A nonconvex model-based combined geometric calibration scheme for micro cone-beam CT with irregular trajectories

Many dedicated cone-beam CT (CBCT) systems have irregular scanning trajectories. Compared with the standard CBCT calibration, accurate calibration for CBCT systems with irregular trajectories is a more complex task, since the geometric parameters for each scanning view are variable. Most of the existing calibration methods assume that the intrinsic geometric relationship of the fiducials in the phantom is precisely known, and rarely delve deeper into the issue of whether the phantom accuracy is adapted to the calibration model.

A high-precision phantom and a highly robust calibration model are interdependent and mutually supportive, and they are both important for calibration accuracy, especially for the high-resolution CBCT. Therefore, we propose a calibration scheme that considers both accurate phantom measurement and robust geometric calibration.

Our proposed scheme consists of two parts: (1) introducing a measurement model to acquire the accurate intrinsic geometric relationship of the fiducials in the phantom; (2) developing a highly noise-robust nonconvex model-based calibration method. The measurement model in the first part is achieved by extending our previous high-precision geometric calibration model suitable for CBCT with circular trajectories. In the second part, a novel iterative method with optimization constraints based on a back-projection model is developed to solve the geometric parameters of each view.

The simulations and real experiments show that the measurement errors of the fiducial ball bearings (BBs) are within the subpixel level. With the help of the geometric relationship of the BBs obtained by our measurement method, the classic calibration method can achieve good calibration based on far fewer BBs. All metrics obtained in simulated experiments as well as in real experiments on Micro CT systems with resolutions of 9 and 4.5 μm show that the proposed calibration method has higher calibration accuracy than the competing classic method. It is particularly worth noting that although our measurement model proves to be very accurate, the classic calibration method based on this measurement model can only achieve good calibration results when the resolution of the measurement system is close to that of the system to be calibrated, but our calibration scheme enables high-accuracy calibration even when the resolution of the system to be calibrated is twice that of the measurement system.

The proposed combined geometrical calibration scheme does not rely on a phantom with an intricate pattern of fiducials, so it is applicable in Micro CT with high resolution. The two parts of the scheme, the "measurement model" and the "calibration model," prove to be of high accuracy. The combination of these two models can effectively improve the calibration accuracy, especially in some extreme cases.