Automatic and Computationally Efficient Alignment in Fan- and Cone-beam Tomography

This work is concerned with fan- and cone-beam computed tomography with circular source trajectory, where the reconstruction inverse problem requires an accurate knowledge of source, detector and rotational axis relative positions and orientations. We address this additional inverse problem as a preceding step of the reconstruction process directly from the acquired projections. In the cone-beam case, we present a method that estimates both the detector shift (orthogonal to both focal and rotational axes) and the in-plane detector rotation (over the focal axis) based on the variable projection optimization approach. In addition and for the fan-beam case, two new strategies with low computational cost are presented to estimate the detector shift based on a fan-beam symmetry condition. The methods are validated with simulated and experimental industrial tomographic data with code examples available for both fan- and cone-beam geometries.