TY - JOUR
T1 - A SVD-based method to assess the uniqueness and accuracy of SPECT geometrical calibration
AU - Ma, Tianyu
AU - Yao, Rutao
AU - Shao, Yiping
AU - Zhou, Rong
N1 - Funding Information:
Manuscript received November 24, 2008; revised March 12, 2009. First published June 23, 2009; current version published November 25, 2009. This work was supported by the Roswell Park Alliance Foundation under Grant 62-2426-01. Asterisk indicates corresponding author.
PY - 2009/12
Y1 - 2009/12
N2 - 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 slitslat 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 for both the center of rotation (COR) estimation of a rotation stage and the slit aperture position (SAP) estimation of a slitslat 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.
AB - 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 slitslat 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 for both the center of rotation (COR) estimation of a rotation stage and the slit aperture position (SAP) estimation of a slitslat 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.
KW - Geometrical calibration
KW - Jacobian matrix
KW - Single photon emission computed tomography (SPECT)
KW - Singular value decomposition (SVD)
KW - Slit-slat collimator
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U2 - 10.1109/TMI.2009.2025696
DO - 10.1109/TMI.2009.2025696
M3 - Article
C2 - 19556192
AN - SCOPUS:70350553232
SN - 0278-0062
VL - 28
SP - 1929
EP - 1939
JO - IEEE Transactions on Medical Imaging
JF - IEEE Transactions on Medical Imaging
IS - 12
M1 - 5109708
ER -