A SVD-Based Method to Assess the Uniqueness and Accuracy of SPECT Geometrical Calibration

Geometrical calibration is critical to obtaining high resolution and artifact-free reconstructed image for SPECT and CT systems. Most published calibration methods use analytical approach to determine the uniqueness condition for a specific calibration problem, and the calibration accuracy is often evaluated through empirical studies. In this work, we present a general method to assess the characteristics of both the uniqueness and the quantitative accuracy of the calibration. The method uses a singular value decomposition (SVD) based approach to analyze the Jacobian matrix from a least-square cost function for the calibration. With this method, the uniqueness of the calibration can be identified by assessing the nonsingularity of the Jacobian matrix, and the estimation accuracy of the calibration parameters can be quantified by analyzing the SVD components. A direct application of this method is that the efficacy of a calibration configuration can be quantitatively evaluated by choosing a figure-of-merit, e.g., the minimum required number of projection samplings to achieve desired calibration accuracy. The proposed method was validated with a slit-slat SPECT system through numerical simulation studies and experimental measurements with point sources and an ultra-micro hot-rod phantom. The predicted calibration accuracy from the numerical studies was confirmed by the experimental point source calibrations at ~ 0.1 mm for both the center of rotation (COR) estimation of a rotation stage and the slit aperture position (SAP) estimation of a slit-slat collimator by an optimized system calibration protocol. The reconstructed images of a hot rod phantom showed satisfactory spatial resolution with a proper calibration and showed visible resolution degradation with artificially introduced 0.3 mm COR estimation error. The proposed method can be applied to other SPECT and CT imaging systems to analyze calibration method assessment and calibration protocol optimization.