Our paper with Andrea Aspri and Otmar Scherzer on Data Driven Regularization by Projection has appeared in Inverse Problems! We show that regularisation can be defined and rigorously studied in the setting when there is no numerical access to the forward operator and the operator is given only via input-output training pairs. Such pairs can be either collected experimentally or obtained from a computationally expensive model prior to solving the inverse problem (which may be useful in time-sensitive applications). We show connections to classical regularisation methods such as regularisation by projection and variational regularisation, study stability of the reconstructions and present numerical experiments on data driven inversion of the Radon transform.
The paper is in open acces and can be found here: DOI:10.1088/1361-6420/abb61b