Lorenzo Rosasco, Alessandro Rudi
    Pages 245-296

  7. Back Matter

    Pages 297-302
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Keywords

About this book

Deep connections exist between harmonic and applied analysis and the diverse yet connected topics of machine learning, data analysis, and imaging science.  This volume explores these rapidly growing areas and features contributions presented at the second and third editions of the Summer Schools on Applied Harmonic Analysis, held at the University of Genova in 2017 and 2019.  Each chapter offers an introduction to essential material and then demonstrates connections to more advanced research, with the aim of providing an accessible entrance for students and researchers.  Topics covered include ill-posed problems; concentration inequalities; regularization and large-scale machine learning; unitarization of the radon transform on symmetric spaces; and proximal gradient methods for machine learning and imaging.  

Editors and Affiliations

  • Dipartimento di Matematica, Università di Genova, Genova, Italy

    Filippo De Mari, Ernesto De Vito

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