Data Driven Regularization
Andrea Aspri - The Johann Radon Institute for Computational and Applied Mathematics
In this talk I will speak about some recent results on the study of linear inverse problems under the premise that the forward operator is not at hand but given indirectly through some input-output training pairs. We show that regularisation by projection and variational regularisation can be formulated by using the training data only and without making use of the forward operator. I will provide some information regarding convergence and stability of the regularised solutions. Moreover, we show, analytically and numerically, that regularisation by projection is indeed capable of learning linear operators, such as the Radon transform. This is a joint work with Yury Korolev (University of Cambridge) and Otmar Scherzer (University of Vienna and RICAM).
Andrea Aspri is currently a research scientist at RICAM (Linz) in the “Inverse Problems and Mathematical Imaging” group, led by Prof. Otmar Scherzer. He has just obtained a post-doc position at University of Pavia, starting from November 1st, 2020, under the supervision of Prof. Elisabetta Rocca and financed by the project “Department of Excellence”. His research topics are mainly focused on uniqueness and stability issues for inverse problems, on data driven regularization algorithms and on shape optimization problems.
2020-12-15 at 3:30 pm