Comparison Between Parallel Hole and Rotating Slat Collimation: Analytical Noise Propagation Models

We have previously proposed a method to compare tomographic systems. It is assumed that each system acquires a tomographic scan of a certain tracer distribution in the same acquisition time. From this scan, each system is forced to reconstruct an image with a predefined spatial resolution. The system that can perform this task with the "most favorable" noise propagation is considered as the best system. The variance on pixel values or region-of-interest (ROI) values is used to assess the noise in the reconstructed image. In this paper, we extend this idea to compare the performance of parallel hole (PH) and rotating slat (RS) collimations. Two different analytical approaches were used to analyze the variance of the reconstructed pixel/ROI values. The first method is based on the filtered-backprojection (FBP) theory, and was applied to the central point of a uniform symmetrical phantom. It yields analytical expressions for the optimal collimator aperture and the corresponding variance of the reconstructed pixel values, but it can only be applied to highly symmetrical configurations. The second method is based on approximations for the Fisher information matrix. It provides numerical results, and it is more general and can be applied to nonsymmetrical objects and shift-variant tomographic systems. The collimations were compared for both planar imaging and volume imaging. The main results are as follows. 1) For cases where both methods are valid, they are in excellent agreement. 2a) The optimal collimator aperture varies linearly with the target resolution. 2b) For a fixed target resolution, the optimal collimator aperture depends on the collimator type and the imaging mode (planar or volume). 2c) The optimal aperture of PH is a factor of √(2) larger than that of RS. 3a) The relative performance of the two collimators is determined by both the object size and the object-to-detector distance. 3b) Pixel variance and variances of ROIs with varying sizes yield very similar relative performance for RS versus PH.