Giovanni S. Alberti
D.Phil. (Oxon.)

Web profiles

orcid.org/0000-0002-8612-3663

Links

Collaborators

I am constantly looking for motivated PhD students and Postdocs (funded by the ERC StG SAMPDE): if you are interested in working with me at MaLGa please email me a CV, a motivation letter, and the contacts of at least two referees.

Recent and future events

• Speaker at BASP Frontiers workshop, Villars-sur-Ollon, Switzerland, February 5-10, 2023
• Speaker at Webinar on Scientific Machine Learning, NYCU, Taiwan, May 5, 2023
• Speaker at 2023 MATH + X Symposiumon Dynamos, Planetary Exploration and General Relativity, Inverse Problems and Machine Learning, Hella, Iceland, May 29-June 1, 2023
• Organiser of Learning for Inverse Problems, INdAM, Rome, June 5-9 2023
• Speaker at Leveraging model- and data-driven methods in medical imaging, Banff International Research Center (Canada), June 25-30, 2023
• Keynote speaker at Deep Learning for Computational Physics, University College London, July 4-6, 2023
• Plenary speaker at Applied Inverse Problems 2023, Göttingen, Germany, September 4-8, 2023
• Speaker at Congresso UMI 2023, University of Pisa, September 4-9, 2023
• Speaker at Control Methods in Hyperbolic Partial Differential Equations, Oberwolfach, November 5-11, 2023
• Speaker at CoMFoS23: Mathematical Aspects of Continuum Mechanics 2023, December 11-12, 2023
• Speaker at Inverse Problems in the Physical Sciences, Puerto Varas, Chile, January 15-18, 2024
• Speaker at Statistics Seminar, University of Cambridge, February 16, 2024
• Speaker at SIAM Conference on Uncertainty Quantification, Trieste, Italy, February 27-March 1, 2024
• Speaker at International Conference on Elliptic and Parabolic Problems: GAETA 2024, Gaeta, Italy, May 20-25, 2024
• Speaker at AMS-UMI Joint Meeting, University of Palermo, July 23-26, 2024
• Speaker at Statistical aspects of non-linear inverse problems, University of Cambridge, September 17-19, 2024
• Participant at Deep Learning for PDE-based Inverse Problems, Oberwolfach, October 27 - November 1, 2024
• Speaker at AIMS conference, NYU Abu Dhabi, December 16-20, 2024

Partial differential equations, functional analysis, applied harmonic analysis, sparse representations, wavelets, compressed sensing, inverse problems, mathematical imaging, machine learning, medical imaging.

Preprints

1. G. S. Alberti, R. Petit and M. Santacesaria, Localization of point scatterers via sparse optimization on measures, preprint (2024), arXiv:2402.00737.
2. G. S. Alberti, L. Ratti, M. Santacesaria and S. Sciutto, Learning a Gaussian Mixture for Sparsity Regularization in Inverse Problems, preprint (2024), arXiv:2401.16612.
3. G. S. Alberti, J. Hertrich, M. Santacesaria and S. Sciutto, Manifold Learning by Mixture Models of VAEs for Inverse Problems, preprint (2023), arXiv:2303.15244, code.
4. G. S. Alberti, A. Felisi, M. Santacesaria and S. I. Trapasso, Compressed sensing for inverse problems and the sample complexity of the sparse Radon transform, preprint (2023), arXiv:2302.03577.
5. G. S. Alberti, M. Santacesaria and S. Sciutto, Continuous Generative Neural Networks, preprint (2022), arXiv:2205.14627.

Journal Articles

1. R. Alaifari, G. S. Alberti and T. Gauksson, Localized adversarial artifacts for compressed sensing MRI, SIAM J. Imaging Sci., 16(4), SC14–SC26, 2023, DOI:10.1137/22M1503221,arXiv:2206.05289.
2. G. S. Alberti, Á. Arroyo and M. Santacesaria, Inverse problems on low-dimensional manifolds, Nonlinearity 36, 734–808, 2023, DOI:10.1088/1361-6544/aca73d, arXiv:2009.00574.
3. G. S. Alberti, Non-zero constraints in elliptic PDE with random boundary values and applications to hybrid inverse problems, Inverse Probl. 38, 124005, 2022, DOI:10.1088/1361-6420/ac9924, arXiv:2205.00994, Emerging Talents 2021.
4. G. S. Alberti and M. Santacesaria, Calderón's Inverse Problem with a Finite Number of Measurements II: Independent Data, Appl. Anal., 101(10), 3636–3654, 2022, DOI:10.1080/00036811.2020.1745192, arXiv:2001.10950.
5. G. S. Alberti and M. Santacesaria, Infinite-dimensional inverse problems with finite measurements, Arch. Rational Mech. Anal., 243(1), 1–31, 2022, DOI:10.1007/s00205-021-01718-4, arXiv:1906.10028.
6. G. S. Alberti and Y. Capdeboscq, Combining the Runge approximation and the Whitney embedding theorem in hybrid imaging, Int. Math. Res. Notices, 2022(6), 4387–4406, 2022, DOI:10.1093/imrn/rnaa162, arXiv:1904.02081.
7. G. S. Alberti, P. Campodonico and M. Santacesaria, Compressed sensing photoacoustic tomography reduces to compressed sensing for undersampled Fourier measurements, SIAM J. Imaging Sci., 14(3), 1039–1077, 2021, DOI:10.1137/20M1375152, arXiv:2010.08388.
8. G. S. Alberti and M. Santacesaria, Infinite dimensional compressed sensing from anisotropic measurements and applications to inverse problems in PDE, Appl. Comput. Harmon. Anal., 50, 105–146, 2021, DOI:10.1016/j.acha.2019.08.002, arXiv:1710.11093.
9. G. S. Alberti, Y. Capdeboscq and Y. Privat, On the randomised stability constant for inverse problems, Math. in Engineering, 2(2), 264–286, 2020, DOI:10.3934/mine.2020013, arXiv:1903.11273.
10. G. S. Alberti, F. Bartolucci, F. De Mari and E. De Vito, Unitarization and Inversion Formulae for the Radon Transform between Dual Pairs, SIAM J. Math. Anal., 51(6), 4356–4381, 2019, DOI:10.1137/18M1225628, arXiv:1810.12809.
11. G. S. Alberti and M. Santacesaria, Calderón's Inverse Problem with a Finite Number of Measurements, Forum Math. Sigma, 7, e35, 2019, DOI:10.1017/fms.2019.31, arXiv:1803.04224.
12. G. S. Alberti, H. Ammari, F. Romero and T. Wintz, Dynamic Spike Superresolution and Applications to Ultrafast Ultrasound Imaging, SIAM J. Imaging Sci., 12(3), 1501–1527, 2019, DOI:10.1137/18M1174775, arXiv:1803.03251, codes.
13. G. S. Alberti, M. Brown, M. Marletta and I. Wood, Essential spectrum for Maxwell's equations, Ann. Henri Poincaré, 20(5), 1471–1499, 2019, DOI:10.1007/s00023-019-00762-x, arXiv:1804.08952.
14. G. S. Alberti, Hölder regularity for Maxwell's equations under minimal assumptions on the coefficients, Calc. Var. Partial Differential Equations, 57(3), 71, 2018, DOI:10.1007/s00526-018-1358-2, arXiv:1604.03741, premio "Gioacchino Iapichino" per l'Analisi Matematica 2017.
15. G. S. Alberti, G. Bal and M. Di Cristo, Critical Points for Elliptic Equations with Prescribed Boundary Conditions, Arch. Rational Mech. Anal., 226(1), 117–141, 2017, DOI:10.1007/s00205-017-1130-3, arXiv:1611.06989.
16. G. S. Alberti, S. Dahlke, F. De Mari, E. De Vito and S. Vigogna, Continuous and discrete frames generated by the evolution flow of the Schrödinger equation, Analysis and Applications, 15(6), 915–937, 2017, DOI:10.1142/S021953051750004X, arXiv:1510.04547.
17. G. S. Alberti, H. Ammari, F. Romero and T. Wintz, Mathematical Analysis of Ultrafast Ultrasound Imaging, SIAM J. Appl. Math., 77(1), 1–25, 2017, DOI:10.1137/16M107102X, arXiv:1604.04604.
18. G. S. Alberti and H. Ammari, Disjoint sparsity for signal separation and applications to hybrid inverse problems in medical imaging, Appl. Comput. Harmon. Anal., 42(2), 319–349, 2017, DOI:10.1016/j.acha.2015.08.013, arXiv:1502.04540.
19. G. S. Alberti, H. Ammari, B. Jin, J.-K. Seo and W. Zhang, The Linearized Inverse Problem in Multifrequency Electrical Impedance Tomography, SIAM J. Imaging Sci., 9(4), 1525–1551, 2016, DOI:10.1137/16M1061564, arXiv:1602.04312.
20. G. S. Alberti, Absence of Critical Points of Solutions to the Helmholtz Equation in 3D, Arch. Rational Mech. Anal., 222(2), 879–894, 2016, DOI:10.1007/s00205-016-1013-z, arXiv:1507.00647.
21. G. S. Alberti, Enforcing local non-zero constraints in PDEs and applications to hybrid imaging problems, Comm. PDE, 40(10), 1855–1883, 2015, DOI:10.1080/03605302.2015.1050733, arXiv:1406.3248.
22. G. S. Alberti, On multiple frequency power density measurements II. The full Maxwell's equations, J. Differ. Equations, 258(8), 2767–2793, 2015, DOI:10.1016/j.jde.2014.12.028, arXiv:1311.7603.
23. G. S. Alberti, F. De Mari, E. De Vito and L. Mantovani, Reproducing Subgroups of SP(2,R). Part II: Admissible Vectors, Monatsh. Math., 173(3), 261–307, 2014, DOI:10.1007/s00605-013-0542-x, arXiv:1212.2743.
24. G. S. Alberti and Y. Capdeboscq, Elliptic regularity theory applied to time harmonic anisotropic Maxwell's equations with less than Lipschitz complex coefficients, SIAM J. Math. Anal., 46(1), 998–1016, 2014, DOI:10.1137/130929539, arXiv:1307.0350.
25. G. S. Alberti, On multiple frequency power density measurements, Inverse Probl., 29(11), 115007, 2013, DOI:10.1088/0266-5611/29/11/115007, arXiv:1301.1508.
26. G. S. Alberti, L Balletti, F. De Mari and E. De Vito, Reproducing Subgroups of SP(2,R). Part I: Algebraic classification, J. Fourier Anal. and Appl., 19(4), 651–682, 2013, DOI:10.1007/s00041-012-9255-0, arXiv:1109.6789.

Book(s)

1. G. S. Alberti and Y. Capdeboscq, Lectures on elliptic methods for hybrid inverse problems, Cours Spécialisés 25, Société Mathématique de France, 2018, (link).

Chapters and proceedings

1. G. S. Alberti, E. De Vito, M. Lassas, L. Ratti and M. Santacesaria, Learning the optimal Tikhonov regularizer for inverse problems, NeurIPS 2021, arXiv:2106.06513.
2. G. S. Alberti, F. Bartolucci, F. De Mari and E. De Vito, Radon Transform: Dual Pairs and Irreducible Representations, in Landscapes of Time-Frequency Analysis, Appl. Numer. Harmon. Anal., 1–28, 2020, DOI:10.1007/978-3-030-56005-8_1, arXiv:2002.01165.
3. R. Alaifari, G. S. Alberti and T. Gauksson, ADef: an Iterative Algorithm to Construct Adversarial Deformations, ICLR 2019, arXiv:1804.07729, codes.
4. G. S. Alberti, S. Dahlke, F. De Mari, E. De Vito and H. Führ, Recent Progress in Shearlet Theory: Systematic Construction of Shearlet Dilation Groups, Characterization of Wavefront Sets, and New Embeddings, in Frames and Other Bases in Abstract and Function Spaces, Appl. Numer. Harmon. Anal., 127–160, 2017, DOI:10.1007/978-3-319-55550-8_7, arXiv:1605.02873.
5. G. S. Alberti and Y. Capdeboscq, On local non-zero constraints in PDE with analytic coefficients, in Imaging, Multi-scale and High Contrast Partial Differential Equations, Contemp. Math., vol. 660, AMS Providence, RI, 2016, pp. 89–97, DOI:10.1090/conm/660/13260, arXiv:1501.01449.
6. G. S. Alberti, H. Ammari and K. Ruan, Multi-frequency acousto-electromagnetic tomography, in A Panorama of Mathematics: Pure and Applied, Contemp. Math., vol. 658, AMS Providence, RI, 2016, pp. 67–79, DOI:10.1090/conm/658/13132, arXiv:1410.4119.
7. G. S. Alberti and Y. Capdeboscq, A propos de certains problèmes inverses hybrides, Seminaire: Equations aux Dérivées Partielles. 2013–2014, Exp. No. II. École Polytech., Palaiseau, 2014, DOI:10.5802/slsedp.50.

Dissertations

1. On local constraints and regularity of PDE in electromagnetics. Applications to hybrid imaging inverse problems - DPhil Thesis, University of Oxford, 2014.
2. Reproducing Subgroups of the Symplectic Group - MSc Thesis, University of Genoa, 2011.
3. La precessione di Thomas - BSc Thesis, University of Genoa, 2009.



Presentations

Selected talks

• Continuous generative neural networks  - BASP 2023.
• Compressed sensing for the sparse Radon transform  - Inverse problems in the desert, NYU Abu Dhabi, 2022.
• Regularity theory for Maxwell's equations  - Online Seminar on Mathematical Methods in the Theory of Electromagnetism, 2021.
• Adversarial deformations for DNNs  - Inverse Problems and Machine Learning workshop, CRM Montreal, 2019.
• Combining the Runge approximation and the Whitney embedding theorem in hybrid imaging  - Reconstruction Methods for Inverse Problems, BIRS, Canada, 2019.
• Mathematical analysis of ultrafast ultrasound imaging  - IPMS 2018, Malta.
• Calderón's Inverse Problem with a Finite Number of Measurements  - Inverse Problems, Imaging and PDEs, IAS, Hong Kong, 2018.
• Mathematical analysis of ultrafast ultrasound imaging  - Applied Inverse Problems Conference, Zhejiang University, Hangzhou, 2017.
• Non-zero constraints in quantitative coupled physics imaging  - Quantitative Tomographic Imaging - Radon meets Bell and Maxwell, Ricam, Linz, 2017.
• Disjoint sparsity for signal separation and applications to hybrid imaging inverse problems  - UCL Seminar, 2015.
• Using multiple frequencies to enforce non-zero constraints in PDE and applications to hybrid imaging problems  - "Inverse Problem Seminar", IHP, Paris, 2015.
• Two-dimensional reproducing formulae arising from the metaplectic representation and their discretisation  - "Real and complex manifolds: geometry, topology and harmonic analysis", Scuola Normale Superiore di Pisa, 2015.
• Elliptic regularity theory applied to time harmonic Maxwell's equations - "6^th South West Regional PDE Winter School", University of Oxford, 2014.

Videos

• Compressed sensing for the sparse Radon transform  - "Leveraging Model- and Data-Driven Methods in Medical Imaging", BIRS 2023.
• Regularity theory for Maxwell's equations  - Cardiff Analysis Seminar, 2021.
• Infinite-dimensional inverse problems with finite measurements  - OneWorld IMAGINE seminar, 2021.
• Infinite-dimensional inverse problems with finite measurements  - "Statistical aspects of non-linear inverse problems", BIRS, Canada, 2021.
• Infinite-dimensional inverse problems with finite measurements  - "IFIP TC7 Conference on System modeling and optimization", 2021.
• Frames of exponentials and compressed sensing photoacoustic tomography  - "Inverse Problems for PDEs: A one day webinar in occasion of the 65th birthday of Sergio Vessella", 2020.
• Combining the Runge approximation and the Whitney embedding theorem in hybrid imaging  - "Reconstruction Methods for Inverse Problems", BIRS, Canada, 2019.
• Disjoint sparsity for signal separation and applications to hybrid imaging inverse problems  - "Hybrid Methods in Imaging", BIRS, Canada, 2015.
• Using multiple frequencies to satisfy local constraints  - Course "Problèmes inverses hybrides" by Yves Capdeboscq, Collège de France, Paris, 2014.
• Using multiple frequencies to satisfy local constraints in PDE and applications to hybrid problems  - "Problèmes inverses et imagerie", IHP Paris, 2014.

Posters

• Disjoint sparsity for signal separation and applications to hybrid imaging problems - "Winter School on Advances in Mathematics of Signal Processing", HIM, 2016.
• Using multiple frequencies to satisfy local constraints in PDE and applications to hybrid problems - "Progrès récents dans l'analyse mathématique et numérique des problèmes inverses", Marseille, 2014.
• Using multiple frequencies in hybrid medical imaging - "Set for Britain", House of Commons, 2014.
• Reproducing Subgroups of SP(2; R) - "FFT 2013", University of Maryland (with Filippo de Mari and Ernesto de Vito), 2013.