List-mode Maximum Likelihood Expectation Maximization Research Articles

Estimation of Compton imager using single 3D position-sensitive LYSO scintillator: Monte Carlo simulation

The performance of a Compton imager using a single three-dimensional position-sensitive LYSO scintillator detector was estimated using a Monte Carlo simulation. The Compton imager consisted of a single LYSO scintillator with a pixelized structure. The size of the scintillator and each pixel were 1.3 × 1.3 × 1.3 cm3 and 0.3 × 0.3 × 0.3 cm3, respectively. The order of γ-ray interactions was determined based on the deposited energies in each detector. After the determination of the interaction sequence, various types of reconstruction algorithms such as simple back-projection, filtered back-projection, and list-mode maximum-likelihood expectation maximization (LM-MLEM) were applied and compared with each other in terms of their angular resolution and signal-to-noise ratio (SNR) for several γ-ray energies. The LM-MLEM reconstruction algorithm exhibited the best performance for Compton imaging in maintaining high angular resolution and SNR. The two sources of 137Cs (662 keV) could be distinguishable if they were more than 17° apart. The reconstructed Compton images showed the precise position and distribution of various radiation isotopes, which demonstrated the feasibility of the monitoring of nuclear materials in homeland security and radioactive waste management applications.

An inner-crystal neutron-scatter camera: Monte carlo simulation

Neutron energy emitted from special nuclear materials (SNMs) can be measured by using neutronproton scattering; also, the scattering angle can be calculated from the ratio of the scattered energy to the incident energy. By using position and energy information, we can image the original source position by using the backprojection and list-mode maximum-likelihood expectation maximization (MLEM) method. In this paper, we propose an inner-crystal neutron scatter camera system in which the detectors are not separated to obtain interactions at a variety of scatter angles; based on this system, we analyzed the characteristics of the corresponding neutron-scattering camera. The factors that affected the neutron-scatter image were the neutron velocity after scattering, the cut-off level of the time of flight (ToF), and the width of the cones used for image reconstruction. To determine the optimal point for the reconstruction of an image, we estimated the performance of the system by using the figure of merit (FoM). The optimal neutron-velocity (d/ToF) was ~0.3 × 107 m/s according to our simulation result, while the optimal cut-off level of the ToF was 4 ns as the latter minimized the noise while maintaining the required efficiency. The widths of the cones (e) also affected the full width at half maximum (FWHM) and the noise of the image. In terms of a simple source-geometry, whereby concepts such as “point source” were used, a large e value was suitable to achieve noise reduction; however, regarding the complicated source geometry, a small e value was favorable for precise reconstruction of the original source geometry for both the backprojection and the list-mode MLEM methods.

Demonstration of three-dimensional imaging based on handheld Compton camera

Compton cameras are potential detectors that are capable of performing measurements across a wide energy range for medical imaging applications, such as in nuclear medicine and ion beam therapy. In previous work, we developed a handheld Compton camera to identify environmental radiation hotspots. This camera consists of a 3D position-sensitive scintillator array and multi-pixel photon counter arrays. In this work, we reconstructed the 3D image of a source via list-mode maximum likelihood expectation maximization and demonstrated the imaging performance of the handheld Compton camera. Based on both the simulation and the experiments, we confirmed that multi-angle data acquisition of the imaging region significantly improved the spatial resolution of the reconstructed image in the direction vertical to the detector. The experimental spatial resolutions in the X, Y, and Z directions at the center of the imaging region were 6.81 mm ± 0.13 mm, 6.52 mm ± 0.07 mm and 6.71 mm ± 0.11 mm (FWHM), respectively. Results of multi-angle data acquisition show the potential of reconstructing 3D source images.

List-mode reconstruction in 2D strip PET

Abstract Using a theory of list-mode maximum likelihood expectation-maximization (MLEM) algorithm, in this contribution, we present a derivation of the system response kernel for a novel positron emission tomography (PET) detector based on plastic scintillators.

Simulations of a micro-PET system based on liquid xenon

The imaging performance of a high-resolution preclinical micro-positron emission tomography (micro-PET) system employing liquid xenon (LXe) as the gamma-ray detection medium was simulated. The arrangement comprises a ring of detectors consisting of trapezoidal LXe time projection ionization chambers and two arrays of large area avalanche photodiodes for the measurement of ionization charge and scintillation light. A key feature of the LXePET system is the ability to identify individual photon interactions with high energy resolution and high spatial resolution in three dimensions and determine the correct interaction sequence using Compton reconstruction algorithms. The simulated LXePET imaging performance was evaluated by computing the noise equivalent count rate, the sensitivity and point spread function for a point source according to the NEMA-NU4 standard. The image quality was studied with a micro-Derenzo phantom. Results of these simulation studies included noise equivalent count rate peaking at 1326 kcps at 188 MBq (705 kcps at 184 MBq) for an energy window of 450–600 keV and a coincidence window of 1 ns for mouse (rat) phantoms. The absolute sensitivity at the center of the field of view was 12.6%. Radial, tangential and axial resolutions of 22Na point sources reconstructed with a list-mode maximum likelihood expectation maximization algorithm were ⩽0.8 mm (full-width at half-maximum) throughout the field of view. Hot-rod inserts of <0.8 mm diameter were resolvable in the transaxial image of a micro-Derenzo phantom. The simulations show that a LXe system would provide new capabilities for significantly enhancing PET images.

Fast image reconstruction for Compton camera using stochastic origin ensemble approach

Compton camera has been proposed as a potential imaging tool in astronomy, industry, homeland security, and medical diagnostics. Due to the inherent geometrical complexity of Compton camera data, image reconstruction of distributed sources can be ineffective and/or time-consuming when using standard techniques such as filtered backprojection or maximum likelihood-expectation maximization (ML-EM). In this article, the authors demonstrate a fast reconstruction of Compton camera data using a novel stochastic origin ensembles (SOE) approach based on Markov chains. During image reconstruction, the origins of the measured events are randomly assigned to locations on conical surfaces, which are the Compton camera analogs of lines-of-responses in PET. Therefore, the image is defined as an ensemble of origin locations of all possible event origins. During the course of reconstruction, the origins of events are stochastically moved and the acceptance of the new event origin is determined by the predefined acceptance probability, which is proportional to the change in event density. For example, if the event density at the new location is higher than in the previous location, the new position is always accepted. After several iterations, the reconstructed distribution of origins converges to a quasistationary state which can be voxelized and displayed. Comparison with the list-mode ML-EM reveals that the postfiltered SOE algorithm has similar performance in terms of image quality while clearly outperforming ML-EM in relation to reconstruction time. In this study, the authors have implemented and tested a new image reconstruction algorithm for the Compton camera based on the stochastic origin ensembles with Markov chains. The algorithm uses list-mode data, is parallelizable, and can be used for any Compton camera geometry. SOE algorithm clearly outperforms list-mode ML-EM for simple Compton camera geometry in terms of reconstruction time. The difference in computational time will be much larger when full Compton camera system model, including resolution recovery, is implemented and realistic Compton camera geometries are used. It was also shown in this article that while correctly reconstructing the relative distribution of the activity in the object, the SOE algorithm tends to underestimate the intensity values and increase variance in the images; improvements to the SOE reconstruction algorithm will be considered in future work.

Three-Dimensional Compton Imaging Using List-Mode Maximum Likelihood Expectation Maximization

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Compton imaging is a gamma ray imaging technique that has many possible applications including homeland security and medical imaging. Using the Compton scattering formula the origin of a scattered <formula formulatype="inline"> <tex Notation="TeX">$\gamma$</tex></formula>-ray can be localized to a point on the surface of a cone using a minimum of two position and energy measurements. List-mode Maximum likelihood expectation maximization (MLEM) is an iterative statistical algorithm that makes successive approximations to the most probable source distribution that would have led to the observed data. Conventional MLEM is often performed in two dimensions, which still requires knowledge of the source-to-detector distance. We propose iteration over all three spatial dimensions in order to maximize the probability in three-dimensional space. This paper reports on the development of a three-dimensional MLEM (3DMLEM) algorithm to reconstruct images from a Compton imager in three dimensions for single, multiple and line sources. Several techniques for reducing convergence times are also discussed. </para>

Extended radiation source imaging with a prototype Compton imager

This paper reports results from a prototype Compton imager (PCI) which consists of three planes of silicon pixel detectors as a scattering detector followed by an array of CsI(Tl) crystals as an absorbing detector. The CsI(Tl) array is mounted directly behind the silicon detectors. Simple back-projection algorithms are not sufficient to resolve extended shapes, but iterative algorithms provide the necessary de-convolution. List-mode maximum likelihood expectation maximization (LM-MLEM) is an iterative algorithm that reconstructs the most probable source distribution for a given data set. LM-MLEM attempts to reconstruct an image by finding successive approximations to the true source data. Each data set imaged is different, but the number of iterations required for convergence is typically 10–30 for the PCI. In this paper, reconstructed images of point and extended sources using measured PCI data are presented. Data are corroborated using GEANT4 simulations.

Data analysis for the MEGA prototype

The data analysis for combined Compton and Pair telescopes like the Medium Energy Gamma-Ray Astronomy telescope (MEGA) separates into three basic steps: the starting point is the calibration and low-level data-analysis. It is followed by the most critical part, the event reconstruction, which has to identify all event types (pair-creation, Compton events, charged particles, etc.) while effectively suppressing different kinds of background (photons from below, chance coincidences, activation, etc.). The last stage, the high level data analysis, is dominated by image reconstruction, which in our case is performed by a technique called list-mode maximum-likelihood expectation-maximization. The current performance of the data analysis algorithms is demonstrated by calibration measurements of the MEGA prototype.