Hybrid Calibration in 3D Cone-Beam Geometry with Sources on a Line

Data consistency conditions (DCCs) such as Helgason-Ludwig conditions for the Radon transform are based on moments of the projection data and can not be used in the case of truncated projections. In this work, we describe a new calibration algorithm in the case of 2D divergent geometry with sources on a line. This algorithm is based on the local information about detected markers. Thus, it can be used with truncated data. The markers are modelled by Diracs. The projections of markers are assumed to be non-truncated. We use the generalization of projections to distributions to compute the projections of a sum of Diracs, moments of Diracs and the generalization of the existing moment conditions (DCCs) to distributions. We called this approach hybrid, because we use markers of only partially known geometry and moment conditions. We applied this approach to the calibration task in the case of 3D divergent geometry with sources on a line. This problem can be reduced to 2D calibration problems. Numerical experiments with noise are presented.