Maximum Likelihood Expectation Maximization Algorithm Research Articles

Enhanced PET image reconstruction utilizing morphological filtering and MLEM algorithm

Positron Emission Tomography (PET) image reconstruction remains a pivotal area in PET technology, critically influencing clinical diagnostic outcomes. Addressing the need for enhanced image quality, this study introduces a novel algorithm for PET image reconstruction. This algorithm integrates a penalty mechanism, morphological filtering, and the Maximum Likelihood Expectation Maximization (MLEM) algorithm, aiming to improve reconstructed image quality significantly. The operational process of the algorithm within each iteration encompasses two primary phases. Initially, image reconstruction is accomplished via the MLEM algorithm, followed by the application of a morphological filter to attenuate noise in the reconstructed image. Simulation experiments demonstrate that this algorithm effectively mitigates noise while preserving crucial details, such as image edges. Notably, this method presents the dual benefits of straightforward parameter configuration and ease of implementation. The results indicate a substantial enhancement in noise suppression and fine structure preservation in the reconstructed images, marking a significant advancement in PET image reconstruction techniques.

Stochastic model for enhanced PET image reconstruction

In this paper, we present a detailed stochastic model of crystal-to-crystal response for PET scanners, which is crucial for addressing their physical constraints. We present both a closed-form solution and several accurate approximations to manage the complexity of the exact mathematical expressions. Through experimental and analytical validation, we demonstrate that the disparities between the best approximations and actual crystal-to-crystal response are negligible. These responses are utilized to develop a compensation model termed a white image. This model is expressed in a single closed-form equation, simplifying its integration into established reconstruction methods. We modify the maximum likelihood expectation maximization (MLEM) algorithm and integrate our white image model into it. Unlike the conventional approach that relies on the system matrix, the modified MLEM algorithm operates on ray-driven projections and back-projections. The system matrix, being large and requiring complex methods and simulations for evaluation, contrasts with the white image, which is smaller and enables efficient computation. Our compensation model provides comprehensive information about the PET system. We validate our approach with both synthetic and real data. For real-world data acquisition, we utilize the Raytest ClearPET camera for small animals and the NEMA NU 4-2008 phantom. The proposed modification outperforms competing uncompensated reconstruction methods, delivering superior Peak Signal-to-Noise Ratio (PSNR) and reduced execution time. This research deepens our understanding of real PET measurement systems, providing improved input for subsequent reconstruction algorithms and ultimately producing high-quality images.

Assessment of the axial resolution of a compact gamma camera with coded aperture collimator

PurposeHandheld gamma cameras with coded aperture collimators are under investigation for intraoperative imaging in nuclear medicine. Coded apertures are a promising collimation technique for applications such as lymph node localization due to their high sensitivity and the possibility of 3D imaging. We evaluated the axial resolution and computational performance of two reconstruction methods.MethodsAn experimental gamma camera was set up consisting of the pixelated semiconductor detector Timepix3 and MURA mask of rank 31 with round holes of 0.08 mm in diameter in a 0.11 mm thick Tungsten sheet. A set of measurements was taken where a point-like gamma source was placed centrally at 21 different positions within the range of 12–100 mm. For each source position, the detector image was reconstructed in 0.5 mm steps around the true source position, resulting in an image stack. The axial resolution was assessed by the full width at half maximum (FWHM) of the contrast-to-noise ratio (CNR) profile along the z-axis of the stack. Two reconstruction methods were compared: MURA Decoding and a 3D maximum likelihood expectation maximization algorithm (3D-MLEM).ResultsWhile taking 4400 times longer in computation, 3D-MLEM yielded a smaller axial FWHM and a higher CNR. The axial resolution degraded from 5.3 mm and 1.8 mm at 12 mm to 42.2 mm and 13.5 mm at 100 mm for MURA Decoding and 3D-MLEM respectively.ConclusionOur results show that the coded aperture enables the depth estimation of single point-like sources in the near field. Here, 3D-MLEM offered a better axial resolution but was computationally much slower than MURA Decoding, whose reconstruction time is compatible with real-time imaging.

Near-field coded-mask technique and its potential for proton therapy monitoring

Objective. Prompt-gamma imaging encompasses several approaches to the online monitoring of the beam range or deposited dose distribution in proton therapy. We test one of the imaging techniques - a coded mask approach - both experimentally and via simulations. Approach. Two imaging setups have been investigated experimentally. Each of them comprised a structured tungsten collimator in the form of a modified uniformly redundant array mask and a LYSO:Ce scintillation detector of fine granularity. The setups differed in detector dimensions and operation mode (1D or 2D imaging). A series of measurements with radioactive sources have been conducted, testing the performance of the setups for near-field gamma imaging. Additionally, Monte Carlo simulations of a larger setup of the same type were conducted, investigating its performance with a realistic gamma source distribution occurring during proton therapy. Main results. The images of point-like sources reconstructed from two small-scale prototypes’ data using the maximum-likelihood expectation maximisation algorithm constitute the experimental proof of principle for the near-field coded-mask imaging modality, both in the 1D and the 2D mode. Their precision allowed us to calibrate out certain systematic offsets appearing due to the limited alignment accuracy of setup elements. The simulation of the full-scale setup yielded a mean distal falloff retrieval precision of 0.72 mm in the studies for beam energy range 89.5–107.9 MeV and with 1 × 108 protons (a typical number for distal spots). The implemented algorithm of image reconstruction is relatively fast—a typical procedure needs several seconds. Significance. Coded-mask imaging appears a valid option for proton therapy monitoring. The results of simulations let us conclude that the proposed full-scale setup is competitive with the knife-edge-shaped and the multi-parallel slit cameras investigated by other groups.

A generalization of the maximum likelihood expectation maximization (MLEM) method: Masked-MLEM

Objective. In our previous work on image reconstruction for single-layer collimatorless scintigraphy, we developed the min–min weighted robust least squares (WRLS) optimization algorithm to address the challenge of reconstructing images when both the system matrix and the projection data are uncertain. Whereas the WRLS algorithm has been successful in two-dimensional (2D) reconstruction, expanding it to three-dimensional (3D) reconstruction is difficult since the WRLS optimization problem is neither smooth nor strongly-convex. To overcome these difficulties and achieve robust image reconstruction in the presence of system uncertainties and projection noise, we propose a generalized iterative method based on the maximum likelihood expectation maximization (MLEM) algorithm, hereinafter referred to as the Masked-MLEM algorithm. Approach. In the Masked-MLEM algorithm, only selected subsets (‘masks’) from the system matrix and the projection contribute to the image update to satisfy the constraints imposed by the system uncertainties. We validate the Masked-MLEM algorithm and compare it to the standard MLEM algorithm using experimental data obtained from both collimated and uncollimated imaging instruments, including parallel-hole collimated SPECT, 2D collimatorless scintigraphy, and 3D collimatorless tomography. Additionally, we conduct comprehensive Monte Carlo simulations for 3D collimatorless tomography to further validate the effectiveness of the Masked-MLEM algorithm in handling different levels of system uncertainties. Main results. The Masked-MLEM and standard MLEM reconstructions are similar in cases with negligible system uncertainties, whereas the Masked-MLEM algorithm outperforms the standard MLEM algorithm when the system matrix is an approximation. Importantly, the Masked-MLEM algorithm ensures reliable image reconstruction across varying levels of system uncertainties. Significance. With a good choice of system uncertainty and without requiring accurate knowledge of the actual system matrix, the Masked-MLEM algorithm yields more robust image reconstruction than the standard MLEM algorithm, effectively reducing the likelihood of erroneously reconstructing higher activities in regions without radioactive sources.

A Portable Three-Layer Compton Camera for Wide-Energy-Range Gamma-ray Imaging: Design, Simulation and Preliminary Testing

(1) Background: The imaging energy range of a typical Compton camera is limited due to the fact that scattered gamma photons are seldom fully absorbed when the incident energies are above 3 MeV. Further improving the upper energy limit of gamma-ray imaging has important application significance in the active interrogation of special nuclear materials and chemical warfare agents, as well as range verification of proton therapy. (2) Methods: To realize gamma-ray imaging in a wide energy range of 0.3~7 MeV, a principle prototype, named a portable three-layer Compton camera, is developed using the scintillation detector that consists of an silicon photomultiplier array coupled with a Gd3Al2Ga3O12:Ce pixelated scintillator array. Implemented in a list-mode maximum likelihood expectation maximization algorithm, a far-field energy-domain imaging method based on the two interaction events is applied to estimate the initial energy and spatial distribution of gamma-ray sources. The simulation model of the detectors is established based on the Monte Carlo simulation toolkit Geant4. The reconstructed images of a 133Ba, a 137Cs and a 60Co point-like sources have been successfully obtained with our prototype in laboratory tests and compared with simulation studies. (3) Results: The proportion of effective imaging events accounts for about 2%, which allows our prototype to realize the reconstruction of the distribution of a 0.05 μSv/h 137Cs source in 10 s. The angular resolution for resolving two 137Cs point-like sources is 15°. Additional simulated imaging of the 6.13 MeV gamma-rays from 14.1 MeV neutron scattering with water preliminarily demonstrates the imaging capability for high incident energy. (4) Conclusions: We conclude that the prototype has a good imaging performance in a wide energy range (0.3~7 MeV), which shows potential in several MeV gamma-ray imaging applications.

Simulation of unfolding fast neutron spectrum from CR-39 track morphology

The aim of this study is to investigate the impact of various factors on neutron spectrum unfolding, including track parameters (major axis, minor axis and depth), polyethylene (PE) thickness, and etching time. The Monte Carlo code Geant4 and proton track parameter calculation program TRACK_P were applied to simulate the response matrix and track parameters spectrum. Four test spectra—252Cf spectrum, Gaussian broadened deuterium–deuterium fusion neutron spectrum, 241Am–Be spectrum, and Gaussian broadened deuterium–tritium fusion neutron spectrum—were studied using the maximum-likelihood expectation maximization algorithm for neutron spectrum unfolding. The unfolded spectra were in good agreement with the reference spectra. Results showed that the major and minor axes were more suitable than the track depth for neutron spectrum unfolding. For high-energy neutrons, a thick PE layer is required. Moreover, etching time does not significantly affect the unfolded spectra. This study explores the factors influencing the unfolding of fast neutron spectrum based on simulation calculations and preliminary experiments that can be useful for applying CR-39 to neutron spectrum measurements.

Machine Learning-based reconstruction of single and double radiation source distribution using plastic scintillation optical fiber

In this study, we propose a novel method for reconstructing the radiation distribution of a one-dimensional radioactive source using Machine Learning (ML) algorithms and plastic scintillation optical fiber. The wavelength spectrum unfolding technique is used to estimate the source position accurately. We compare the accuracy and time efficiency of three different algorithms, namely, Generalized reduced gradient (GRG), Maximum likelihood expectation maximization (MLEM), and ML, in the single-source and dual-source cases. Our results demonstrate that MLEM algorithm has a shorter reconstruction time with comparable accuracy of position and intensity compared to GRG algorithm for single-source case. For dual-source case, ML algorithm provides real-time estimation of position and intensity with acceptable errors, while GRG algorithm has a larger error in intensity estimation and longer computation time. Our proposed ML algorithms offer useful guidance for practical applications in radiation source location.

Simulation of a new respiratory phase sorting method for 4D-imaging using optical surface information towards precision radiotherapy

BackgroundRespiratory signal detection is critical for 4-dimensional (4D) imaging. This study proposes and evaluates a novel phase sorting method using optical surface imaging (OSI), aiming to improve the precision of radiotherapy. MethodBased on 4D Extended Cardiac-Torso (XCAT) digital phantom, OSI in point cloud format was generated from the body segmentation, and image projections were simulated using the geometries of Varian 4D kV cone-beam-CT (CBCT). Respiratory signals were extracted respectively from the segmented diaphragm image (reference method) and OSI respectively, where Gaussian Mixture Model and Principal Component Analysis (PCA) were used for image registration and dimension reduction respectively. Breathing frequencies were compared using Fast-Fourier-Transform. Consistency of 4DCBCT images reconstructed using Maximum Likelihood Expectation Maximization algorithm was also evaluated quantitatively, where high consistency can be suggested by lower Root-Mean-Square-Error (RMSE), Structural-Similarity-Index (SSIM) value closer to 1, and larger Peak-Signal-To-Noise-Ratio (PSNR) respectively. ResultsHigh consistency of breathing frequencies was observed between the diaphragm-based (0.232 Hz) and OSI-based (0.251 Hz) signals, with a slight discrepancy of 0.019Hz. Using end of expiration (EOE) and end of inspiration (EOI) phases as examples, the mean±1SD values of the 80 transverse, 100 coronal and 120 sagittal planes were 0.967, 0,972, 0.974 (SSIM); 1.657 ± 0.368, 1.464 ± 0.104, 1.479 ± 0.297 (RMSE); and 40.501 ± 1.737, 41.532 ± 1.464, 41.553 ± 1.910 (PSNR) for the EOE; and 0.969, 0.973, 0.973 (SSIM); 1.686 ± 0.278, 1.422 ± 0.089, 1.489 ± 0.238 (RMSE); and 40.535 ± 1.539, 41.605 ± 0.534, 41.401 ± 1.496 (PSNR) for EOI respectively. ConclusionsThis work proposed and evaluated a novel respiratory phase sorting approach for 4D imaging using optical surface signals, which can potentially be applied to precision radiotherapy. Its potential advantages were non-ionizing, non-invasive, non-contact, and more compatible with various anatomic regions and treatment/imaging systems.

A 3D reconstruction method of bubble flow field based on multi-view images by bi-direction filtering maximum likelihood expectation maximization algorithm

Aiming at the problem of the three-dimensional (3D) reconstruction of bubble flow field, a Bi-Direction Filtering Maximum Likelihood Expectation Maximization (BDF-MLEM) algorithm based on multi-view bubble images was proposed in this work. The calibration method for the multi-view was studied to unify the world coordinate systems and obtain the mapping relationship between the 3D world and the projection images. Combined with the calibration results, a 3D reconstruction algorithm of BDF-MLEM for bubble flow field was developed from MLEM. In BDF-MLEM, the setting method of iterative initial value was optimized and the projection and back projection methods in the iterative process was improved based on bi-direction filtering. The experimental results have shown that, compared with SART algorithm and MLEM algorithm, both the reconstruction speed and reconstruction accuracy of the proposed BDF-MLEM algorithm were greatly improved. In addition, the reconstruction results of overlapped bubbles have been improved to some extent by using the proposed method.

On the correction of respiratory motion-induced image reconstruction errors in positron-emission tomography-guided radiation therapy

Free breathing (FB) positron emission tomography (PET) images are routinely used in radiotherapy for lung cancer patients. Respiration-induced artifacts in these images compromise treatment response assessment and obstruct clinical implementation of dose painting and PET-guided radiotherapy. The purpose of this study is to develop a blurry image decomposition (BID) method to correct motion-induced image-reconstruction errors in FB-PETs. Assuming a blurry PET is represented as an average of multi-phase PETs. A four-dimensional computed-tomography image is deformably registered from the end-inhalation (EI) phase to other phases. With the registration-derived deformation maps, PETs at other phases can be deformed from a PET at the EI phase. To reconstruct the EI-PET, the difference between the blurry PET and the average of the deformed EI-PETs is minimized using a maximum-likelihood expectation-maximization algorithm. The developed method was evaluated with computational and physical phantoms as well as PET/CT images acquired from three patients. The BID method increased the signal-to-noise ratio from 1.88±1.05 to 10.5±3.3 and universal-quality index from 0.72±0.11 to 1.0 for the computational phantoms, and reduced the motion-induced error from 69.9% to 10.9% in the maximum of activity concentration and from 317.5% to 8.7% in the full width at half maximum of the physical PET-phantom. The BID-based corrections increased the maximum standardized-uptake values by 17.7±15.4% and reduced tumor volumes by 12.5±10.4% on average for the three patients. The proposed image-decomposition method reduces respiration-induced errors in PET images and holds potential to improve the quality of radiotherapy for thoracic and abdominal cancer patients.

Improving Gas Distribution Tomography: Evaluation of Algorithms and Fan-Beam Measurement Geometries Indoors

Gas distribution mapping (GDM) is widely used to evaluate the efficiency of environmental control systems and locate pollution sources. In this study, the optimized fan-beam measurement geometries and tomography algorithms were proposed for mapping the gas distributions indoors accurately. The airflow and gas distributions in two different types of rooms were predicted using the validated computational fluid dynamics (CFD) method. Then, the performances of five algorithms, including iterative and Tikhonov regularization methods, were quantitatively compared, and the measurement geometries (i.e., number of optical paths, grid resolution, and laser emitter amount) were investigated. The effect of measurement noise on reconstruction accuracy was also analyzed. The results have shown that the simultaneous algebraic reconstruction technique (SART) and the maximum likelihood expectation maximization (MLEM) algorithms were better than the other algorithms, and their averaged relative root mean square errors (RRMSEs) were at least 39% lower with the iteration residual of 0.0015. The optimum grid resolution and the number of optical paths were <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$10\times20$ </tex-math></inline-formula> grid cells and 200 paths, respectively. In addition, the sensitivity of the SART and MLEM algorithms to noise was almost the same, and the addition of the laser emitter could improve the reconstruction accuracy of most cases in this study.

Quantitative comparison of planar coded aperture imaging reconstruction methods

Imaging distributions of radioactive sources plays a substantial role in nuclear medicine as well as in monitoring nuclear waste and its deposit. Coded Aperture Imaging (CAI) has been proposed as an alternative to parallel or pinhole collimators, but requires image reconstruction as an extra step. Multiple reconstruction methods with varying run time and computational complexity have been proposed. Yet, no quantitative comparison between the different reconstruction methods has been carried out so far.This paper focuses on a comparison based on three sets of hot-rod phantom images captured with an experimental γ-camera consisting of a Tungsten-based MURA mask with a 2 mm thick 256 × 256 pixelated CdTe semiconductor detector coupled to a Timepix© readout circuit.Analytical reconstruction methods, MURA Decoding, Wiener Filter and a convolutional Maximum Likelihood Expectation Maximization (MLEM) algorithm were compared to data-driven Convolutional Encoder-Decoder (CED) approaches. The comparison is based on the contrast-to-noise ratio as it has been previously used to assess reconstruction quality. For the given set-up, MURA Decoding, the most commonly used CAI reconstruction method, provides robust reconstructions despite the assumption of a linear model. For single image reconstruction, however, MLEM performed best of all analytical reconstruction methods, but took on average 45 times longer than MURA Decoding. The fastest reconstruction method is the Wiener Filter with a run time 4.3 times faster compared to MURA Decoding and a mediocre quality. The CED with a specifically tailored training set was able to succeed the most commonly used MURA decoding on average by a factor between 1.37 and 2.60 and an equal run time.

Simulation of a novel, non-invasive radiation detector to measure the arterial input function for dynamic positron emission tomography.

Dynamic positron emission tomography (dPET) is a nuclear medicine imaging technique providing functional images for organs of interest with applications in oncology, cardiology, and drug discovery. This technique requires the acquisition of the time-course arterial plasma activity concentration, called the arterial input function (AIF), which is conventionally acquired via arterial bloodsampling. The aim of this study was to (A) optimize the geometry for a novel and cost efficient non-invasive detector called NID designed to measure the AIF for dPET scans through Monte Carlo simulations and (B) develop a clinical data analysis chain to successfully separate the arterial component of a simulated AIF signal from the venouscomponent. The NID was optimized by using an in-house Geant4-based software package. The sensitive volume of the NID consists of a band of 10 cm long and 1mm in diameter scintillating fibers placed over a wrist phantom. The phantom was simulated as a cylinder, 10 cm long and 6.413 cm in diameter comprised of polyethylene with two holes placed through it to simulate the patient's radial artery and vein. This phantom design was chosen to match the wrist phantom used in our previous proof of concept work. Two geometries were simulated with different arrangements of scintillating fibers. The first design used a single layer of 64 fibers. The second used two layers, an inner layer with 29 fibers and an outer layer with 30 fibers. Four positron emitting radioisotopes were simulated: 18 F, 11 C, 15 O, and 68 Ga with 100 million simulated decay events per run. The total and intrinsic efficiencies of both designs were calculated as well as the full width half maximum (FWHM) of the signal. In addition, contribution by the annihilation photons versus positrons to the signal was investigated. The results obtained from the two simulated detector models were compared. A clinical data analysis chain using an expectation maximization maximum likelihood algorithm was tested. This analysis chain will be used to separate arterial counts from the totalsignal. The second NID design with two layers of scintillating fibers had a higher efficiency for all simulations with a maximum increase of 17% total efficiency for 11 C simulation. All simulations had a significant annihilation photon contribution. The signal for 18 F and 11 C was almost entirely due to photons. The clinical data analysis chain was within 1% of the true value for 434 out of 440 trials. Further experimental studies to validate these simulations will berequired. The design of the NID was optimized and its efficiency increased through Monte Carlo simulations. A clinical data analysis chain was successfully developed to separate the arterial component of an AIF signal from the venous component. The simulations show that the NID can be used to accurately measure the AIF non-invasively for dPETscans.

PET Image Reconstruction Incorporating Deep Image Prior and a Forward Projection Model

Convolutional neural networks (CNNs) have recently achieved remarkable performance in positron emission tomography (PET) image reconstruction. In particular, CNN-based direct PET image reconstruction, which directly generates the reconstructed image from the sinogram, has potential applicability to PET image enhancements because it does not require image reconstruction algorithms, which often produce some artifacts. However, these deep learning-based, direct PET image reconstruction algorithms have the disadvantage that they require a large number of high-quality training datasets. In this study, we propose an unsupervised direct PET image reconstruction method that incorporates a deep image prior framework. Our proposed method incorporates a forward projection model with a loss function to achieve unsupervised direct PET image reconstruction from sinograms. To compare our proposed direct reconstruction method with the filtered back projection (FBP) and maximum likelihood expectation maximization (ML-EM) algorithms, we evaluated using Monte Carlo simulation data of brain [$^{18}$F]FDG PET scans. The results demonstrate that our proposed direct reconstruction quantitatively and qualitatively outperforms the FBP and ML-EM algorithms with respect to peak signal-to-noise ratio and structural similarity index.

A hybrid coded-aperture and Compton camera based on cerium-doped Gd3Al2Ga3O12 scintillators coupled with multi-pixel photon counter arrays.

In this study, we propose a hybrid coded-aperture and Compton camera based on cerium-doped Gd3Al2Ga3O12 (GAGG:Ce) scintillator arrays coupled with Multi-Pixel Photon Counter (MPPC) arrays. The sensitive detector of the gamma camera consists of a single GAGG:Ce crystal coupled with a single-chip MPPC unit module. An impedance bridge circuit and a 64-channel data acquisition system were employed to record the code-aperture events and Compton coincidence events. After the calibration of position and energy, the total energy resolution for 662keV gamma-rays from 137Cs was 6.6%. The hybrid camera had the characteristics of mechanical collimation and electronic collimation at the same time. In the code aperture mode, the reconstructed images were obtained by direct deconvolution and maximum likelihood expectation maximization (MLEM) methods. In the Compton imaging mode, the energy-dependent method was applied to order the sequence of Compton scatter events. The simple back-projection algorithm and list-mode MLEM algorithm were adopted for image reconstruction. Practical performances demonstrated that the angular resolutions in two modes were measured as 5.2° and 11.4°, respectively. In addition, the hybrid camera had a desirable imaging capability in a wide energy range (32 keV-2.6MeV) and a wide field of view (∼210° in the horizontal direction). As for the sensitivity, the camera had a commercially available sensitivity level of localizing a 137Cs point source, producing ∼0.026 µSv/h in 5min. Furthermore, the function of distinction for different radiation sources was preliminarily realized.

Development of modified scintillator-based single-crystal position-sensitive 4[formula omitted] Compton camera for a portable radiation imaging device

After the nuclear accident at the Fukushima Daiichi Nuclear Power Plant, researchers focused on the accident and studied the effects of leaked radiation based on radiation detection and measurement. Many methods can be used for monitoring and mapping natural and leaked radionuclides; however, portable detectors installed in unmanned ground or aerial vehicles (UAVs) can measure radioactivity near the target point, preventing damage to the human body from radiation in highly contaminated areas. Compton cameras have a wider field-of-view (FOV) and less weight than a detector system that uses a mechanical collimator. In a previous study, a position-sensitive 4π Compton camera based on a lutetium–yttrium oxyorthosilicate (LYSO) scintillator attached to silicon photomultipliers (SiPMs) was developed. Compared with a semiconductor-based Compton camera operating with a power device supplying more than a thousand volts, our system requires a maximum of approximately several tens of volts. In addition, our Compton camera has a single-crystal structure; hence, it has advantages in terms of FOV and efficiency over a Compton camera that utilizes separate detectors. In this study, a modified scintillator-based Compton camera was created using an advanced SiPM model and a gadolinium aluminum gallium garnet (GAGG) scintillator. In the experiment, 133Ba, 22Na, and 137Cs radionuclides were used for data acquisition, and simple back-projection and list-mode maximum likelihood expectation maximization algorithms were used to reconstruct the Compton images. The 4π FOV coverage was evaluated using Compton imaging and angular resolution measure (ARM), and the results indicated that FOV coverage was degraded when the angle between the radiation source and the perpendicular axis of the detector was near 45°. The degradation of the ARM reflected as the bimodal distribution became more severe for the Compton camera based on the LYSO scintillator than that based on the GAGG scintillator, which was attributed to the intrinsic radiation of LYSO from 176Lu considered as background noise. In the evaluation of intrinsic efficiency, the influence of intrinsic radiation was significantly large. Without background noise rejection, the intrinsic efficiencies for 356, 511, and 662 keV radiation were 0.66%–1.28%, and 1.50%–3.05% for the detection system based on the GAGG and LYSO scintillators, respectively. After background noise rejection, the intrinsic efficiencies were re-calculated as 0.64%–1.27% and 1.39%–1.72% for the detection system based on the GAGG and LYSO scintillator, respectively.

Neutron spectrum unfolding of the magnetic proton recoil spectrometer using the GRAVEL and MLEM algorithms

The magnetic proton recoil (MPR) spectrometer is a high-resolution neutron spectrometer, which provides critical information about the deuterium–tritium (DT) fusion yield, collective fuel velocity, and ion temperature. For precise measurements, the MPR spectrometer operates in a high-resolution mode; however, its detection efficiency is low. The trade-off between energy resolution and detection efficiency limits its widespread applications. Herein, we apply the spectrum unfolding technique to obtain a precise energy spectrum using the MPR spectrometer in a low-resolution mode and to achieve high detection efficiency. Numerical experiments and Geant4 simulations are conducted to compare the GRAVEL and the maximum likelihood expectation maximization (MLEM) algorithms in different cases. A new stopping criterion for iterations is adopted and works well. The source focuses on the primary DT neutrons with single Gaussian, asymmetric, and dual Gaussian distributions. All the cases demonstrate an accurate and stable unfolded energy spectrum, revealing the potential of the MPR spectrometer in a wide range of applications.

Performing tomographic reconstructions from a satellite looking toward Earth. Part 1: implementation and limitations.

For imaging instruments that are in space looking toward the Earth, there are a variety of nuisance signals that can get in the way of performing certain imaging tasks, such as reflections from clouds, reflections from the ground, and emissions from the OH-airglow layer. A method for separating these signals is to perform tomographic reconstructions from the collected data. A lingering struggle for this method is altitude-axis resolution and different methods for helping with it are discussed. An implementation of the maximum likelihood expectation maximization algorithm is given and analyzed.

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.