Regularization methods for inverse problems can be based on mathematical forward methods which represent the Physics and Chemistry
as precise as possible. With the rise of the area of big data, methods that combine forward modelling with data driven techniques have been
being developed. In this talk we demonstrate that regularisation by projection can be formulated in a purely data driven setting
when the linear forward operator is given only through training data. We study convergence and stability of the regularised solutions.
We discuss counter examples on convergence of the method of regularization by projection by Seidman in this context.
This is joint work with Andrea Aspri (RICAM, Linz), Yury Korolev (Cambridge).