On Learned Operator Correction in Inverse Problems
This addresses the challenge of model inaccuracies in inverse problems for applications like medical imaging, though it appears incremental as it builds on existing correction frameworks.
The paper tackles the problem of learning data-driven explicit model corrections for inverse problems within a variational framework, proposing a forward-adjoint correction method that corrects in both data and solution spaces, and shows that solutions converge to those with the correct operator under certain conditions, with evaluation on limited view photoacoustic tomography.
We discuss the possibility to learn a data-driven explicit model correction for inverse problems and whether such a model correction can be used within a variational framework to obtain regularised reconstructions. This paper discusses the conceptual difficulty to learn such a forward model correction and proceeds to present a possible solution as 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 Bayesian approximation error method.