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
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
The research focus on frames that are defined in terms of square-integrable unitary representations of a locally compact group
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.
The activity is mainly devoted to show the interplay between learning theory and inverse problems.
Giovanni S.
Alberti
Filippo
De Mari
Ernesto
De Vito
Matteo
Santacesaria
Elena
Rizzo
Alessandro
Felisi
Işıl
Guleken
Paolo
Angella
Simone
Sanna
Shiwei
Sun
Romain
Petit
Anupam
Gumber
Markus
Holzleitner
Dennis
Elbrächter
Edgar
Desainte-Marév…
Sara
Farinelli
Silvia Sciutto | 2020 → 2023 | PhD student | Inverse Problems
Lorenzo Sacchi | 2023 | Student
Luca Ratti | 2020 → 2023 | Post-doctoral fellow | Inverse Problems and Machine Learning
Simone Sanna | 2023 | Student
Salvatore Ivan Trapasso | 2020 → 2022 | Post-doctoral fellow
Matteo Monti | 2019 → 2022 | PhD student | Harmonic Analysis
Stefano Vigogna | 2019 → 2021 | PhD student | Harmonic Analysis
Simone Sanna | 2021 | Student | Compressed Sensing
Geraldo Macoj | 2021 | Student | Machine Learning
Beatrice Ravera | 2021 | Student | Analysis
Lorenzo Bozzi | 2021 | Student | Analysis
Silvia Sciutto | 2020 | Student | Signal Analysis
Giuseppe Carta | 2020 | Student | Analysis
Ángel Arroyo | 2019 → 2020 | Post-doctoral fellow | Inverse problems
Filippo Papallo | 2020 | Student | Analysis
Giulia Bollo | 2020 | Student | Machine Learning
Francesca Bartolucci | 2020 | PhD student | Harmonic Analysis
Title | Year | Author | Venue |
---|---|---|---|
Continuous wavelet frames on the sphere: The group-theoretic approach revisited | 9999 | Dahlke S.; De Mari F.; De Vito E.; Hansen M.; Hasannasab M.; Quellmalz M.; Steidl G.; Teschke G. | APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS |
Market areas in general equilibrium | 2023 | Lanzara G.; Santacesaria M. | JOURNAL OF ECONOMIC THEORY |
Inverse problems on low-dimensional manifolds | 2023 | Alberti G.; Arroyo A.; Santacesaria M. | NONLINEARITY |
Short Communication: Localized Adversarial Artifacts for Compressed Sensing MRI | 2023 | Alaifari Rima; Alberti Giovanni S.; Gauksson Tandri | SIAM JOURNAL ON IMAGING SCIENCES |
Neural networks for classification of strokes in electrical impedance tomography on a 3D head model | 2022 | Candiani V.; Santacesaria M. | MATHEMATICS IN ENGINEERING |