Maximum Likelihood Expectation Maximization Research Articles

Development of a Position-Sensitive 4π Compton Camera Based on a Single Segmented Scintillator

Scintillator-based Compton cameras, which comprise of a separated scatter and absorption detectors, neglect the Compton scattering that is followed by a photoelectric effect in a single set of scintillators, wherein the detection efficiency is severely limited. In this study, we propose a 3-D position-sensitive Compton camera that uses a single set of scintillators, wherein radiation interactions inside the scintillator can be discriminated. The proposed Compton camera comprises a segmented lutetium–yttrium oxyorthosilicate scintillator coupled with two position-sensitive silicon photomultipliers on both sides. Compton image reconstruction algorithms, such as simple back-projection, list-mode maximum likelihood expectation maximization (MLEM), and filtered back-projection, were applied and compared. The single position-sensitive Compton camera identified the positions of multiple radiation sources with various energies in a $4\pi $ field of view. The signal-to-noise ratio (SNR) and full-width at half-maximum (FWHM) of a reconstructed 511-keV point source were approximately 12° and 22°, respectively, after MLEM was applied, and the two 511-keV sources with an angle difference of 40° were separately reconstructed. The intrinsic efficiency of the proposed Compton camera was $2.23\times 10^{-2}$ for 511 keV.

Accelerated strategy for the MLEM algorithm.

A statistical method called maximum likelihood expectation maximization (MLEM) is quite attractive, especially in PET/SPECT. However, the convergence rate of the iterative scheme of MLEM is quite slow. This study aims to develop and test a new method to speed up the convergence rate of the MLEM algorithm. We introduce a relaxation parameter in the conventional MLEM iterative formula and propose the relaxation strategy on the condition that the spectral radius of the derived iterative matrix from the iterative scheme with the accelerated parameter reaches a minimum value. Experiments with Shepp-Logan phantom and an annual tree image demonstrate that the new computational strategy effectively accelerates computation time while maintains reasonable image quality. The proposed new computational method involving the relaxation strategy has a faster convergence speed than the original method.

3D TOF-PET image reconstruction using total variation regularization.

In this paper we introduce a semi-analytic algorithm for 3-dimensional image reconstruction for positron emission tomography (PET). The method consists of the back-projection of the acquired data into the most likely image voxel according to time-of-flight (TOF) information, followed by the filtering step in the image space using an iterative optimization algorithm with a total variation (TV) regularization. TV regularization in image space is more computationally efficient than usual iterative optimization methods for PET reconstruction with full system matrix that use TV regularization. The efficiency comes from the one-time TOF back-projection step that might also be described as a reformatting of the acquired data. An important aspect of our work concerns the evaluation of the filter operator of the linear transform mapping an original radioactive tracer distribution into the TOF back-projected image. We obtain concise, closed-form analytical formula for the filter operator. The proposed method is validated with the Monte Carlo simulations of the NEMA IEC phantom using a one-layer, 50cm-long cylindrical device called Jagiellonian PET scanner. The results show a better image quality compared with the reference TOF maximum likelihood expectation maximization algorithm.

Design, simulation and reconstruction for a fast speed two-phase flow CT with 241Am gamma ray sources

Computer tomography (CT) is a useful probe to measure two-phase flow parameters. Because of the dynamic characteristic of the two-phase flow, the high temporal CT is required. A compact CT system, consists of seven isotope γ-ray sources, seven groups of cadmium zinc telluride (CdZnTe) detectors and collimators, is proposed. The 241Am is selected as the source by balancing its ability to distinguish water and air and transmission power for the acrylic pipeline. The virtual pixels are interpolated to increase the number of projections from Monte Carlo simulation. The reconstruction accuracy and speed for different phantoms with maximum likelihood expectation maximization (MLEM), Tikhonov regularization, total variation (TV) regularization and genetic algorithm (GA) are compared. The results show TV algorithm achieves a good balance between accuracy and speed, and GA has the highest accuracy but lowest speed in high spatial resolution reconstruction. The temporal resolution can be increased by sacrificing the spatial resolution.

Reconstructing the Position and Intensity of Multiple Gamma-Ray Point Sources With a Sparse Parametric Algorithm

We present an experimental demonstration of Additive Point Source Localization (APSL), a sparse parametric imaging algorithm that reconstructs the 3D positions and activities of multiple gamma-ray point sources. Using a handheld gamma-ray detector array and up to four $8$ ${\mu}$Ci $^{137}$Cs gamma-ray sources, we performed both source-search and source-separation experiments in an indoor laboratory environment. In the majority of the source-search measurements, APSL reconstructed the correct number of sources with position accuracies of ${\sim}20$ cm and activity accuracies (unsigned) of ${\sim}20\%$, given measurement times of two to three minutes and distances of closest approach (to any source) of ${\sim}20$ cm. In source-separation measurements where the detector could be moved freely about the environment, APSL was able to resolve two sources separated by $75$ cm or more given only ${\sim}60$ s of measurement time. In these source-separation measurements, APSL produced larger total activity errors of ${\sim}40\%$, but obtained source separation distances accurate to within $15$ cm. We also compare our APSL results against traditional Maximum Likelihood-Expectation Maximization (ML-EM) reconstructions, and demonstrate improved image accuracy and interpretability using APSL over ML-EM. These results indicate that APSL is capable of accurately reconstructing gamma-ray source positions and activities using measurements from existing detector hardware.

SQUID-Based Magnetic Resonance Imaging at Ultra-Low Field Using the Backprojection Method

Ultra-low field magnetic resonance imaging (ULF MRI) is an effective imaging technique that applies the ultrasensitive detector of superconducting quantum interference device (SQUID) sensor to detect the MR signal at a microtesla field range. In this work, we designed and developed a SQUID-based ULF MRI system with a frequency-adjustable measurement field, the performance of which was characterized via water phantoms. In order to enhance the MR signals, a 500 mT Halbach magnet was used to prepolarize the magnetization of the sample prior to excitation. The signal-to-noise-ratio (SNR) of the spin-echo- (SE-) based pulse sequence can reach up to 70 in a single scan. The images were then reconstructed successfully by using the maximum likelihood expectation maximization (MLEM) algorithm based on the backprojection imaging method. It was demonstrated that an in-plane resolution of 1.8 × 1.8 mm2 can be achieved which indicated the feasibility of SQUID-based MRI at the ULF.

Feasibility study on image reconstruction for single-photon emission computed tomography with limited projections by neural networks

This study investigated the feasibility of using a neural network for single-photon emission computed tomography (SPECT) in boron neutron capture therapy (BNCT) with limited projection data. In order to determine the therapeutic dose for use in BNCT under neutron irradiation, a real-time reconstruction method is required. However, BNCT-SPECT has limitations related to the projection angle range and number of projection points. It is not easy to reconstruct an image under these projection limitations using a conventional filtered back-projection (FBP) method. Therefore, a convolutional neural network (CNN) was adopted to reconstruct radioactivity distribution images using the responses from radiation detectors arranged to surround a system. An original dataset of radioactivity distribution images with specific conditions was prepared, and the CNN was trained using the training data. The performances of the CNN for BNCT-SPECT with the limited projections were evaluated. The conditions were the limitations on the number of projections in 180° and on the projection angle range at a constant step angle. The results were compared with those of the FBP method and maximum likelihood-expectation maximization (ML-EM) method. The CNN could be used to estimate radioactivity distributions for BNCT-SPECT with a limited projection angle range. Under the condition of only five projection angles in 180°, the CNN and ML-EM methods could reconstruct images more accurately than the FBP method. In the case of the limitation on the projection angle range, the tolerance of the projection angle range with a step angle of 5° for CNNs was greater than approximately 45°.

Corrección de eventos dispersos en algoritmos de reconstrucción tomográfica para PET

La Tomografía por Emisión de Positrones (PET) permite cuantificar el metabolismo celular, siendo una de las técnicas más poderosas en el diagnóstico precoz deenfermedades cardíacas, oncológicas y neurológicas. Las imágenes se obtienen mediante la administración de un radiofármaco que marca el proceso metabólico a estudiar. Los rayos gamma que emite el radiotrazador, inciden en detectores ubicados alrededor del paciente generando eventos que se almacenan para la reconstrucción de la imagen. Para obtener imágenes cuantificables, se realizan diversas correcciones a los eventos, entre ellas por eventos dispersos. Con el objetivo de implementar la corrección por eventos dispersos, se realiza, en primera instancia, el modelado de los mismos por medio del algoritmo Single Scatter Simulation (SSS) obteniendo una estimación de la dispersión. Posteriormente se realiza la corrección en la imagen de emisión. Para la corrección se incorpora al algoritmo de reconstrucción MLEM (maximum-likelihood expectation–maximization) la estimación obtenida con el modelado. Los resultados preliminares, obtenidos en simulaciones de volúmenes de actividad constante, han demostrado que la implementación realizada mejora la homogeneidad de la imagen de emisión.

Alfa Laval AB, Sweden

The tomographic reconstruction of biological specimens requires robust algorithms, able to deal with low density contrast and low element concentrations. At the IST/ITN microprobe facility new GPU-accelerated reconstruction software, JPIXET, has been developed, which can significantly increase the speed of quantitative reconstruction of Proton Induced X-ray Emission Tomography (PIXE-T) data. It has a user-friendly graphical user interface for pre-processing, data analysis and reconstruction of PIXE-T and Scanning Transmission Ion Microscopy Tomography (STIM-T). The reconstruction of PIXE-T data is performed using either an algorithm based on a GPU-accelerated version of the Maximum Likelihood Expectation Maximisation (MLEM) method or a GPU-accelerated version of the Discrete Image Space Reconstruction Algorithm (DISRA) (Sakellariou (2001) [2]). The original DISRA, its accelerated version, and the MLEM algorithm, were compared for the reconstruction of a biological sample of Caenorhabditis elegans – a small worm. This sample was analysed at the microbeam line of the AIFIRA facility of CENBG, Bordeaux. A qualitative PIXE-T reconstruction was obtained using the CENBG software package TomoRebuild (Habchi et al. (2013) [6]). The effects of pre-processing and experimental conditions on the elemental concentrations are discussed.

Impact of aperture-thickness on the real-time imaging characteristics of coded-aperture gamma cameras

The mask parameters of a coded aperture are critical design features when optimizing the performance of a gamma-ray camera. In this paper, experiments and Monte Carlo simulations were performed to derive the minimum detectable activity (MDA) when one seeks a real-time imaging capability. First, the impact of the thickness of the modified uniformly redundant array (MURA) mask on the image quality is quantified, and the imaging of point, line, and surface radiation sources is demonstrated using both cross-correlation (CC) and maximum likelihood expectation maximization (MLEM) methods. Second, the minimum detectable activity is also derived for real-time imaging by altering the factors used in the image quality assessment, consisting of the peak-to-noise ratio (PSNR), the normalized mean square error (NMSE), the spatial resolution (full width at half maximum; FWHM), and the structural similarity (SSIM), all evaluated as a function of energy and mask thickness. Sufficiently sharp images were reconstructed when the mask thickness was approximately 2 cm for a source energy between 30 keV and 1.5 MeV and the minimum detectable activity for real-time imaging was 23.7 MBq at 1 m distance for a 1 s collection time.

Extension of the ML-EM algorithm for dose estimation using PET in proton therapy: application to an inhomogeneous target

Positron emission tomography (PET) has been used for in vivo treatment verification, mainly for range verification, in proton therapy. Evaluating the direct dose from PET measurements remains challenging; however, it is highly desirable from a clinical perspective. In this study, a method for estimating the dose distribution from the positron emitter distributions was developed using the maximum likelihood expectation maximization algorithm. The 1D spatial relationship between positron emitter distributions and a dose distribution in an inhomogeneous target was inputted into the system matrix based on a filter framework. In contrast, spatial resolution of the PET system and total variation regularization (as prior knowledge for dose distribution) were considered in the 3D image-space. The dose estimation was demonstrated using Monte Carlo simulated PET activity distributions with substantial noise in a head and neck phantom. This mimicked the single field irradiation of the spread-out Bragg peak beams at clinical dose levels. Besides the simple implementation of the algorithm, this strategy achieved a high-speed calculation (30 s for a 3D dose estimation) and accurate dose and range estimations (less than 10% and 2 mm errors at 1-σ values, respectively). The proposed method could be key for using PET for in vivo dose monitoring.

Passive gamma emission tomography with ordered subset expectation maximization method

Gamma-ray emission tomography (GET) was developed as a potential verification tool to visualize the passive gamma-ray emitter sources of fuel rods. In GET, maximum likelihood–expectation maximization (MLEM) was employed as an iterative reconstruction method. However, as convergence iteration in the algorithm is proportional to the pixel size, convergence is slow and the calculation cost for practical application is high. Therefore, an ordered subset expectation maximization method (OSEM) was used, and the rod-wise relative gamma-ray emitter distribution of a BWR 10 × 10 mock-up fuel assembly was reconstructed to evaluate the performance of the OSEM. The OSEM enabled reconstruction comparable to that of MLEM with an effective decrease in the number of iterations.

Voxelization based PoCA point cloud filtration algorithm for image reconstruction for Muon Tomography

Multiple Coulomb Scattering (MCS) based muon tomography technique has been considered to be a well-known tool to identify, discriminate, and to image the high-density objects placed inside closed volumes. The two most famous reconstruction algorithms are Point of Closest Approach (PoCA) and Maximum Likelihood Expectation Maximization (MLEM). PoCA is fast but purely geometrical and as a result of this, it gives a lot of false positives, i.e. sometimes the PoCA point lies outside the target object and hence it forms an envelope of false-positive which results in a smeared image. On the other hand, MLEM is an iterative algorithm and is much more computation-intensive. In this work a new and innovative method is proposed which is based on the concept of voxelization to handle the known problem of false positives of the PoCA algorithm, and hence provide a clear reconstructed image. These algorithms remove the false positives PoCA points from the 3D point cloud and will give useful information in terms of regions or voxels within a voxelized volume 'V' to do a clear image reconstruction. The advantages of the proposed algorithm to the existing algorithms are also discussed. The status of the experimental setup of the proposed facility using Resistive Plate Chamber(RPC) with spatial resolution of ∼ 1cm as muon detector, is also discussed. The preliminary data from the current experimental setup, showing detector performance and cosmic muon tracks are also shown. Since the experimental setup is not fully ready, the effectiveness of the developed algorithms and the results are evaluated using the data from the Geant4 simulation of the muon tomography setup.

Maximum likelihood reconstructions for rotating scatter mask imaging

The rotating scatter mask system is capable of determining the direction of a single point gamma or neutron source. However, the point source approximation does not hold for many realistic applications, requiring more detailed reconstructions with this system. This study is the first to characterize the rotating scatter mask as a gamma imager, or camera, through a detailed analysis of the relative error, precision, noise, and convergence time as a measure of reconstruction performance. Simulated 137Cs sources and detector responses were generated in MCNP v6.1.4 and v6.2 with high fidelity and low statistical uncertainty. An analysis of variance was applied to maximum-likelihood expectation–maximization algorithms to determine the most significant factors in reconstructing the image, focusing on the source’s shape, size, and direction relative to the detector. Parameters for a Median Root Prior smoothing function were optimized to balance performance over a variety of source distributions. The algorithm performed reasonably well for point sources and for sources that spanned less than 30° in size and were located near the equatorial region of the rotating system. In most other scenarios, the algorithm either oversmoothed the image, resulting in blurry images, or completely failed to reconstruct the image. Increasing the resolution improved the reconstruction quality, while increasing the neighborhood size for the Median Root Prior reduced the image’s noise, but at a significant cost to computational efficiency. These results demonstrate that rotating scatter mask imaging is possible and introduces a potential alternative to other imagers. However, they also demonstrate that new techniques must be developed to increase the system’s performance and robustness for gamma imaging applications.

Design and simulation of a helmet brain PET system

The desire to obtain a reconstruction image with high resolution using a short scanning duration motivates us to design a new brain positron emission tomography (PET) system. We design and simulate a wearable helmet brain PET system. This helmet PET scanner has a radius of 185 mm and comprises five parts (bottom, face, forehead, head, and top). The entire helmet PET system has 512 Lu1.8Y0.2SiO5: Ce (LYSO) PET detector blocks. Each PET detector is made of 12 × 12 LYSO crystals with 1.5 × 1.5 × 10 mm3elements. The proposed scanner has a global absolute sensitivity of 3.08% and a global scatter fraction of 0.56. Maximum likelihood expectation maximization (MLEM) reconstruction of the simulated data shows that full width at half maximum (FWHM) is 1.97 mm and full width at tenth maximum (FWTM) is 2.80 mm at the center of the field of view. In the radial direction, the FWHM increases from 1.97 mm to 3.82 mm, and the FWTM increases from 2.80 mm to 5.64 mm. In the axial direction, FWHM and FWTM are 1.98 mm and 2.80 mm, respectively. We use simulated line sources, a Derenzo phantom, and an MRI image to test the imaging ability of the simulated brain helmet PET. The scanner achieves higher resolution and higher sensitivity than a clinical PET scanner and will be of practical use in the diagnosis of brain illness.

Image reconstruction for a multi-layer Compton telescope: an analytical model for three interaction events

Compton Cameras are electronically collimated photon imagers suitable for sub-MeV to few MeV gamma-ray detection. Such features are desirable to enable in vivo range verification in hadron therapy, through the detection of secondary Prompt Gammas. A major concern with this technique is the poor image quality obtained when the incoming gamma-ray energy is unknown. Compton Cameras with more than two detector planes (multi-layer Compton Cameras) have been proposed as a solution, given that these devices incorporate more signal sequences of interactions to the conventional two interaction events. In particular, three interaction events convey more spectral information as they allow inferring directly the incident gamma-ray energy. A three-layer Compton Telescope based on continuous Lanthanum (III) Bromide crystals coupled to Silicon Photomultipliers is being developed at the IRIS group of IFIC-Valencia. In a previous work we proposed a spectral reconstruction algorithm for two interaction events based on an analytical model for the formation of the signal. To fully exploit the capabilities of our prototype, we present here an extension of the model for three interaction events. Analytical expressions of the sensitivity and the System Matrix are derived and validated against Monte Carlo simulations. Implemented in a List Mode Maximum Likelihood Expectation Maximization algorithm, the proposed model allows us to obtain four-dimensional (energy and position) images by using exclusively three interaction events. We are able to recover the correct spectrum and spatial distribution of gamma-ray sources when ideal data are employed. However, the uncertainties associated to experimental measurements result in a degradation when real data from complex structures are employed. Incorrect estimation of the incident gamma-ray interaction positions, and missing deposited energy associated with escaping secondaries, have been identified as the causes of such degradation by means of a detailed Monte Carlo study. As expected, our current experimental resolution and efficiency to three interaction events prevents us from correctly recovering complex structures of radioactive sources. However, given the better spectral information conveyed by three interaction events, we expect an improvement of the image quality of conventional Compton imaging when including such events. In this regard, future development includes the incorporation of the model assessed in this work to the two interaction events model in order to allow using simultaneously two and three interaction events in the image reconstruction.

Design study of fully wearable high-performance brain PETs for neuroimaging in free movement

A practical wearable brain PET scanner capable of dynamic neuroimaging during free bodily movement will enable potential breakthrough basic neuroscience studies and help develop imaging-based neurological diagnoses and treatments. Weight, brain coverage, and sensitivity are three fundamental technical obstacles in the development of Fully Wearable High-Performance (FWHP) brain PET scanners. The purpose of this study is to investigate the feasibility of building a FWHP brain PET using a limited volume of lutetium–yttrium oxyorthosilicate (LYSO) scintillator crystals. Six scanners, consisted of the same volume (2.66 kg) of LYSO scintillators with combinations of 2 different crystal pitches (3 mm and 1.5 mm) and 3 different crystal lengths (20 mm, 10 mm, and 5 mm), were simulated. The performances of the six scanners were assessed and compared with Siemen’s HRRT brain PET and mCT whole-body PET, in terms of aperture, axial field of views (AFOV), sensitivity, spatial resolution, count rates, and image noise property. The time-of-flight (TOF) information was included in the image reconstruction to improve the effective sensitivity. The effects of the TOF was assessed by scanning a Jaszczak phantom and reconstructing images with the maximum likelihood expectation maximization (MLEM) algorithm with different timing settings (non-TOF, 500 ps, 200 ps, 100 ps and 50 ps Coincidence Time Resolution, CTR). The signal-noise ratio (SNR) of the images were assessed and compared with those of the HRRT scanner and mCT scanner. The results show that it is possible to construct a FWHP brain PET with better spatial resolution than the dedicated HRRT brain PET, comparable effective sensitivity (with 50 ∼ 100 ps CTR), and whole-brain coverage (23.7 cm inner diameter and 13.4 cm axial field of view) using 2.66 kg of LYSO.

3-D Reconstruction Benchmark of a Compton Camera Against a Parallel-Hole Gamma Camera on Ideal Data

Compton cameras (CCs) and collimated gamma cameras are competing devices suitable for prompt gamma detection in range verification of particle therapy. In this article, we evaluate the first approach from the point of view of the tomographic reconstruction step by comparing it to the second. We clear any technological constraints by considering a simple geometry, ideal detecting stages, a mono-energetic synthetic phantom. To this end, both analytic (filtered back-projection) and iterative (list-mode maximum-likelihood expectation-maximization) algorithms are applied in conjunction with total variation denoising. It was shown in the previous studies that compared to the mechanically collimated camera, the CC has a higher efficiency. Factors between ten and one hundred were reported. Meanwhile, for each detected event, the emission position of the original photon lies on a conical surface for CCs, instead of a line for collimated cameras. This leads to a supplementary degree of freedom that logically calls during image reconstruction for a larger data set and may cancel out the benefits of the superior efficiency. We consider here a static CC and a rotating collimated camera with similar angular coverage. We show empirically that reconstruction from conical projections requires ten times more detected events to obtain at least the same image quality. In some experiments, the CC allows to avoid severe artifacts produced by the limited-angle geometry of the collimated camera. In addition, the CC should be better suited for imaging high-energy and poly-energetic sources.

Comparison of Compton Image Reconstruction Algorithms for Estimation of Internal Radioactivity Distribution in Concrete Waste During Decommissioning of Nuclear Power Plant

Concrete waste accounts for approximately 70~80% of the total waste generated during the decommissioning of nuclear power plants (NPPs). Based upon the concentration of each radionuclide, the concrete waste from the decommissioning can be used in the determination of the clearance threshold used to classify waste as radioactive. To reduce the cost of radioactive concrete waste disposal, it is important to perform decontamination before self-disposal or limited recycling. Therefore, it is necessary to estimate the internal radioactivity distribution of radioactive concrete waste to ensure effective decontamination. In this study, the performance metrics of various Compton reconstruction algorithms were compared in order to identify the best strategy to estimate the internal radioactivity distribution in concrete waste during the decommissioning of NPPs. Four reconstruction algorithms, namely, simple back-projection, filtered back-projection, maximum likelihood expectation maximization (MLEM), and energy-deconvolution MLEM (E-MLEM) were used as Compton reconstruction algorithms. Subsequently, the results obtained by using these various reconstruction algorithms were compared with one another and evaluated, using quantitative evaluation methods. The MLEM and E-MLEM reconstruction algorithms exhibited the best performance in maintaining a high image resolution and signal-to-noise ratio (SNR), respectively. The results of this study demonstrate the feasibility of using Compton images in the estimation of the internal radioactive distribution of concrete during the decommissioning of NPPs.

Benchmark evaluation of tomographic algorithms for simultaneous reconstruction of temperature and volume fraction fields of soot and metal-oxide nanoparticles in non-uniform flames

With the growing applications of nanofluid flame, the monitoring and controlling of its combustion process is of paramount importance. Thus, it is necessary to develop diagnosing methods which can simultaneously image important parameters such as temperature and volume fractions of soot, metal-oxide nanoparticles. Tomographic emission spectroscopy is an effective method which has been proposed for this purpose. However, the inversion process was only reported with least-squares QR decomposition (LSQR) so far and there are numerous well-established reconstruction algorithms which have not been utilized yet. Thus, this work aims to perform systematic comparative studies on several representative algorithms for the inversion process. In the simulative studies, algorithms including Tikhonov regularization, algebraic reconstruction technique (ART), LSQR, Landweber algorithm, maximum likelihood expectation maximization (MLEM), and ordered subset expectation maximization (OSEM) were discussed. The effects of the number of iterations, the signal-to-noise ratio, and the number of projections and the calibration error in projection angles on the performance of the algorithms were investigated. Advice on selecting the suitable algorithms under different application conditions is then provided according to the extensive numerical studies.