Line Of Response Research Articles

Positron emission particle tracking: A powerful technique for flow studies

Positron emission particle tracking (PEPT) has developed into a flexible applied nuclear technique for measuring the trajectory of a single tracer particle moving in a system of granular or liquid flow or attached to a moving rigid body. The tracer particle is labelled with a radionuclide (such as [Formula: see text]F or [Formula: see text]Ga) that decays via positron emission. The nearly collinear 511 keV annihilation gamma rays are detected in coincidence by a modified positron emission tomography (PET) camera, which defines their line of response (LOR). The chronologically measured LORs may then be used to triangulate the position of the moving tracer particle. We present an introduction to PEPT and illustrate the quality of measurements possible with a high-resolution PET scanner. Data are presented and discussed with reference to a few fundamental measurement scenarios and a framework for the metrology of PEPT is introduced.

Fast and accurate generation method of PSF-based system matrix for PET reconstruction**Supported by National Natural Science Foundation of China (81301348) and China Postdoctoral Science Foundation (2015M570154)

This work investigates the positional single photon incidence response (P-SPIR) to provide an accurate point spread function (PSF)-contained system matrix and its incorporation within the image reconstruction framework. Based on the Geant4 Application for Emission Tomography (GATE) simulation, P-SPIR theory takes both incidence angle and incidence position of the gamma photon into account during crystal subdivision, instead of only taking the former into account, as in single photon incidence response (SPIR). The response distribution obtained in this fashion was validated using Monte Carlo simulations. In addition, two-block penetration and normalization of the response probability are introduced to improve the accuracy of the PSF. With the incorporation of the PSF, the homogenization model is then analyzed to calculate the spread distribution of each line-of-response (LOR). A primate PET scanner, Eplus-260, developed by the Institute of High Energy Physics, Chinese Academy of Sciences (IHEP), was employed to evaluate the proposed method. The reconstructed images indicate that the P-SPIR method can effectively mitigate the depth-of-interaction (DOI) effect, especially at the peripheral area of field-of-view (FOV). Furthermore, the method can be applied to PET scanners with any other structures and list-mode data format with high flexibility and efficiency.

Model-Based Normalization of a Fractional-Crystal Collimator for Small-Animal PET Imaging.

Previously, we proposed to use a coincidence collimator to achieve fractional-crystal resolution in PET imaging. We have designed and fabricated a collimator prototype for a small-animal PET scanner, A-PET. To compensate for imperfections in the fabricated collimator prototype, collimator normalization, as well as scanner normalization, is required to reconstruct quantitative and artifact-free images. In this study, we develop a normalization method for the collimator prototype based on the A-PET normalization using a uniform cylinder phantom. We performed data acquisition without the collimator for scanner normalization first, and then with the collimator from eight different rotation views for collimator normalization. After a reconstruction without correction, we extracted the cylinder parameters from which we generated expected emission sinograms. Single scatter simulation was used to generate the scattered sinograms. We used the least-squares method to generate the normalization coefficient for each LOR based on measured, expected and scattered sinograms. The scanner and collimator normalization coefficients were factorized by performing two normalizations separately. The normalization methods were also verified using experimental data acquired from A-PET with and without the collimator. In summary, we developed a model-base collimator normalization that can significantly reduce variance and produce collimator normalization with adequate statistical quality within feasible scan time.

Quantitative image reconstruction for total-body PET imaging using the 2-meter long EXPLORER scanner

The EXPLORER project aims to build a 2 meter long total-body PET scanner, which will provide extremely high sensitivity for imaging the entire human body. It will possess a range of capabilities currently unavailable to state-of-the-art clinical PET scanners with a limited axial field-of-view. The huge number of lines-of-response (LORs) of the EXPLORER poses a challenge to the data handling and image reconstruction. The objective of this study is to develop a quantitative image reconstruction method for the EXPLORER and compare its performance with current whole-body scanners. Fully 3D image reconstruction was performed using time-of-flight list-mode data with parallel computation. To recover the resolution loss caused by the parallax error between crystal pairs at a large axial ring difference or transaxial radial offset, we applied an image domain resolution model estimated from point source data. To evaluate the image quality, we conducted computer simulations using the SimSET Monte–Carlo toolkit and XCAT 2.0 anthropomorphic phantom to mimic a 20 min whole-body PET scan with an injection of 25 MBq 18F-FDG. We compare the performance of the EXPLORER with a current clinical scanner that has an axial FOV of 22 cm. The comparison results demonstrated superior image quality from the EXPLORER with a 6.9-fold reduction in noise standard deviation comparing with multi-bed imaging using the clinical scanner.

Influence of Rotation Increments on Imaging Performance for a Rotatory Dual-Head PET System.

For a rotatory dual-head positron emission tomography (PET) system, how to determine the rotation increments is an open problem. In this study, we simulated the characteristics of a rotatory dual-head PET system. The influences of different rotation increments were compared and analyzed. Based on this simulation, the imaging performance of a prototype system was verified. A reconstruction flowchart was proposed based on a precalculated system response matrix (SRM). The SRM made the relationships between the voxels and lines of response (LORs) fixed; therefore, we added the interpolation method into the flowchart. Five metrics, including spatial resolution, normalized mean squared error (NMSE), peak signal-to-noise ratio (PSNR), contrast-to-noise (CNR), and structure similarity (SSIM), were applied to assess the reconstructed image quality. The results indicated that the 60° rotation increments with the bilinear interpolation had advantages in resolution, PSNR, NMSE, and SSIM. In terms of CNR, the 90° rotation increments were better than other increments. In addition, the reconstructed images of 90° rotation increments were also flatter than that of 60° increments. Therefore, both the 60° and 90° rotation increments could be used in the real experiments, and which one to choose may depend on the application requirement.

A feature point identification method for positron emission particle tracking with multiple tracers

A novel detection algorithm for Positron Emission Particle Tracking (PEPT) with multiple tracers based on optical feature point identification (FPI) methods is presented. This new method, the FPI method, is compared to a previous multiple PEPT method via analyses of experimental and simulated data. The FPI method outperforms the older method in cases of large particle numbers and fine time resolution. Simulated data show the FPI method to be capable of identifying 100 particles at 0.5mm average spatial error. Detection error is seen to vary with the inverse square root of the number of lines of response (LORs) used for detection and increases as particle separation decreases.

Data-Driven Methods for the Determination of Anterior-Posterior Motion in PET.

Physiological motion combined with elongated scanning times in PET leads to image degradation and quantification errors. Correction approaches usually require 1-D signals that can be obtained with hardware-based or data-driven methods. Most of the latter are optimized or limited to capture internal motion along the superior-inferior (S-I) direction. In this work we present methods for also extracting anterior-posterior (A-P) motion from PET data and propose a set of novel weighting mechanisms that can be used to emphasize certain lines-of-response (LORs) for an increased sensitivity and better signal-to-noise ratio (SNR). The proper functioning of the methods was verified in a phantom experiment. Further, their application to clinical [18F]-FDG-PET data of 72 patients revealed that using the weighting mechanisms leads to signals with significantly higher spectral respiratory weights, i.e. signals with higher quality. Information about multi-dimensional motion is contained in PET data and can be derived with data-driven methods. Motion models or correction techniques such as respiratory gating might benefit from the proposed methods as they allow to describe the three-dimensional movements of PET-positive structures more precisely.

CERN breakthrough technologies for non-invasive, in vivo, image-guided diagnosis

CERN, the largest laboratory for particle physics worldwide is at the forefront of detector technology development for many different applications. Over recent decades, many important medical diagnostic and therapeutic techniques have been developed from CERN’s fundamental research results or from technological progresses in these areas. A short description of these technologies and their application to medicine will be given. Focus will be made on new, higher performance imaging tools with multimodal capabilities including PET. These tools introduce breakthrough technologies for novel endoscopic procedures in diagnostic and therapeutic endoscopy and in surgical oncology aiming at diagnosing more patients with earlier tumour stages and improving patient outcome and therapy, as well as reducing health costs. Technical objectives include: a very high sensitivity allowed by the endoscopic approach and the proximity of the target. A spatial resolution of 1 mm to delineate early tumours. A time resolution of 200 ps corresponding to a spatial resolution of 3 cm along the Line of Response (LOR) in a dual-head system, allowing a direct (and therefore fast) 3-dimensional reconstruction through a limited number of angular projections only, and an efficient rejection of background coming from outside of the few cubic centimetres region of interest (ROI). The presentation will also emphasize on the number of challenges that have been addressed, both technically and clinically, which have led to the development and introduction of cutting edge technologies in three technological areas: scintillator performances and production methods, light transport and photo-detectors.

Application of the compress sensing theory for improvement of the TOF resolution in a novel J-PET instrument

Abstract Nowadays, in positron emission tomography (PET) systems, a time of flight (TOF) information is used to improve the image reconstruction process. In TOF-PET, fast detectors are able to measure the difference in the arrival time of the two gamma rays, with the precision enabling to shorten significantly a range along the line-of-response (LOR) where the annihilation occurred. In the new concept, called J-PET scanner, gamma rays are detected in plastic scintillators. In a single strip of J-PET system, time values are obtained by probing signals in the amplitude domain. Owing to compressive sensing (CS) theory, information about the shape and amplitude of the signals is recovered. In this paper, we demonstrate that based on the acquired signals parameters, a better signal normalization may be provided in order to improve the TOF resolution. The procedure was tested using large sample of data registered by a dedicated detection setup enabling sampling of signals with 50-ps intervals. Experimental setup provided irradiation of a chosen position in the plastic scintillator strip with annihilation gamma quanta.

Recovering the triple coincidence of non-pure positron emitters in preclinical PET**Parts of this work were presented at the 2012 Annual Congress of the European Association of Nuclear Medicine.

Non-pure positron emitters, with their long half-lives, allow for the tracing of slow biochemical processes which cannot be adequately examined by the commonly used short-lived positron emitters. Most of these isotopes emit high-energy cascade gamma rays in addition to positron decay that can be detected and create a triple coincidence with annihilation photons. Triple coincidence is discarded in most scanners, however, the majority of the triple coincidence contains true photon pairs that can be recovered. In this study, we propose a strategy for recovering triple coincidence events to raise the sensitivity of PET imaging for non-pure positron emitters. To identify the true line of response (LOR) from a triple coincidence, a framework utilizing geometrical, energy and temporal information is proposed. The geometrical criterion is based on the assumption that the LOR with the largest radial offset among the three sub pairs of triple coincidences is least likely to be a true LOR. Then, a confidence time window is used to test the valid LOR among those within triple coincidence. Finally, a likelihood ratio discriminant rule based on the energy probability density distribution of cascade and annihilation gammas is established to identify the true LOR. An Inveon preclinical PET scanner was modeled with GATE (GEANT4 application for tomographic emission) Monte Carlo software. We evaluated the performance of the proposed method in terms of identification fraction, noise equivalent count rates (NECR), and image quality on various phantoms. With the inclusion of triple coincidence events using the proposed method, the NECR was found to increase from 11% to 26% and 19% to 29% for I-124 and Br-76, respectively, when 7.4–185 MBq of activity was used. Compared to the reconstructed images using double coincidence, this technique increased the SNR by 5.1–7.3% for I-124 and 9.3–10.3% for Br-76 within the activity range of 9.25–74 MBq, without compromising the spatial resolution or contrast. We conclude that the proposed method can improve the counting statistics of PET imaging for non-pure positron emitters and is ready to be implemented on current PET systems.

Using triple gamma coincidences with a pixelated semiconductor Compton-PET scanner: a simulation study

The Voxel Imaging PET (VIP) Pathfinder project presents a novel design using pixelated semiconductor detectors for nuclear medicine applications to achieve the intrinsic image quality limits set by physics. The conceptual design can be extended to a Compton gamma camera. The use of a pixelated CdTe detector with voxel sizes of 1 × 1 × 2 mm3 guarantees optimal energy and spatial resolution. However, the limited time resolution of semiconductor detectors makes it impossible to use Time Of Flight (TOF) with VIP PET. TOF is used in order to improve the signal to noise ratio (SNR) by using only the most probable portion of the Line-Of-Response (LOR) instead of its entire length. To overcome the limitation of CdTe time resolution, we present in this article a simulation study using β+-γ emitting isotopes with a Compton-PET scanner. When the β+ annihilates with an electron it produces two gammas which produce a LOR in the PET scanner, while the additional gamma, when scattered in the scatter detector, provides a Compton cone that intersects with the aforementioned LOR. The intersection indicates, within a few mm of uncertainty along the LOR, the origin of the beta-gamma decay. Hence, one can limit the part of the LOR used by the image reconstruction algorithm.

High performance volume-of-intersection projectors for 3D-PET image reconstruction based on polar symmetries and SIMD vectorisation

For high-resolution, iterative 3D PET image reconstruction the efficient implementation of forward-backward projectors is essential to minimise the calculation time. Mathematically, the projectors are summarised as a system response matrix (SRM) whose elements define the contribution of image voxels to lines-of-response (LORs). In fact, the SRM easily comprises billions of non-zero matrix elements to evaluate the tremendous number of LORs as provided by state-of-the-art PET scanners. Hence, the performance of iterative algorithms, e.g. maximum-likelihood-expectation-maximisation (MLEM), suffers from severe computational problems due to the intensive memory access and huge number of floating point operations.Here, symmetries occupy a key role in terms of efficient implementation. They reduce the amount of independent SRM elements, thus allowing for a significant matrix compression according to the number of exploitable symmetries. With our previous work, the PET REconstruction Software TOolkit (PRESTO), very high compression factors (>300) are demonstrated by using specific non-Cartesian voxel patterns involving discrete polar symmetries. In this way, a pre-calculated memory-resident SRM using complex volume-of-intersection calculations can be achieved. However, our original ray-driven implementation suffers from addressing voxels, projection data and SRM elements in disfavoured memory access patterns. As a consequence, a rather limited numerical throughput is observed due to the massive waste of memory bandwidth and inefficient usage of cache respectively.In this work, an advantageous symmetry-driven evaluation of the forward-backward projectors is proposed to overcome these inefficiencies. The polar symmetries applied in PRESTO suggest a novel organisation of image data and LOR projection data in memory to enable an efficient single instruction multiple data vectorisation, i.e. simultaneous use of any SRM element for symmetric LORs. In addition, the calculation time is further reduced by using simultaneous multi-threading (SMT). A global speedup factor of 11 without SMT and above 100 with SMT has been achieved for the improved CPU-based implementation while obtaining equivalent numerical results.

LOR-Based Reconstruction for Super-Resolved 3D PET Image on GPU

Positron emission tomography (PET) images usually suffer from low spatial resolution mainly because of the finite dimension of crystals. To improve the spatial resolution based on wobble scanning, we previously proposed a sinogram-based super-resolution (SR) algorithm using a space-variant blur matrix. However, the algorithm may cause unwanted resolution loss owing to an inevitable interpolation process for preparing evenly spaced projections. In this article, we propose a novel one-step line of response (LOR)-based SR framework for 3D PET images. In the framework, we efficiently determine a large number of space-variant point spread functions (PSFs) in the image space by using the scanner symmetries and the proposed PSF interpolation scheme based on nonrigid registration. Furthermore, to minimize the resolution degradation in the evenly spaced parallel-beam rebinning and to reduce the computational time in the graphics processing unit (GPU) implementation, we introduce parallel-friendly LOR reconstruction based on cone-beam reordering. We then obtain a high resolution image via a one-step super-resolved 3D PET image reconstruction with the determined PSFs. The proposed framework provides noticeable improvement on the spatial resolution of PET images with a considerable reduction of computational time.

Real Time Artificial Neural Network FPGA Implementation for Triple Coincidences Recovery in PET

In small-animal Positron Emission Tomography (PET), spatial resolution improvements rely on detector minimization in size and often come at the expense of lowering the detector photoelectric fraction. As a result, Inter-Crystal Scatter (ICS) occurrences are increased and affect the overall PET detection efficiency. To reclaim some lost efficiency, previous work used an artificial neural network (ANN) to identify the true line of response (LOR) for the simplest multiple event detection case, three coincident singles known as triplets. Despite promising results, this method is limited to an offline processing which is impractical when a limited data bandwidth is present between the scanner and the PC. This paper demonstrates the capability of processing triplets in real time using an ANN implemented in the field-programmable gate array (FPGA). The ANN pipelined architecture can process over 1 million triplets/second using less than 6000 FPGA slices. Real time processing on the LabPET I scanner yielded an overall 39.7% increase in detection efficiency relative to traditional high resolution settings with a 360-660 keV energy window along with a slight Contrast-to-Noise Ratio ( $CNR$ ) degradation. Although improvements are still possible, the proposed FPGA implementation proves the usability of an ANN in real time PET applications in conditions where spare computational resources are limited and the data rate to be processed is high.

Ultra fast, accurate PET image reconstruction for the Siemens hybrid MR/BrainPET scanner using raw LOR data.

Fast PET image reconstruction algorithms usually use a Line-of-Response (LOR) preprocessing step where the detected raw LOR data are interpolated either to evenly spaced sinogram projection bins or alternatively to a generic projection space as for example proposed by the PET Reconstruction Software Toolkit (PRESTO) [1]. In this way, speed-optimised, versatile geometrical projectors can be implemented for iterative image reconstruction independent of the underlying scanner geometry. However, all strategies of projection data interpolation unavoidably lead to a loss of original information and result in some degradation of image quality. Here, direct LOR reconstructions overcome this evident drawback at cost of a massively enhanced computational burden. Therefore, computational optimisation techniques are essential to make such demanding approaches attractive and economical for widespread usage in the clinical environment. In this paper, we demonstrate for the Siemens Hybrid MR/BrainPET with 240 million physical LORs that a very fast quantitative direct LOR reconstruction can be realized using a modified version of PRESTO. Now, PRESTO is also capable to directly use sets of symmetric physical LORs instead of interpolating LORs to a generic projection space. Exploiting basic scanner symmetries together with the technique of Single Instruction Multipe Data (SIMD) and Simultaneous Multi-Threading (SMT) results in an overall calculation time of 2-3 minutes per frame on a single multi-core machine, i.e. neither requiring a cluster of mutliple machines nor Graphics Processing Units (GPUs).

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

We investigate the question of how the blob approach is related to tube of response based modelling of the system matrix. In our model, the tube of response (TOR) is approximated as a cylinder with constant density (TOR-CD) and the cubic voxels are replaced by spheres. Here we investigate a modification of the TOR model that makes it effectively equivalent to the blob model, which models the intersection of lines of response (LORs) with radially variant basis functions (‘blobs’) replacing the cubic voxels. Implications of the achieved equivalence regarding the necessity of final resampling in blob-based reconstructions are considered. We extended TOR-CD to a variable density tube model (TOR-VD) that yields a weighting function (defining all system matrix elements) which is essentially identical to that of the blob model. The variable density of TOR-VD was modelled by a Gaussian and a Kaiser–Bessel function, respectively. The free parameters of both model functions were determined by fitting the corresponding weighting function to the weighting function of the blob model. TOR-CD and the best-fitting TOR-VD were compared to the blob model with a final resampling step (BLOB-RS) and without resampling (BLOB-NRS) in phantom studies. For three different contrast ratios and two different voxel sizes, resolution noise curves were generated. TOR-VD and BLOB-NRS lead to nearly identical images for all investigated contrast ratios and voxel sizes. Both models showed strong Gibbs artefacts at 4 mm voxel size, while at 2 mm voxel size there were no Gibbs artefacts visible. The spatial resolution was similar to the resolution with TOR-CD in all cases. The resampling step removed most of the Gibbs artefacts and reduced the noise level but also degraded the spatial resolution substantially. We conclude that the blob model can be considered just as a special case of a TOR-based reconstruction. The latter approach provides a more natural description of the detection process and allows for modifications that are not readily representable within the blob framework.

Recovery and normalization of triple coincidences in PET.

Triple coincidences in positron emission tomography (PET) are events in which three γ-rays are detected simultaneously. These events, though potentially useful for enhancing the sensitivity of PET scanners, are discarded or processed without special consideration in current systems, because there is not a clear criterion for assigning them to a unique line-of-response (LOR). Methods proposed for recovering such events usually rely on the use of highly specialized detection systems, hampering general adoption, and/or are based on Compton-scatter kinematics and, consequently, are limited in accuracy by the energy resolution of standard PET detectors. In this work, the authors propose a simple and general solution for recovering triple coincidences, which does not require specialized detectors or additional energy resolution requirements. To recover triple coincidences, the authors' method distributes such events among their possible LORs using the relative proportions of double coincidences in these LORs. The authors show analytically that this assignment scheme represents the maximum-likelihood solution for the triple-coincidence distribution problem. The PET component of a preclinical PET/CT scanner was adapted to enable the acquisition and processing of triple coincidences. Since the efficiencies for detecting double and triple events were found to be different throughout the scanner field-of-view, a normalization procedure specific for triple coincidences was also developed. The effect of including triple coincidences using their method was compared against the cases of equally weighting the triples among their possible LORs and discarding all the triple events. The authors used as figures of merit for this comparison sensitivity, noise-equivalent count (NEC) rates and image quality calculated as described in the NEMA NU-4 protocol for the assessment of preclinical PET scanners. The addition of triple-coincidence events with the authors' method increased peak NEC rates of the scanner by 26.6% and 32% for mouse- and rat-sized objects, respectively. This increase in NEC-rate performance was also reflected in the image-quality metrics. Images reconstructed using double and triple coincidences recovered using their method had better signal-to-noise ratio than those obtained using only double coincidences, while preserving spatial resolution and contrast. Distribution of triple coincidences using an equal-weighting scheme increased apparent system sensitivity but degraded image quality. The performance boost provided by the inclusion of triple coincidences using their method allowed to reduce the acquisition time of standard imaging procedures by up to ∼25%. Recovering triple coincidences with the proposed method can effectively increase the sensitivity of current clinical and preclinical PET systems without compromising other parameters like spatial resolution or contrast.

Sensitivity Increase Through a Neural Network Method for LOR Recovery of ICS Triple Coincidences in High-Resolution Pixelated- Detectors PET Scanners

Scanner sensitivity is often critical in high-resolution Positron Emission Tomography (PET) dedicated to molecular imaging. In neighboring pixelated detectors with individual readout, sensitivity decreases because of multiple coincidences produced by Compton scattering. Correct analysis of those coincidences would enable a substantial sensitivity increase. However, including scattering byproducts in the image often lead to image quality degradation because of inaccurate Line-of-Response (LOR) assessment. In such scanners, to support high count rates, multiple coincidences are usually discarded when image degradation is not acceptable, or blindly accepted for a low computational burden. This paper presents a new, real-time capable method that includes Inter-Crystal Scatter (ICS) triple coincidences in the image without significant quality degradation. The method computes the LOR using a neural network fed by preprocessed raw data. As a proof of principle, this paper analyzes the simplest ICS scenario, triple coincidences where one photoelectric 511-keV event coincides with two more whose energy sum is also 511 keV. The paper visits the algorithm structure, presents Monte Carlo assessment with the LabPET model, and displays images reconstructed from real data. With an energy window of 360-660 keV and a singles energy threshold of 125 keV, the inclusion of triple coincidences yielded a sensitivity increase of 54%, a resolution degradation similar to that of other sensitivity-increasing methods, and only a slight contrast degradation for real LabPET data, with potential for numerous further improvements.

LOR-interleaving image reconstruction for PET imaging with fractional-crystal collimation

Positron emission tomography (PET) has become an important modality in medical and molecular imaging. However, in most PET applications, the resolution is still mainly limited by the physical crystal sizes or the detector’s intrinsic spatial resolution. To achieve images with better spatial resolution in a central region of interest (ROI), we have previously proposed using collimation in PET scanners. The collimator is designed to partially mask detector crystals to detect lines of response (LORs) within fractional crystals. A sequence of collimator-encoded LORs is measured with different collimation configurations. This novel collimated scanner geometry makes the reconstruction problem challenging, as both detector and collimator effects need to be modeled to reconstruct high-resolution images from collimated LORs. In this paper, we present a LOR-interleaving (LORI) algorithm, which incorporates these effects and has the advantage of reusing existing reconstruction software, to reconstruct high-resolution images for PET with fractional-crystal collimation. We also develop a 3D ray-tracing model incorporating both the collimator and crystal penetration for simulations and reconstructions of the collimated PET. By registering the collimator-encoded LORs with the collimator configurations, high-resolution LORs are restored based on the modeled transfer matrices using the non-negative least-squares method and EM algorithm. The resolution-enhanced images are then reconstructed from the high-resolution LORs using the MLEM or OSEM algorithm. For validation, we applied the LORI method to a small-animal PET scanner, A-PET, with a specially designed collimator. We demonstrate through simulated reconstructions with a hot-rod phantom and MOBY phantom that the LORI reconstructions can substantially improve spatial resolution and quantification compared to the uncollimated reconstructions. The LORI algorithm is crucial to improve overall image quality of collimated PET, which can have significant implications in preclinical and clinical ROI imaging applications.

Pre-computed system matrix calculation based on a piece-wise method for PET.

A system matrix (SM) is the basic component of iterative image reconstruction algorithms. Calculation of the SM needs a considerable amount of time due to an enormous number of lines of response (LORs) being modeled. In this study, we developed a technique based on a piece-wise calculation method in which symmetry and further division of the voxels are applied. The detector response function for all detectable pairs of photons along certain LORs originating from each voxel is calculated analytically. The total number of LORs in 300×300×120 voxels (with 2×2×2mm(3)) is ~44 billion, and the SM was calculated by the use of three different computers independently; the calculation time was 5h. The SM took 5days when calculated by the use of the conventional method (where symmetry and the piece-wise method are not used). The sensitivity correction factor was stored; it had a size of 42MB in a four-byte computer memory.