System matrix parameterization for HRRT reconstruction

Objectives To achieve optimal HRRT listmode reconstruction,we developed a method to derive a component-based system matrix which was implemented as a large table of point spread functions (PSF) [1]. The purpose of this study is to parameterize the system matrix to allow finer sampling of the components involved without increasing the size and statistical requirement of system matrix.

Methods With the component based method, the conventional voxel and line-of-response (LOR) indices for retrieving a system matrix element were replaced by physical components that critically affect the magnitude of system matrix elements: detector layer (L), photon-to-crystal incident angles (AX and TX), voxel relative location along LOR (D) and in the plane perpendicular to the LOR (R and U). To parameterize the matrix, the PSF of each voxel-LOR group, i.e. the combination (L, AX, TX and D), was fit to a 3D elliptic function in terms of 3 parameters: obliqueness angle and the sizes of the major and minor axes. These parameters were then used for extrapolating the PSFs with fine samples in incident angles and location along LOR. We used a Monte Carlo simulated uniform cylinder for PSF derivation and a hot-rod phantom for evaluating the performance of the parameterized matrix.

Results The component based system matrix provided images with higher resolution and lower noise as compared to using iso-Gaussian PSF. The parameters of the elliptical PSF model showed consistent trends over the LOR incident angles and the voxel location along LOR.

Conclusions We developed a technique to obtain parameterized system matrix. It allowed using finely sampled system matrix with dramatically reduced computer memory requirements.

Research Support This work was supported by NIH grant 1R01NS058360-01A1.