An analytic geometric calibration method for circular cone-beam CT

Objectives To develop a new geometric calibration method for the cone-beam CT imaging geometry for artifacts-free image reconstruction.

Methods The new geometric calibration method is applicable to x-ray CT, cone-beam SPECT and pinhole SPECT imaging geometries. It is known that seven parameters completely describe these imaging geometries. We developed a new analytic method for obtaining all seven parameters using a minimum of 3 point sources with known distances among any 2-point combinations. Our method is general in that none of the seven parameters are assumed to be zero. Moreover, it is accurate in the noise-free case and can accommodate shorter calibration scan range (<= 360o) and projection data truncation without affecting the accuracy of the result. First the in-plane detector rotation angle (η) is determined using a geometrical construction. The outcome of this step includes the estimated η and the point correspondence between a set of projection locations and a few characteristic positions of the point sources in the object space. These positions are such that at least one of their (x, y, z) coordinates is zero. The simplicity of these projection equations enables a simple analytical inversion to obtain the other six parameters.

Results We performed computer simulations to study the robustness of the proposed method under different projection noise levels and using different data acquisition ranges. In the presence of noise, the effects on the parameter estimates using shorter data acquisition ranges are similar to increased noise level in the projection data. Accommodating projection truncations in the calibration scan may allow more flexible positioning of the point source ensemble. Some favorable placements of the point sources lead to more accurate geometric parameters.

Conclusions Possible future extensions include generalizing our method to multi-pinhole SPECT systems and the mechanically unstable C-Arm X-ray systems. In either case, the requirements on point source ensembles and the complete set of geometrical parameters are different than in a circular cone-beam case and both need to be reconsidered.

Research Support R01 EB00873