Neural Networks-based Regularization of Large-Scale Inverse Problems in Medical Imaging

--In this paper we present a generalized Deep Learning-based approach to solve ill-posed large-scale inverse problems occurring in medical imaging. Recently, Deep Learning methods using iterative neural networks and cascaded neural networks have been reported to achieve excellent image quality for the task of image reconstruction in different imaging modalities. However, the fact that these approaches employ the forward and adjoint operators repeatedly in the network architecture requires the network to process the whole images or volumes at once, which for some applications is computationally infeasible. In this work, we follow a different reconstruction strategy by decoupling the regularization of the solution from ensuring consistency with the measured data. The regularization is given in the form of an image prior obtained by the output of a previously trained neural network which is used in a Tikhonov regularization framework. By doing so, more complex and sophisticated network architectures can be used for the removal of the artefacts or noise than it is usually the case in iterative networks. Due to the large scale of the considered problems and the resulting computational complexity of the employed networks, the priors are obtained by processing the images or volumes as patches or slices. We evaluated the method for the cases of 3D cone-beam low dose CT and undersampled 2D radial cine MRI and compared it to a total variation-minimization-based reconstruction algorithm as well as to a method with regularization based on learned overcomplete dictionaries. The proposed method outperformed all the reported methods with respect to all chosen quantitative measures and further accelerates the regularization step in the reconstruction by several orders of magnitude. N inverse problems, the goal is to recover an object of interest from a set of indirect and possibly incomplete observations. M. Haltmeier is with the Department of Mathematics, University of Innsbruck, Innsbruck, Austria (email: markus.haltmeier@uibk.ac.at) T. Schaeffter is with the Physikalisch-Technische Bundesanstalt (PTB), Braunschweig and Berlin, Germany, King's College London, London, UK and the Department of Medical Engineering, Technical University of Berlin, Berlin, Germany (email: tobias.schaeffter@ptb.de) M. Dewey is with the Department of Radiology, Charit e - Univer-sit atsmedizin Berlin, Berlin, Germany and the Berlin Institute of Health, Berlin, Germany (email: marc.dewey@charite.de) C. Kolbitsch is with the Physikalisch-Technische Bundesanstalt (PTB), Braunschweig and Berlin, Germany and King's College London, London, UK (email: christoph.kolbitsch@ptb.de) The reconstruction from the measured data can be an ill-posed inverse problem for different reasons.