A novel calibration method incorporating nonlinear optimization and ball-bearing markers for cone-beam CT with a...

Cone-beam (CB) CT is a powerful noninvasive imaging modality, and is widely used in many applications. Accurate geometric parameters are essential for high-quality image reconstruction. Usually, a CBCT system with higher spatial resolution, particularly on the order of microns or nanometers, will be more sensitive to the parametric accuracy. Here, we propose a novel calibration method combining a simple phantom containing ball bearing markers and an advanced optimization procedure. This method can be applied to CBCT with reproducible geometry and frame-to-frame invariant geometric parameters.

Our proposed simplex-simulated annealing procedure minimizes the cost function that associates the geometrical parameters with the degree to which the back projections of the ball bearings in projections from various viewing angles converge, and the global minimum of the cost function corresponds to the actual geometric parameters. Specifically, six geometric parameters can be directly obtained by minimizing the cost function, and the last parameter, the distance from source to rotation axis (SRD), can be obtained using prior knowledge of the phantom - the spacing between the two ball bearings.

Numerical simulation was performed to validate that the proposed method with various noise levels. With the proposed method, the mean errors and standard deviations can be reduced to ∼10% and less than 1/3 of a competing benchmark method in the case of strong Gaussian noise (sigma = 200% of the pixel size) and large tilt angle (tilt angle =  $$ ). The calibration experiments with micro-CT and high-resolution CT scanners demonstrate that the proposed method recovers imaging parameters accurately, leading to superior image quality.

The proposed method can obtain accurate geometric parameters of a CBCT system with a circular trajectory. While in the case of micro-CT the proposed method has a performance comparable to the competing method, for high-resolution CT, which is more sensitive to geometric calibration, the proposed method demonstrates higher calibration accuracy and more robustness than the benchmark algorithm.