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charml

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

People

Grants

TitlePrincipal InvestigatorFundingStartEndAmount
Machine Learning for Inverse ProblemsGiovanni S. Alberti, Matteo Santacesaria - co-Principal InvestigatorAFOSR - Air Force Office of Scientific Research20202023220k
Compressed sensing for inverse problems in PDEGiovanni S. Alberti - Principal InvestigatorUniGe2021202385k
Infinite-dimensional inverse problems with finite measurementsGiovanni S. Alberti - Principal InvestigatorUniGe | UniGe Starting grant2019202159k
Applied harmonic analysis and PDEs for inverse problems in imagingGiovanni S. Alberti - Principal InvestigatorETH Postdoctoral Fellowship: ETH Zurich & Marie-Curie actions20162018215k

Publications

TitleYearAuthorVenueAttachment
Linear Lipschitz and C1 extension operators through random projection2020E. Bruè S. Di Marino F. StraJournal of Functional Analysis
A tumor growth model of Hele-Shaw type as a gradient flow2020L. Chizat S. Di MarinoESAIM: Control, Optimisation and Calculus of …
Cone-adapted shearlets and Radon transforms2020F. Bartolucci F. De Mari E. De VitoAdvances in Microlocal and Time …
Calderón's inverse problem with a finite number of measurements II: independent data2020GS. Alberti M. SantacesariaApplicable Analysis
Neural networks for classification of strokes in electrical impedance tomography on a 3D head model2020V. Candiani M. SantacesariaarXiv preprint arXiv:2011.02852