On Learned Operator Correction in Inverse Problems

2020/05/14 by Lunz, Sebastian, Hauptmann, Andreas, Tarvainen, Tanja +2
#Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Image and Video Processing (eess.IV) #Machine Learning (cs.LG) #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #electronic engineering #information engineering

paper · doi:10.48550/arxiv.2005.07069

Abstract

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.

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