An automatic algorithm to exploit the symmetries of the system response matrix in positron emission tomography iterative reconstruction

Abstract

Positron emission tomography (PET) iterative 3D reconstruction is a very computational demanding task. One of the main issues of the iterative reconstruction concerns the management of the system response matrix (SRM). The SRM models the relationship between the projection and the voxel space and its memory footprint can easily exceed hundreds of GB. Moreover, in order to make the reconstruction fast enough not to hinder its practical application, the SRM must be stored in the random access memory of the workstation used for the reconstruction. This issue is normally solved by implementing efficient storage schemes and by reducing the number of redundant patterns in the SRM through symmetries. However, finding a sufficient number of symmetries is often non-trivial and is typically performed using dedicated solutions that cannot be exported to different detectors and geometries. In this paper, an automatic approach to reduce the memory footprint of a pre-computed SRM is described. The proposed approach was named symmetry search algorithm (SSA) and consists in an algorithm that searches for some of the redundant patterns present in the SRM, leading to its lossy compression. This approach was built to detect translations, reflections and coordinates swap in voxel space. Therefore, it is particularly well suited for those scanners where some of the rotational symmetries are broken, e.g. small animal scanner where the modules are arranged in a polygonal ring made of few elements, and dual head planar PET systems. In order to validate this approach, the SSA is applied to the SRM of a preclinical scanner (the IRIS PET/CT). The data acquired by the scanner were reconstructed with a dedicated maximum likelihood estimation maximization algorithm with both the uncompressed and the compressed SRMs. The results achieved show that the information lost due to the SSA compression is negligible. Compression factors up to 52 when using the SSA together with manually inserted symmetries and up to 204 when using the SSA alone, can be obtained for the IRIS SRM. These results come without significant differences in the values and in the main quality metrics of the reconstructed images, i.e. spatial resolution and noise. Although the compression factors depend on the system considered, the SSA is applicable to any SRM and therefore it can be considered a general tool to reduce the footprint of a pre-computed SRM.

Towards quantitative small-animal imaging on hybrid PET/CT and PET/MRI systems

“…Considering the cylindrical symmetries of the MADPET-II scanner, 72 cylindrical symmetries were reported [82]. Recently, a general algorithm called symmetry search algorithm was proposed to automatically depict the geometrical symmetries in various scanners, leading to higher compression factors compared to conventional methods [83]. One of the most distinctive approaches to compress the prohibitive size of the SRM with multi-layered crystals with DOI capability was suggested by Li et al, in which the DOI information from all layers was summarized in a smaller virtual ring around the object, leading to a drastic reduction in SRM dimension by a factor of 2 × 10 7 [84].…”

Model construction of photon propagation based on the geometrical symmetries and GPU technology for the quad-head PET system

“…The multi-ray model is a classical method to model photon propagation. It is used not only in the quad-head PET system [32] but also in the ring PET system [33,34]. The multi-ray model has good parallelism [20], it is suitable to apply the GPU technology.…”