L. Ratti, Learned reconstruction methods for inverse problems: sample error estimates - Data-driven Models in Inverse Problems vol. 31, 2024, doi.org/10.1515/9783111251233-005
D. Lazzaro, S. Morigi, L. Ratti, Oracle-Net for Nonlinear Compressed Sensing in Electrical Impedance Tomography Reconstruction Problems - Journal of Scientific Computing, 101(2), 2024, doi.org/10.1007/s10915-024-02689-w
J.B. Fest, T. Heikkilä, I. Loris, S. Martin, L. Ratti, S. Rebegoldi and G. Sarnighausen, On a fixed-point continuation method for a convex optimization problem - Advanced Techniques in Optimization for Machine Learning and Imaging. Springer, 2024, doi.org/10.1007/978-981-97-6769-4_2
M. Benning, T.A. Bubba, L. Ratti, D. Riccio, Trust your source: quantifying source condition elements for variational regularisation methods - IMA Journal of Applied Mathematics, 2024, doi.org/10.1093/imamat/hxae008
T.A. Bubba, M. Burger, T. Helin, L. Ratti, Convex regularization in statistical inverse learning problems - Inverse Problems and Imaging, 2023, 17(6): 1193-1225. doi: 10.3934/ipi.2023013
E. Beretta, C. Cerutti, D. Pierotti, L. Ratti, On the reconstruction of cavities in a nonlinear model arising from cardiac electrophysiology - ESAIM: Control, Optimisation and Calculus of Variations 29 (2023): 36, https://doi.org/10.1051/cocv/2023026
T.A. Bubba, L. Ratti, Shearlet-based regularization in statistical inverse learning with an application to X-ray tomography, Inverse Problems 38.5, 2022: 054001
G.S. Alberti, E. De Vito, M. Lassas, L. Ratti, M. Santacesaria, Learning the optimal Tikhonov regularizer for inverse problems - Advances in Neural Information Processing Systems 34, 2021- NeurIPS website.
T.A. Bubba, M. Galinier, M. Lassas, M. Prato, L. Ratti, S. Siltanen, Deep neural networks for inverse problems with pseudodifferential operators: an application to limited-angle tomography - SIAM J. Imaging Sci., 14(2), 470-505, 2021, https://doi.org/10.1137/20M1343075.
E. Beretta, M. C. Cerutti, L. Ratti, Lipschitz stable determination of small conductivity inclusions in a semilinear equation from boundary data - Mathematics in Engineering, 3(1), 2020, 10.3934/mine.2021003
E. Beretta, C. Cavaterra, L. Ratti, On the determination of ischemic regions in the monodomain model of cardiac electrophysiology from boundary measurements - Nonlinearity, 33 (11), 2020, https://dx.doi.org/10.1088/1361
L. Ratti, M. Verani, A posteriori error estimates for the monodomain model in cardiac electrophysiology - Calcolo, 56 (3), 2019, https://doi.org/10.1007/s10092-019-0327-2
E. Beretta, L. Ratti, M. Verani, A phase-field approach for the interface reconstruction in a nonlinear elliptic problem arising from cardiac electrophysiology - Communications in Mathematical Sciences, 16 (7), 2018, http://dx.doi.org/10.4310/CMS.2018.v16.n7.a10
E. Beretta, C. Cavaterra, M. C. Cerutti, A. Manzoni, L. Ratti, An inverse problem for a semilinear parabolic equation arising from cardiac electrophysiology - Inverse Problems, 33 (10), 2017, https://doi.org/10.1088/1361-6420/aa8737
E. Beretta, A. Manzoni, L. Ratti, A reconstruction algorithm based on topological gradient for an inverse problem related to a semilinear elliptic boundary value problem - Inverse Problems, 33 (3), 2017, https://doi.org/10.1088/1361-6420/aa5c0a
Preprints
G.S. Alberti, L. Ratti, M. Santacesaria, S. Sciutto, Learning a Gaussian Mixture for Sparsity Regularization in Inverse Problems - arXiv preprint (2024), arXiv:2401.16612
T.A. Bubba, T. Heikkilä, D. Labate, L. Ratti, Regularization with optimal space-time priors -arxiv preprint (2024): arXiv.2405.06337