A geometric calibration method for a multi-segment static CT based on ordered subsets of sources and detectors

Multi-segment static computed tomography (MS-staticCT) is a generalized and efficient configuration of static CT systems, achieving high temporal resolution imaging by sequentially firing x-ray sources, instead of rotation. However, it contains numerous geometric parameters. Due to the dense arrangement of both the x-ray sources and detectors within their respective configurations, there are some coupled illumination relationships where some x-ray sources simultaneously illuminate multiple detectors. To address these calibration challenges, we propose a geometric calibration method based on ordered subsets. We categorize two types of ordered subsets of sources and detectors: source subsets and detector subsets. Each source subset includes a group of sources that illuminate the same detectors, along with the illuminated detectors. Similarly, each detector subset includes a group of detectors illuminated by the same sources, along with the sources that illuminate them. The calibration of the sources in source subsets and the detectors in detector subsets is performed alternately until convergence, ensuring that the calibrated geometry to accurately describe all the illumination relationships. These calibration steps are detailed in a workflow. During each step, the estimations for different ordered subsets are independent and parallelizable to significantly improving computational efficiency. A calibration phantom is involved in our method. During the calibration, we iteratively estimate the parameters by minimizing the average re-projection error (aRPE) of the balls in the calibration phantom. We evaluated the proposed method by simulation and actual experiments. The aRPE was reduced to 0.0087 mm and the reconstructed images were clear without obvious misalignment in simulation. Compared to estimating all parameters together, our method improved computational efficiency by a factor of 2.20. The targeted spatial resolution (2.5 lp·mm^-1) of an actual MS-staticCT system was obtained. These results verified the efficiency and accuracy of the proposed method.