A parallelizable compression scheme for Monte Carlo scatter system matrices in PET image reconstruction

Influences of 3D PET scanner components on increased scatter evaluated by a Monte Carlo simulation

Monte Carlo simulation is widely applied to evaluate the performance of three-dimensional positron emission tomography (3D-PET). For accurate scatter simulations, all components that generate scatter need to be taken into account. The aim of this work was to identify the components that influence scatter. The simulated geometries of a PET scanner were: a precisely reproduced configuration including all of the components; a configuration with the bed, the tunnel and shields; a configuration with the bed and shields; and the simplest geometry with only the bed. We measured and simulated the scatter fraction using two different set-ups: (1) as prescribed by NEMA-NU 2007 and (2) a similar set-up but with a shorter line source, so that all activity was contained only inside the field-of-view (FOV), in order to reduce influences of components outside the FOV. The scatter fractions for the two experimental set-ups were, respectively, 45% and 38%. Regarding the geometrical configurations, the former two configurations gave simulation results in good agreement with the experimental results, but simulation results of the simplest geometry were significantly different at the edge of the FOV. From the simulation of the precise configuration, the object (scatter phantom) was the source of more than 90% of the scatter. This was also confirmed by visualization of photon trajectories. Then, the bed and the tunnel were mainly the sources of the rest of the scatter. From the simulation results, we concluded that the precise construction was not needed; the shields, the tunnel, the bed and the object were sufficient for accurate scatter simulations.

Reconstruction of scattered and unscattered PET coincidences using TOF and energy information

In positron emission tomography (PET), a typical reconstruction algorithm relies on a method to estimate and subtract the scatter from the net trues coincidences. The remaining unscattered coincidences are then used to reconstruct an image of the original activity distribution. The introduction of time-of-flight (TOF) PET opens the possibility to change this scheme, and use the spatial information carried by the scattered events for the reconstruction. The combined knowledge of TOF difference and detected photon energy provides spatial information on the position of the source even after single scattering, and can be used for the reconstruction of scattered photons, using a 'scatter back projector' in addition to the conventional 'trues back projector'. In the scatter back projector, the scattering angle is derived from the energy of the scattered photon through Compton kinematics, and this identifies a set of possible scattering trajectories, or 'broken' line of response (LOR). The TOF information localizes the position of the source along the set of broken LOR. The advantages of this proposed method are twofold: including the spatial information about the origin of the scattered pairs could improve the image quality particularly in low count datasets; and the threshold of the energy window can be lowered to include more scatter, thus increasing sensitivity. In this work, this novel approach to scatter in PET is introduced, different implementations are discussed, and the performance of a preliminary version of the 'scatter back projector' is presented.

A scatter and randoms weighted (SRW) iterative PET reconstruction

PURPOSE

In positron emission tomography (PET) imaging, the main function of scatter and randoms corrections is to improve contrast and quantitative accuracy. Both corrections are essential and critically important. Several iterative reconstruction schemes incorporating scatter and randoms corrections have been developed over the years. In this work, the authors propose a new method to incorporate the scatter and randoms corrections into the iterative image reconstruction, which has shown promising results in regards to improving reconstruction performance and image quality as compared to the standard methods.

METHODS

The authors describe a scatter and randoms weighted (SRW) iterative PET reconstruction algorithm. The SRW method is based on the estimation of the trues fraction (TF) within the prompts. Once the TF is estimated, it is then incorporated into the weighting component of the system matrix, and the net result is a scatter and randoms weighting in the sensitivity image similar to the attenuation correction weighting. Although using the measured prompts in the TF estimation was demonstrated to achieve the fastest convergence at high statistics, it is not reliable in low counts situations due to the sparse and noisy nature of the measured prompts. Therefore, a mean estimation of the prompts derived from the forward projection of the reconstructed prompts image was introduced into the TF estimation. A contrast phantom was scanned, and the data were reconstructed using the standard and the SRW methods.

RESULTS

The contrast vs noise, precision vs accuracy in contrast, absolute error vs number of iterations comparisons, and standard deviation image over different realizations of the same object were evaluated at low counts situations, and it was observed that the SRW method outperforms the standard approaches such as the scatter and randoms data precorrection and the ordinary Poisson methods. The image intensity (activity) outside the object can also be minimized using the SRW method. In addition, further improvement in accuracy, precision, convergence, and noise properties can be achieved by further improving the TF and the prompts estimate.

CONCLUSIONS

The authors have developed a practical scatter and randoms weighting scheme in the sensitivity image for iterative PET reconstructions. Our proposed SRW method has a number of advantages over the conventional methods, and it has shown promising results with additional optimization for various applications to be further investigated.

Geometrical and Monte Carlo projectors in 3D PET reconstruction

PURPOSE

In the present work, the authors compare geometrical and Monte Carlo projectors in detail. The geometrical projectors considered were the conventional geometrical Siddon ray-tracer (S-RT) and the orthogonal distance-based ray-tracer (OD-RT), based on computing the orthogonal distance from the center of image voxel to the line-of-response. A comparison of these geometrical projectors was performed using different point spread function (PSF) models. The Monte Carlo-based method under consideration involves an extensive model of the system response matrix based on Monte Carlo simulations and is computed off-line and stored on disk.

METHODS

Comparisons were performed using simulated and experimental data of the commercial small animal PET scanner rPET.

RESULTS

The results demonstrate that the orthogonal distance-based ray-tracer and Siddon ray-tracer using PSF image-space convolutions yield better images in terms of contrast and spatial resolution than those obtained after using the conventional method and the multiray-based S-RT. Furthermore, the Monte Carlo-based method yields slight improvements in terms of contrast and spatial resolution with respect to these geometrical projectors.

CONCLUSIONS

The orthogonal distance-based ray-tracer and Siddon ray-tracer using PSF image-space convolutions represent satisfactory alternatives to factorizing the system matrix or to the conventional on-the-fly ray-tracing methods for list-mode reconstruction, where an extensive modeling based on Monte Carlo simulations is unfeasible.

Advances in PET Image Reconstruction

Until recently, the most widely used methods for image reconstruction were direct analytic techniques. Iterative techniques, although computationally much more intensive, produce improved images (principally arising from more accurate modeling of the acquired projection data), enabling these techniques to replace analytic techniques not only in research settings but also in the clinic. This article offers an overview of image reconstruction theory and algorithms for PET, with a particular emphasis on statistical iterative reconstruction techniques. Future directions for image reconstruction in PET are considered, which concern mainly improving the modeling of the data acquisition process and task-specific specification of the parameters to be estimated in image reconstruction.