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Computational Harmonic Analysis & Machine Learning

  • Our scientific interests focus on harmonic analysis, inverse problems, PDE and machine learning according to the following belief:

    The analysis of massive, high-dimensional, noisy, time-varying data sets has become a critical issue for a large number of scientists and engineers. Major theoretical and algorithmic advances in analyzing massive and complex data are crucial, including methods of exploiting sparsity, clustering and classification, data mining, anomaly detection, and many more.

  • In the last decade we have witnessed significant advances in many individual core areas of data analysis, including machine learning, signal processing, statistics, optimization, and of course harmonic analysis. It appears highly likely that the next major breakthroughs will occur at the intersection of these disciplines (from Applied Harmonic Analysis, Massive Data Sets, Machine Learning, and Signal Processing).

    Background image of the Needle tower by Kenneth Snelson at Kröller-Müller Museum

Research

  • Signal Processing and Harmonic Analysis
  • Harmonic Analysis and Signal Processing

    The research focus on frames that are defined in terms of square-integrable unitary representations of a locally compact group

    Researchers: Giovanni Alberti, Filippo De Mari, Ernesto De Vito, Francesca Odone

    Collaboration with: Stephan Dahlke (Philipps-Universität Marburg), Gerd Teschke (University of Applied Sciences, Neubrandenburg) Gabriele Steidl (Technische Universität, Kaiserslautern)

    Image credits: Filippo De Mari

  • Inverse Problems for PDEs

    We are interested in inverse problems for elliptic and hyperbolic equations, including Calderon's problem for electrical impedance tomography (EIT), photo-acoustic tomography (PAT), inverse scattering, Gel'fand-Calderon's problem.

    Researchers: Giovanni Alberti, Matteo Santacesaria

    Collaboration with: Habib Ammari, Elena Beretta, Sarah Hamilton, Andreas Hauptmann, Matti Lassas, Samuli Siltanen.

  • Inverse Problems for PDEs
  • Signal Processing and Harmonic Analysis
  • Mathematics of Machine Learning

    The activity is mainly devoted to show the interplay between learning theory and inverse problems.

    Researchers: Ernesto De Vito, Lorenzo Rosasco