On Learned Operator Correction in Inverse Problems

We discuss the possibility of learning a data-driven explicit model correction for inverse problems and whether such a model correction can be used within a variational framework to obtain regularized reconstructions. This paper discusses the conceptual difficulty of learning such a forward model correction and proceeds to present a possible solution as a forward-adjoint correction that explicitly corrects in both data and solution spaces. We then derive conditions under which solutions to the variational problem with a learned correction converge to solutions obtained with the correct operator. The proposed approach is evaluated on an application to limited view photoacoustic tomography and compared to the established framework of the Bayesian approximation error method.

Automated summary

This paper discusses the potential of learning a data-driven explicit model correction for inverse problems within a variational framework. It presents a solution of forward-adjoint correction that explicitly corrects in both data and solution spaces, and derives conditions under which solutions to the variational problem with a learned correction converge to solutions obtained with the correct operator. The proposed approach is evaluated on limited view photoacoustic tomography and compared to the established Bayesian approximation error method, showing potential applications in this field.