A new virtual ring-based system matrix generator for iterative image reconstruction in high resolution small volume PET systems

A common approach to improving the spatial resolution of small animal PET scanners is to reduce the size of scintillation crystals and/or employ high resolution pixellated semiconductor detectors. The large number of detector elements results in the system matrix--an essential part of statistical iterative reconstruction algorithms--becoming impractically large. In this paper, we propose a methodology for system matrix modelling which utilises a virtual single-layer detector ring to greatly reduce the size of the system matrix without sacrificing precision. Two methods for populating the system matrix are compared; the first utilises a geometrically-derived system matrix based on Siddon's ray tracer method with the addition of an accurate detector response function, while the second uses Monte Carlo simulation to populate the system matrix. The effectiveness of both variations of the proposed technique is demonstrated via simulations of PETiPIX, an ultra high spatial resolution small animal PET scanner featuring high-resolution DoI capabilities, which has previously been simulated and characterised using classical image reconstruction methods. Compression factors of 5 x 10(7) and 2.5 x 10(7)are achieved using this methodology for the system matrices produced using the geometric and Monte Carlo-based approaches, respectively, requiring a total of 0.5-1.2 GB of memory-resident storage. Images reconstructed from Monte Carlo simulations of various point source and phantom models, produced using system matrices generated via both geometric and simulation methods, are used to evaluate the quality of the resulting system matrix in terms of achievable spatial resolution and the CRC, CoV and CW-SSIM index image quality metrics. The Monte Carlo-based system matrix is shown to provide the best image quality at the cost of substantial one-off computational effort and a lower (but still practical) compression factor. Finally, a straightforward extension of the virtual ring method to a three dimensional virtual cylinder is demonstrated using a 3D DoI PET scanner.