Massively parallelizable list‐mode reconstruction using a Monte Carlo‐based elliptical Gaussian model

Abstract

Purpose: A fully three-dimensional (3D) massively parallelizable list-mode ordered-subsets expectation-maximization (LM-OSEM) reconstruction algorithm has been developed for highresolution PET cameras. System response probabilities are calculated online from a set of parameters derived from Monte Carlo simulations. The shape of a system response for a given line of response (LOR) has been shown to be asymmetrical around the LOR. This work has been focused on the development of efficien region-search techniques to sample the system response probabilities, which are suitable for asymmetric kernel models, including elliptical Gaussian models that allow for high accuracy and high parallelization efficien y. The novel region-search scheme using variable kernel models is applied in the proposed PET reconstruction algorithm. Methods: A novel region-search technique has been used to sample the probability density function in correspondence with a small dynamic subset of the fiel of view that constitutes the region of response (ROR). The ROR is identifie around the LOR by searching for any voxel within a dynamically calculated contour. The contour condition is currently define as a fi ed threshold over the posterior probability, and arbitrary kernel models can be applied using a numerical approach. The processing of the LORs is distributed in batches among the available computing devices, then, individual LORs are processed within different processing units. In this way, both multicore and multiple many-core processing units can be efficientl exploited. Tests have been conducted with probability models that take into account the noncolinearity, positron range, and crystal penetration effects, that produced tubes of response with varying elliptical sections whose axes were a function of the crystal's thickness and angle of incidence of the given LOR. The algorithm treats the probability model as a 3D scalar fiel define within a reference system aligned with the ideal LOR. Results:This new technique provides superior image quality in terms of signal-to-noise ratio as compared with the histogram-mode method based on precomputed system matrices available for a commercial small animal scanner. Reconstruction times can be kept low with the use of multicore, many-core architectures, including multiple graphic processing units. Conclusions: A highly parallelizable LM reconstruction method has been proposed based on Monte Carlo simulations and new parallelization techniques aimed at improving the reconstruction speed and the image signal-to-noise of a given OSEM algorithm. The method has been validated using simulated and real phantoms. A special advantage of the new method is the possibility of definin dynamically the cut-off threshold over the calculated probabilities thus allowing for a direct control on the trade-off between speed and quality during the reconstruction.

A new PET prototype for proton therapy: comparison of data and Monte Carlo simulations

“…To reconstruct the acquired coincidences a fully three-dimensional list-mode Maximum Likelihood Expectation Maximization (MLEM) algorithm was implemented. For a detailed description of the algorithm the reader is referred to [10].…”

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

“…Reconstruction algorithms can be roughly divided into three different categories [2]: algorithms making use of a pre-computed SRM, algorithms that compute the SRM "on-the-fly" during the reconstruction process and hybrid approaches. The pre-computed approach is typically implemented on ordinary multi-cores and clusters architectures [3,4,5,6] whereas "on the fly" SRM calculation is usually performed on many-cores architectures [7,8]. An SRM can be implemented either by a semi-analytic algorithm [9,5], by using a Monte Carlo simulation [10,11,3], by experimental measurements [12] or by a combination of these methods [13].…”

On the relation between Kaiser–Bessel blob and tube of response based modelling of the system matrix in iterative PET image reconstruction

“…A further strategy is the inclusion of resolution recovery modelling into the projector by replacing the LOR with a tube of response (TOR) of suitable cross section (Ollinger andGoggin 1996, Popescu andLewitt 2004) and optionally variable density (Qi et al 1998, Selivanov et al 2000, Yamaya et al 2005, Iriarte et al 2009, Yao et al 2012, Sportelli et al 2013, Jian et al 2015. This provides a direct way of modelling the detection process but can be computationally more demanding than image-based PSF modelling.…”