### 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

### 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

### 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.

### Mathematics of Machine Learning

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

Giovanni S.

AlbertiFilippo

De MariErnesto

De VitoMatteo

SantacesariaElena

RizzoAlessandro

FelisiIşıl

GulekenPaolo

AngellaSimone

SannaShiwei

SunRomain

PetitAnupam

GumberMarkus

HolzleitnerDennis

ElbrächterEdgar

Desainte-Marév…Sara

Farinelli

People

**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

### Sample complexity for inverse problems in PDE

Unit CHarMLLeading scientist Giovanni S. AlbertiRole within the project Principal InvestigatorDuration 2022 - 2027Sponsors EU | ERC StGTotal funding 1.15 M€- CLOSED
### Compressed sensing for inverse problems in PDE

Unit CHarMLLeading scientist Giovanni S. AlbertiRole within the project Principal InvestigatorDuration 2021 - 2023Sponsors UniGeTotal funding 85 k€ - CLOSED
### Machine Learning for Inverse Problems

Unit CHarMLLeading scientist Giovanni S. Alberti, Matteo SantacesariaRole within the project co-Principal InvestigatorDuration 2020 - 2023Sponsors AFOSRTotal funding 220 k€ - CLOSED
### Infinite-dimensional inverse problems with finite measurements

Unit CHarMLLeading scientist Giovanni S. AlbertiRole within the project Principal InvestigatorDuration 2019 - 2021Sponsors UniGe Starting grantTotal funding 59.5 k€

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 |