Accurate and efficient modeling of the detector response in small animal multi-head PET systems

OMEGA-open-source emission tomography software

In this paper we present OMEGA, an open-source software, for efficient and fast image reconstruction in positron emission tomography (PET). OMEGA uses the scripting language of MATLAB and GNU Octave allowing reconstruction of PET data with a MATLAB or GNU Octave interface. The goal of OMEGA is to allow easy and fast reconstruction of any PET data, and to provide a computationally efficient, easy-access platform for development of new PET algorithms with built-in forward and backward projection operations available to the user as a MATLAB/Octave class. OMEGA also includes direct support for GATE simulated data, facilitating easy evaluation of the new algorithms using Monte Carlo simulated PET data. OMEGA supports parallel computing by utilizing OpenMP for CPU implementations and OpenCL for GPU allowing any hardware to be used. OMEGA includes built-in function for the computation of normalization correction and allows several other corrections to be applied such as attenuation, randoms or scatter. OMEGA includes several different maximum-likelihood and maximum a posteriori (MAP) algorithms with several different priors. The user can also input their own priors to the built-in MAP functions. The image reconstruction in OMEGA can be computed either by using an explicitly computed system matrix or with a matrix-free formalism, where the latter can be accelerated with OpenCL. We provide an overview on the software and present some examples utilizing the different features of the software.

Resolution modeling in projection space using a factorized multi-block detector response function for PET image reconstruction

Positron emission tomography (PET) images usually suffer from limited resolution and statistical uncertainties. However, a technique known as resolution modeling (RM) can be used to improve image quality by accurately modeling the system's detection process within the iterative reconstruction. In this study, we present an accurate RM method in projection space based on a simulated multi-block detector response function (DRF) and evaluate it on the Siemens hybrid MR-BrainPET system. The DRF is obtained using GATE simulations that consider nearly all the possible annihilation photons from the field-of-view (FOV). Intrinsically, the multi-block DRF allows the block crosstalk to be modeled. The RM blurring kernel is further generated by factorizing the blurring matrix of one line-of-response (LOR) into two independent detector responses, which can then be addressed with the DRF. Such a kernel is shift-variant in 4D projection space without any distance or angle compression, and is integrated into the image reconstruction for the BrainPET insert with single instruction multiple data (SIMD) and multi-thread support. Evaluation of simulations and measured data demonstrate that the reconstruction with RM yields significantly improved resolutions and reduced mean squared error (MSE) values at different locations of the FOV, compared with reconstruction without RM. Furthermore, the shift-variant RM kernel models the varying blurring intensity for different LORs due to the depth-of-interaction (DOI) dependencies, thus avoiding severe edge artifacts in the images. Additionally, compared to RM in single-block mode, the multi-block mode shows significantly improved resolution and edge recovery at locations beyond 10 cm from the center of BrainPET insert in the transverse plane. However, the differences have been observed to be low for patient data between single-block and multi-block mode RM, due to the brain size and location as well as the geometry of the BrainPET insert. In conclusion, the RM method proposed in this study can yield better reconstructed images in terms of resolution and MSE value, compared to conventional reconstruction without RM.

A Monte Carlo detector response model for the IRIS PET preclinical scanner

PET preclinical studies require high spatial resolution due to the limited size of the animal under investigation. To achieve this target, iterative image reconstruction algorithms are commonly preferred over the analytical methods because they offer the possibility of accurately modeling the whole imaging process. In this work, we propose an accurate factorized system matrix for the INVISCAN IRIS preclinical PET scanner to be used with an iterative algorithm. The model includes two components: the geometric component and the detector response of the system. The main innovative aspect of the work is the creation of the detector matrix using a Monte Carlo simulation, with a particular focus on the optimization of the simulation process to reduce the calculation time. The new system model is compared with the current IRIS model to evaluate the image quality, following the NEMA Standards NU 4-2008. The comparison showed an enhancement of the image quality, in terms of uniformity and recovery coefficients. This work confirms that the inclusion of the detector response into the system model leads to improved reconstruction results.

Sinogram Blurring Matrix Estimation From Point Sources Measurements With Rank-One Approximation for Fully 3-D PET

An accurate system matrix is essential in positron emission tomography (PET) for reconstructing high quality images. To reduce storage size and image reconstruction time, we factor the system matrix into a product of a geometry projection matrix and a sinogram blurring matrix. The geometric projection matrix is computed analytically and the sinogram blurring matrix is estimated from point source measurements. Previously, we have estimated a 2-D blurring matrix for a preclinical PET scanner. The 2-D blurring matrix only considers blurring effects within a transaxial sinogram and does not compensate for inter-sinogram blurring effects. For PET scanners with a long axial field of view, inter-sinogram blurring can be a major problem influencing the image quality in the axial direction. Hence, the estimation of a 4-D blurring matrix is desirable to further improve the image quality. The 4-D blurring matrix estimation is an ill-conditioned problem due to the large number of unknowns. Here, we propose a rank-one approximation for each blurring kernel image formed by a row vector of the sinogram blurring matrix to improve the stability of the 4-D blurring matrix estimation. The proposed method is applied to the simulated data as well as the real data obtained from an Inveon microPET scanner. The results show that the newly estimated 4-D blurring matrix can improve the image quality over those obtained with a 2-D blurring matrix and requires less point source scans to achieve similar image quality compared with an unconstrained 4-D blurring matrix estimation.

Assessment of a fully 3D Monte Carlo reconstruction method for preclinical PET with iodine-124

Iodine-124 is a radionuclide well suited to the labeling of intact monoclonal antibodies. Yet, accurate quantification in preclinical imaging with I-124 is challenging due to the large positron range and a complex decay scheme including high-energy gammas. The aim of this work was to assess the quantitative performance of a fully 3D Monte Carlo (MC) reconstruction for preclinical I-124 PET. The high-resolution small animal PET Inveon (Siemens) was simulated using GATE 6.1. Three system matrices (SM) of different complexity were calculated in addition to a Siddon-based ray tracing approach for comparison purpose. Each system matrix accounted for a more or less complete description of the physics processes both in the scanned object and in the PET scanner. One homogeneous water phantom and three heterogeneous phantoms including water, lungs and bones were simulated, where hot and cold regions were used to assess activity recovery as well as the trade-off between contrast recovery and noise in different regions. The benefit of accounting for scatter, attenuation, positron range and spurious coincidences occurring in the object when calculating the system matrix used to reconstruct I-124 PET images was highlighted. We found that the use of an MC SM including a thorough modelling of the detector response and physical effects in a uniform water-equivalent phantom was efficient to get reasonable quantitative accuracy in homogeneous and heterogeneous phantoms. Modelling the phantom heterogeneities in the SM did not necessarily yield the most accurate estimate of the activity distribution, due to the high variance affecting many SM elements in the most sophisticated SM.