Origin Ensemble Algorithm Research Articles

Comparison of reconstructed prompt gamma emissions using maximum likelihood estimation and origin ensemble algorithms for a Compton camera system tailored to proton range monitoring

Compton-based prompt gamma (PG) imaging is being investigated by several groups as a potential solution for in vivo range monitoring in proton therapy. The performance of this technique depends on the detector system as well as the ability of the reconstruction method to obtain good spatial resolution to establish a quantitative correlation between the PG emission and the proton beam range in the patient. To evaluate the feasibility of PG imaging for range monitoring, we quantitatively evaluated the emission distributions reconstructed by a Maximum Likelihood Expectation Maximization (MLEM) and a Stochastic Origin Ensemble (SOE) algorithm. To this end, we exploit experimental and Monte Carlo (MC) simulation data acquired with the Polaris-J Compton Camera (CC) prototype. The differences between the proton beam range (RD) defined as the 80% distal dose fall-off and the PG range (RPG), obtained by fitting the distal end of the reconstructed profile with a sigmoid function, were quantified. A comparable performance of both reconstruction algorithms was found. For both experimental and simulated irradiation scenarios, the correlation between RD and RPG was within 5 mm. These values were consistent with the ground truth distance (RD-RPGg≈ 3 mm) calculated by using the expected PG emission available from MC simulation. Furthermore, shifts of 3 mm in the proton beam range were resolved with the MLEM algorithm by calculating the relative difference between the RPG for each reconstructed profile. In non-homogeneous targets, the spatial changes in the PG emission due to the different materials could not be fully resolved from the reconstructed profiles; however, the fall-off region still resembled the ground truth emission. For this scenario, the PG correlation (RD-RPG) varied from 0.1 mm to 4 mm, which is close to the ground truth correlation (3 mm). This work provides a framework for the evaluation of the range monitoring capabilities of a CC device for PG imaging. The two investigated image reconstruction algorithms showed a comparable and consistent performance for homogeneous and heterogeneous targets.

Rapid compton camera imaging for source terms investigation in the nuclear decommissioning with a subset-driven origin ensemble algorithm

As the nuclear facilities (e.g. nuclear power plants) built in the last century gradually reached their life cycle, some nuclear facilities entered the decommissioning stage. Radioactivity measurement runs through the entire process of nuclear decommissioning, and source terms investigation is particularly important. Compton camera is a new technical method in nuclear facility decommissioning, and has the unique advantage of direct visualization of radiation pollution in nuclear facilities. This paper proposed a subset-driven origin ensemble algorithm with resolution recovery, which is suitable for rapid reconstruction of large space via Compton cameras. The proposed algorithm can correct the projection data deviation caused by the inherent spatial and energy resolution of the Compton camera as well as the Doppler broadening effect, and realize the rapid positioning of the spatial radiation source within a few seconds. We used both the Monte Carlo simulation based on Geant4 and the experiments of the double-layer Compton camera prototype to verify the feasibility of this new algorithm in real-time radiation source detection. This research can provide a promising method for the spatial radiation field reconstruction of nuclear facilities based on Compton cameras and the refined management of nuclear facilities decommissioning.

Radiopharmaceutical imaging based on 3D-CZT Compton camera with 3D-printed mouse phantom

PurposeThe study proposes the use of three-dimensional CdZnTe Compton camera (3D-CZT CC) for radiopharmaceutical imaging and investigates the influence factors using a 3D-printed mouse phantom. MethodsThe event selection method and image reconstruction algorithm are optimized by Monte Carlo simulations and mouse phantom experiments. ResultsSimulation results show that the intrinsic energy resolution and spatial resolution of 3D-CZT cause a certain deviation in the calculated Compton scattering angle and Compton axis. Such deviation causes the imaging quality to deteriorate. By selecting events whose distance between Compton and photoelectronic interactions are larger than 10 mm, the mean deviation of the Compton axis could be reduced to less than 10%. Using the ordered origin ensemble algorithm with resolution recovery, the artifacts around organs where the radiopharmaceutical was placed are reduced, and the quality of the reconstruction results are improved compared to the results with simple back projection and origin ensembles algorithms. The phantom study shows that the 3D-CZT CC imaging device could visualize the radiopharmaceuticals distribution by 15 min detection. ConclusionsThrough the analysis of this study, the feasibility of 3D-CZT CC for in-vivo distribution measurement of radiopharmaceuticals is demonstrated, and the quality of reconstruction result has been improved.

Monte Carlo evaluation of a LYSO-based Compton camera using two origin ensemble algorithms with resolution recovery.

Due to the lack of depth-of-interaction information, a Compton camera made of lutetium-yttrium orthosilicate (LYSO) crystals suffers from poor spatial resolution, which may lead to an unreliable range verification in proton therapy. The aim of this study is to evaluate the performance of a LYSO-based Compton camera using the origin ensemble algorithm with resolution recovery (OE-RR). We also proposed a regularized version of OE-RR called ROE-RR. We simulated a two-layer LYSO-based Compton camera which was used to detect prompt gammas (PGs) produced by a proton beam irradiated on a water phantom. PG images reconstructed by the OE-RR algorithm were evaluated and compared with those reconstructed by the proposed ROE-RR algorithm. Our simulated results show that both the OE-RR and ROE-RR algorithms could provide an accurate estimate of the Bragg peak position, with a mean positioning error of 2.5mm. Compared to the OE-RR algorithm, the proposed ROE-RR algorithm is less sensitive with respect to initial conditions and requires less iterations for converging to equilibrium. More importantly, the proposed ROE-RR algorithm could provide better image quality than the OE-RR algorithm, especially in low-count data. For LYSO-based Compton cameras, using a resolution-recovery image reconstruction algorithm is essential for reliable range verification.

A noise smoothing origin ensemble algorithm based on local filtering

An origin ensemble (OE) image reconstruction algorithm can be used for the fast reconstruction of unconventional geometrical images, e.g. in a Compton camera (CC) system. Due to the low-count rate in the emission data, the reconstructed image is often noisy and inhomogeneous in density. In this study, we propose a way to smooth out the noise in the OE algorithm. During the OE reconstruction, the algorithm stochastically modifies the current location to a random new voxel along the probable corresponding curve of each event depending on the relative event density of the new and old locations. In the original OE technique, the event density is simply the number of events in the voxel. In the proposed method, the event density is estimated from the filtering of a kernel window centered on the voxel. Incorporating the regional filtering is similar to performing an OE algorithm on a smoothed image at each iteration and enables the reconstruction of a smoother image. A Flangeless Esser PET phantom and a multi-activity phantom are used to study the property of the new reconstruction algorithm. The results indicate that the proposed method performs better than a conventional OE algorithm in terms of normalized mean square error (NMSE) and structural similarity (SSIM). Both contrast noise ratio (CNR) and reconstruction accuracy of the new method are better than the conventional OE algorithm and their performances improve with the increase of object size. The median-OE possesses the highest overall image quality and recovery rate among the three filter-OE algorithms and is the method of choice for image reconstruction. Comparing to conventional post-smoothing OEs, the NMSE of median-OE improves 57.6% (46.9%) and the SSIM increased by 73.2% (51.1%) for the Esser (multi-activity) phantom. The proposed OE algorithm is simple and efficient for noise smoothing without complex calculations and highly suited for low-count cases.

Compton-based prompt gamma imaging using ordered origin ensemble algorithm with resolution recovery in proton therapy

Prompt gamma ray (PG) imaging based on Compton camera (CC) is promising to realize in vivo verification during the proton therapy. However, the finite spatial and energy resolution of current CC, as well as the Doppler broaden effect, degrade the quality and resolution of PG images. In addition, due to the inherent geometrical complexity of Compton camera data, PG imaging can be time-consuming and difficult to reconstruct in real-time, while using standard techniques such as filtered back-projection or maximum likelihood-expectation maximization. In this paper, we propose three modifications of origin ensembles with resolution recovery (OE-RR) algorithm based on Markov chains to accelerate the convergence to equilibrium of OE-RR algorithm and improve the image quality. For evaluation, we performed a Monte Carlo simulation of a three-stage CZT Compton camera with resolution loss to detect the PG produced by a proton beam in a water phantom, and evaluate image quality of the gamma rays emitted during proton irradiation. The results show that our ordered OE-RR algorithm realized a good resolution recovery and accurate estimation of the position, including the peak and the distal falloff of the PG emission with remarkably faster reconstruction, thus demonstrating the feasibility of this new method in non-idealized PG-based proton range verification.

PET image reconstruction using the Origin Ensemble algorithm and geometric constraints

Abstract The Origin Ensemble method allows image reconstruction of photon-limited emission tomography data to be performed entirely in the image domain. This offers attractive perspectives such as including scatter events for image reconstruction in Positron Emission Tomography. In this work, the probability of single Compton scatter along a line-of-response is estimated by the Single Scatter Simulation algorithm; for every event a decision is made whether this event is reconstructed along a line or an area confined by two circular arcs holding potential scatter points. First results of 2D simulations show visual agreement with the reference and locally increased contrast recovery coefficient values.

Reconstruction of multiple-pinhole micro-SPECT data using origin ensembles.

The authors are currently developing a dual-resolution multiple-pinhole microSPECT imaging system based on three large NaI(Tl) gamma cameras. Two multiple-pinhole tungsten collimator tubes will be used sequentially for whole-body "scout" imaging of a mouse, followed by high-resolution (hi-res) imaging of an organ of interest, such as the heart or brain. Ideally, the whole-body image will be reconstructed in real time such that data need only be acquired until the area of interest can be visualized well-enough to determine positioning for the hi-res scan. The authors investigated the utility of the origin ensemble (OE) algorithm for online and offline reconstructions of the scout data. This algorithm operates directly in image space, and can provide estimates of image uncertainty, along with reconstructed images. Techniques for accelerating the OE reconstruction were also introduced and evaluated. System matrices were calculated for our 39-pinhole scout collimator design. SPECT projections were simulated for a range of count levels using the MOBY digital mouse phantom. Simulated data were used for a comparison of OE and maximum-likelihood expectation maximization (MLEM) reconstructions. The OE algorithm convergence was evaluated by calculating the total-image entropy and by measuring the counts in a volume-of-interest (VOI) containing the heart. Total-image entropy was also calculated for simulated MOBY data reconstructed using OE with various levels of parallelization. For VOI measurements in the heart, liver, bladder, and soft-tissue, MLEM and OE reconstructed images agreed within 6%. Image entropy converged after ∼2000 iterations of OE, while the counts in the heart converged earlier at ∼200 iterations of OE. An accelerated version of OE completed 1000 iterations in <9 min for a 6.8M count data set, with some loss of image entropy performance, whereas the same dataset required ∼79 min to complete 1000 iterations of conventional OE. A combination of the two methods showed decreased reconstruction time and no loss of performance when compared to conventional OE alone. OE-reconstructed images were found to be quantitatively and qualitatively similar to MLEM, yet OE also provided estimates of image uncertainty. Some acceleration of the reconstruction can be gained through the use of parallel computing. The OE algorithm is useful for reconstructing multiple-pinhole SPECT data and can be easily modified for real-time reconstruction.

Resolution recovery for Compton camera using origin ensemble algorithm.

Compton cameras (CCs) use electronic collimation to reconstruct the images of activity distribution. Although this approach can greatly improve imaging efficiency, due to complex geometry of the CC principle, image reconstruction with the standard iterative algorithms, such as ordered subset expectation maximization (OSEM), can be very time-consuming, even more so if resolution recovery (RR) is implemented. We have previously shown that the origin ensemble (OE) algorithm can be used for the reconstruction of the CC data. Here we propose a method of extending our OE algorithm to include RR. To validate the proposed algorithm we used Monte Carlo simulations of a CC composed of multiple layers of pixelated CZT detectors and designed for imaging small animals. A series of CC acquisitions of small hot spheres and the Derenzo phantom placed in air were simulated. Images obtained from (a) the exact data, (b) blurred data but reconstructed without resolution recovery, and (c) blurred and reconstructed with resolution recovery were compared. Furthermore, the reconstructed contrast-to-background ratios were investigated using the phantom with nine spheres placed in a hot background. Our simulations demonstrate that the proposed method allows for the recovery of the resolution loss that is due to imperfect accuracy of event detection. Additionally, tests of camera sensitivity corresponding to different detector configurations demonstrate that the proposed CC design has sensitivity comparable to PET. When the same number of events were considered, the computation time per iteration increased only by a factor of 2 when OE reconstruction with the resolution recovery correction was performed relative to the original OE algorithm. We estimate that the addition of resolution recovery to the OSEM would increase reconstruction times by 2-3 orders of magnitude per iteration. The results of our tests demonstrate the improvement of image resolution provided by the OE reconstructions with resolution recovery. The quality of images and their contrast are similar to those obtained from the OE reconstructions from scans simulated with perfect energy and spatial resolutions.

Time-of-flight PET image reconstruction using origin ensembles

The origin ensemble (OE) algorithm is a novel statistical method for minimum-mean-square-error (MMSE) reconstruction of emission tomography data. This method allows one to perform reconstruction entirely in the image domain, i.e. without the use of forward and backprojection operations. We have investigated the OE algorithm in the context of list-mode (LM) time-of-flight (TOF) PET reconstruction. In this paper, we provide a general introduction to MMSE reconstruction, and a statistically rigorous derivation of the OE algorithm. We show how to efficiently incorporate TOF information into the reconstruction process, and how to correct for random coincidences and scattered events. To examine the feasibility of LM-TOF MMSE reconstruction with the OE algorithm, we applied MMSE-OE and standard maximum-likelihood expectation-maximization (ML-EM) reconstruction to LM-TOF phantom data with a count number typically registered in clinical PET examinations. We analyzed the convergence behavior of the OE algorithm, and compared reconstruction time and image quality to that of the EM algorithm. In summary, during the reconstruction process, MMSE-OE contrast recovery (CRV) remained approximately the same, while background variability (BV) gradually decreased with an increasing number of OE iterations. The final MMSE-OE images exhibited lower BV and a slightly lower CRV than the corresponding ML-EM images. The reconstruction time of the OE algorithm was approximately 1.3 times longer. At the same time, the OE algorithm can inherently provide a comprehensive statistical characterization of the acquired data. This characterization can be utilized for further data processing, e.g. in kinetic analysis and image registration, making the OE algorithm a promising approach in a variety of applications.

Evaluation of Origin Ensemble algorithm for image reconstruction for pixelated solid-state detectors with large number of channels

The Voxel Imaging PET (VIP) Pathfinder project intends to show the advantages of using pixelated solid-state technology for nuclear medicine applications. It proposes designs for Positron Emission Tomography (PET), Positron Emission Mammography (PEM) and Compton gamma camera detectors with a large number of signal channels (of the order of 106). For PET scanners, conventional algorithms like Filtered Back-Projection (FBP) and Ordered Subset Expectation Maximization (OSEM) are straightforward to use and give good results. However, FBP presents difficulties for detectors with limited angular coverage like PEM and Compton gamma cameras, whereas OSEM has an impractically large time and memory consumption for a Compton gamma camera with a large number of channels. In this article, the Origin Ensemble (OE) algorithm is evaluated as an alternative algorithm for image reconstruction. Monte Carlo simulations of the PET design are used to compare the performance of OE, FBP and OSEM in terms of the bias, variance and average mean squared error (MSE) image quality metrics. For the PEM and Compton camera designs, results obtained with OE are presented.