This work is concerned with 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 problem as a preceding step of the reconstruction process directly from the acquired projections. The method estimates both the detector shift (orthogonal to focal and rotational axes) and the in-plane detector rotation, relative to source and rotational axis. The obtained algorithm is based on a fan-beam symmetry condition and the variable projection optimization approach with a low computational cost. Therefore, the alignment problem for fan-beam tomography is addressed as well. The methods are validated with simulated and real industrial tomographic data with code examples available for both fan- and cone-beam geometries.

翻译：本文聚焦于圆形源轨迹下的锥束计算机断层扫描成像，其中重建逆问题需要精确掌握源、探测器及旋转轴的相对位置与取向。我们将其作为重建过程的预处理步骤，直接利用采集的投影数据进行处理。该方法可同时估计探测器相对于源和旋转轴的偏移量（垂直于聚焦轴与旋转轴方向）及面内探测器旋转角。所构建的算法基于扇束对称性条件及低计算成本的变量投影优化方法，因此同样适用于扇束层析成像的校准问题。通过工业层析模拟与真实数据验证了方法的有效性，并提供了适用于扇束与锥束几何构型的代码示例。