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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


  • Machine Learning for Inverse Problems
    Giovanni S. Alberti, Matteo Santacesaria - co-Principal Investigator
    AFOSR - Air Force Office of Scientific Research

    Start 2020

    End 2023

  • Infinite-dimensional inverse problems with finite measurements
    Giovanni S. Alberti - Principal Investigator
    UniGe | UniGe Starting grant

    Start 2019

    End 2021

  • Applied harmonic analysis and PDEs for inverse problems in imaging
    Giovanni S. Alberti - Principal Investigator
    ETH Postdoctoral Fellowship: ETH Zurich & Marie-Curie actions

    Start 2016

    End 2018


  • 2020

    Linear Lipschitz and C1 extension operators through random projection
    E. Bruè S. Di Marino F. Stra
    Journal of Functional Analysis

  • A tumor growth model of Hele-Shaw type as a gradient flow
    L. Chizat S. Di Marino
    ESAIM: Control, Optimisation and Calculus of …

  • Cone-adapted shearlets and Radon transforms
    F. Bartolucci F. De Mari E. De Vito
    Advances in Microlocal and Time …

  • Calderón's inverse problem with a finite number of measurements II: independent data
    GS. Alberti M. Santacesaria
    Applicable Analysis

  • Neural networks for classification of strokes in electrical impedance tomography on a 3D head model
    V. Candiani M. Santacesaria
    arXiv preprint arXiv:2011.02852