Determination of collimator and acquisition parameters for astigmatic SPECT imaging

Collimator and acquisition parameters including focal lengths, radius-of-rotation, and mechanical shifts are important for image reconstruction but often partly unknown. Determination of the unknown parameters based on the projections of a point source at various projection angles has been studied for fan beam and cone beam collimators. The authors extend these previous approaches of parameter determination to astigmatic collimation. For the astigmatic parameter determination, the authors' study focuses on two fundamental issues: (1) Can parameters be uniquely determined by using radioactive point sources, and (2) what is the condition for accurate determination of the parameters? Algebraic analysis as well as Monte Carlo simulation are employed to address these issues. Results of the analysis and simulation show that if the locations of the point sources used for parameter determination are unknown, the coordinate of the point source position along the axis-of-rotation and the component of the mechanical shift in the same direction cannot be uniquely determined. More importantly, determining a relatively small mechanical shift along the axis-of-rotation is difficult. Accurate a priori knowledge about the axial component of the point source position is important for an accurate estimate of the axial mechanical shift. In addition, the authors' Monte Carlo study shows that the accuracy of parameter determination is improved as the distance between the point source and the origin of the underlying Cartesian coordinate system for image reconstruction is increased.