Automatic symmetry exploitation of the system response matrix for PET iterative reconstruction

Aim  State of the art Positron Emission Tomography (PET) iterative reconstruction can be a very demanding task due to the amount of computational power and memory required to implement a realistic system model. One of the main issues with the iterative PET reconstruction concerns the size of the System Response Matrix (SRM) that for modern scanners can easily exceed 10 Gb. Many authors reported different strategies to overcome this issue including SRM factorization in different components, ‘on the fly’ calculation of SRM parts as well as implementation of quasi-symmetries and symmetries tailored to a specific scanner geometry or configuration. In this paper a novel approach to exploit symmetries of the SRM is proposed. Materials and methods The proposed approach consists in a ‘lossy’ compression algorithm that doesn’t rely on any geometry or scanner dependent assumption. The algorithm searches for translation and reflection symmetries in the full pre-computed SRM and returns a list of fundamental Lines Of Response (LOR) together with the transformations needed to obtain all the other non fundamental LORs. The algorithm and its performance will be shown and discussed using acquisitions performed with the IRIS PET/CT pre-clinical scanner. The data will be reconstructed with a SRM evaluated with a multi-ray ‘Siddon’ algorithm and using the Maximum Likelihood Expectation Maximization (MLEM) and the Order Subset Expectation Maximization (OSEM) algorithms. Results and Conclusions The results obtained on phantoms show that the information lost during the compression procedure is not relevant and factors up to 30 can be obtained without any significant difference in the values of the reconstructed images. The compressed SRM was obtained in few hours and without the need of dedicated settings.Threfore, it is foreseen that, this method can be easily applied to other scanner configurations.