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Deep learning based reconstruction methods deliver outstanding results forsolving inverse problems and are therefore becoming increasingly important. Arecently invented class of learning-based reconstruction methods is theso-called NETT (for Network Tikhonov Regularization), which contains a trainedneural network as regularizer in generalized Tikhonov regularization. Theexisting analysis of NETT considers fixed operator and fixed regularizer andanalyzes the convergence as the noise level in the data approaches zero. Inthis paper, we extend the frameworks and analysis considerably to reflectvarious practical aspects and take into account discretization of the dataspace, the solution space, the forward operator and the neural network definingthe regularizer. We show the asymptotic convergence of the discretized NETTapproach for decreasing noise levels and discretization errors. Additionally,we derive convergence rates and present numerical results for a limited dataproblem in photoacoustic tomography.

Discretization of learned NETT regularization for solving inverse problems