Modified Gaussian Interpolations with Geometric Calibrations for Rapid Constructions of Circular-Orbit Pinhole SPECT System Matrices

For high-spatial-resolution reconstructions in SPECT imaging, an accurate and fine system matrix ( H matrix) should be constructed. In this study, the modified Gaussian interpolation method (GIM) and the modified GIM combined with geometric parameter estimations (GIMGPE) are developed to rapidly construct the complete H matrices of circular-orbit 1-pinhole/4-pinhole SPECT systems. The multi-module multi-resolution (M 3 R) pinhole SPECT system (in the Center for Gamma-Ray Imaging, University of Arizona) is utilized to verify the usefulness of the proposed interpolation methods. The modified GIM and GIMGPE apply a geometric calibration, a rough grid-scan experiment, and point response parameterization based on Gaussian fitting to construct the full H matrices with a 0.5-mm voxel size and 60 projection angles. The geometric calibration uses a 3-point calibration phantom projected at 60 projection angles to construct the geometric projection model. In the rough grid-scan experiment, a point source is stepped on a regular grid pattern with a 1-mm grid spacing to measure the point response functions (PRFs) at the 0° projection angle. Sequentially, the measured PRFs are parameterized into two-dimensional Gaussians. The PRFs of full H matrices are interpolated by the relations between the Gaussian coefficients and the geometric parameters. The processing time of constructing the complete H matrices with the modified GIM and GIMGPE are respectively reduced by about 347× and 336×, compared to that of the full three-dimensional grid-scan experiment. According to the results of geometric calibration, the magnification of M 3 R with 1- and 4-pinhole patterns are 1.9× and 2.6×, respectively. The reconstructions of a hot-rod phantom show that the spatial resolutions of M 3 R with 1- and 4-pinhole patterns are 1.4 mm and 1.0 mm, respectively.