Maximum Likelihood Expectation Maximization Research Articles

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.

Study on the PET image quality according to various scintillation detectors based on the Monte Carlo simulation

Purpose: Positron emisson tomography (PET) is a crucial medical imaging scanner for the detection of cancer lesions. In order to maintain the improved image quality, it is crucial to apply detectors of superior performance. Therefore, the purpose of this study was to compare PET image quality using Monte Carlo simulation based on the detector materials of BGO, LSO, and LuAP. Materials and Methods: The Geant4 Application for Tomographic Emission (GATE) was used to design the PET detector. Scintillations with BGO, LSO and LuAP were modelled, with a size of 3.95 × 5.3 mm2 (width × height) and 25.0 mm (thickness). The PET detector consisted of 34 blocks per ring and a total of 4 rings. A line source of 1 MBq was modelled and acquired with a radius of 1 mm and length of 20 mm for 20 seconds. The acquired image was reconstructed maximum likelihood expectation maximization with 2 iteration and 10 subsets. The count comparison was carried out. Results and Discussion: The highest true, random, and scatter counts were obtained from the BGO scintillation detector compared to LSO and LuAP. Conclusion: The BGO scintillation detector material indicated excellent performance in terms of detection of gamma rays from emitted PET phantom.

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.

A stochastic alternative technique for Compton Maximum Likelihood Expectation-Maximization (MLEM) reconstruction

Even though iterative methods and particularly Maximum Likelihood Expectation-Maximization (MLEM) algorithms have been established in reconstruction with Compton data, their detailed design with respect to physical rules and processes dominate their plain implementation in the form of a system matrix. A new elementary but efficient alternative for the well-known system matrix with respect to Compton Camera image reconstruction is presented in this work. For each detected event there is a weighting factor inserted as an accumulated probability which carries all the necessary information. This probability which involves only the Compton scattering angle of the incident photon corresponds to a map that correlates all events within all possible source origins. Based on maximizing likelihood principles, the proposed model weights in a stochastic way the difference of the scatterer-to-source angle θ0, as it is determined by the deposited energy on the absorber, and any other potential scattering angle θJ, specified by the position coordinates on the reconstruction matrix. Obtained image spatial resolution, angular distortions and response to focal length determination are a few of the studied cases for the algorithms’ evaluation via simulations in GEANT4/GATE with a set of radioactive sources and phantoms with in- and out-of-plane arrangement.

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.

Fully 3D implementation of the end-to-end deep image prior-based PET image reconstruction using block iterative algorithm

Objective. Deep image prior (DIP) has recently attracted attention owing to its unsupervised positron emission tomography (PET) image reconstruction method, which does not require any prior training dataset. In this paper, we present the first attempt to implement an end-to-end DIP-based fully 3D PET image reconstruction method that incorporates a forward-projection model into a loss function. Approach. A practical implementation of a fully 3D PET image reconstruction could not be performed at present because of a graphics processing unit memory limitation. Consequently, we modify the DIP optimization to a block iteration and sequential learning of an ordered sequence of block sinograms. Furthermore, the relative difference penalty (RDP) term is added to the loss function to enhance the quantitative accuracy of the PET image. Main results. We evaluated our proposed method using Monte Carlo simulation with [18F]FDG PET data of a human brain and a preclinical study on monkey-brain [18F]FDG PET data. The proposed method was compared with the maximum-likelihood expectation maximization (EM), maximum a posteriori EM with RDP, and hybrid DIP-based PET reconstruction methods. The simulation results showed that, compared with other algorithms, the proposed method improved the PET image quality by reducing statistical noise and better preserved the contrast of brain structures and inserted tumors. In the preclinical experiment, finer structures and better contrast recovery were obtained with the proposed method. Significance. The results indicated that the proposed method could produce high-quality images without a prior training dataset. Thus, the proposed method could be a key enabling technology for the straightforward and practical implementation of end-to-end DIP-based fully 3D PET image reconstruction.

Study of Alternative Imaging Methods for In Vivo Boron Neutron Capture Therapy.

Boron Neutron Capture Therapy (BNCT) is an innovative and highly selective treatment against cancer. Nowadays, in vivo boron dosimetry is an important method to carry out such therapy in clinical environments. In this work, different imaging methods were tested for dosimetry and tumor monitoring in BNCT based on a Compton camera detector. A dedicated dataset was generated through Monte Carlo tools to study the imaging capabilities. We first applied the Maximum Likelihood Expectation Maximization (MLEM) iterative method to study dosimetry tomography. As well, two methods based on morphological filtering and deep learning techniques with Convolutional Neural Networks (CNN), respectively, were studied for tumor monitoring. Furthermore, clinical aspects such as the dependence on the boron concentration ratio in image reconstruction and the stretching effect along the detector position axis were analyzed. A simulated spherical gamma source was studied in several conditions (different detector distances and boron concentration ratios) using MLEM. This approach proved the possibility of monitoring the boron dose. Tumor monitoring using the CNN method shows promising results that could be enhanced by increasing the training dataset.

MLEM Neutron Spectra Unfolding in a Radiotherapy Bunker Using Bonner Sphere Spectrometer

High-energy radiotherapy treatments of a medical Linear Accelerator (LinAc) generate secondary neutrons that can produce health damage on the human body as the induction of secondary cancers. The energy spectrum of these neutrons must be determined to estimate the extra dose received by patients inside a radiotherapy room during radiotherapy treatment. To quantify the neutron production, a Ludlum Bonner sphere spectrometer (BSS) is used for measurement at different points of a LinAc bunker at the Hospital Universitari i Politècnic La Fe de València. With the neutron measured data and a set of response detector curves obtained by Monte Carlo simulations with MCNP6.1.1, the Maximum Likelihood Expectation Maximization unfolding method is used to unfold the energy neutron spectrum. Unfolded neutron spectra at different locations were compared to those obtained by Monte Carlo simulation of the same setup, showing the same energetic behavior. The fluence rate decreases with source distance, and the shape changes from a fast neutron peak in the nearest LinAc head location to a prominent thermal neutron peak in the bunker maze region. Moreover, the neutron ambient equivalent dose was obtained from the unfolded spectra and compared to Berthold detector measurements, being consistent.

Dynamic low-count PET image reconstruction using spatio-temporal primal dual network

Objective. Dynamic positron emission tomography (PET) imaging, which can provide information on dynamic changes in physiological metabolism, is now widely used in clinical diagnosis and cancer treatment. However, the reconstruction from dynamic data is extremely challenging due to the limited counts received in individual frame, especially in ultra short frames. Recently, the unrolled model-based deep learning methods have shown inspiring results for low-count PET image reconstruction with good interpretability. Nevertheless, the existing model-based deep learning methods mainly focus on the spatial correlations while ignore the temporal domain. Approach. In this paper, inspired by the learned primal dual (LPD) algorithm, we propose the spatio-temporal primal dual network (STPDnet) for dynamic low-count PET image reconstruction. Both spatial and temporal correlations are encoded by 3D convolution operators. The physical projection of PET is embedded in the iterative learning process of the network, which provides the physical constraints and enhances interpretability. Main results. The experiments of both simulation data and real rat scan data have shown that the proposed method can achieve substantial noise reduction in both temporal and spatial domains and outperform the maximum likelihood expectation maximization, spatio-temporal kernel method, LPD and FBPnet. Significance. Experimental results show STPDnet better reconstruction performance in the low count situation, which makes the proposed method particularly suitable in whole-body dynamic imaging and parametric PET imaging that require extreme short frames and usually suffer from high level of noise.

Compressed sensing reconstruction shortens the acquisition time for myocardial perfusion imaging: a simulation study.

Compressed sensing (CS) has been used to improve image quality in single-photon emission tomography (SPECT) imaging. However, the effects of CS on image quality parameters in myocardial perfusion imaging (MPI) have not been investigated in detail. This preliminary study aimed to compare the performance of CS-iterative reconstruction (CS-IR) with filtered back-projection (FBP) and maximum likelihood expectation maximization (ML-EM) on their ability to reduce the acquisition time of MPI. A digital phantom that mimicked the left ventricular myocardium was created. Projection images with 120 and 30 directions (360°), and with 60 and 15 directions (180°) were generated. The SPECT images were reconstructed using FBP, ML-EM, and CS-IR. The coefficient of variation (CV) for the uniformity of myocardial accumulation, septal wall thickness, and contrast ratio (Contrast) of the defect/normal lateral wall were calculated for evaluation. The simulation was performed ten times. The CV of CS-IR was lower than that of FBP and ML-EM in both 360° and 180° acquisitions. The septal wall thickness of CS-IR at the 360° acquisition was inferior to that of ML-EM, with a difference of 2.5mm. Contrast did not differ between ML-EM and CS-IR for the 360° and 180° acquisitions. The CV for the quarter-acquisition time in CS-IR was lower than that for the full-acquisition time in the other reconstruction methods. CS-IR has the potential to reduce the acquisition time of MPI.

Development of a compact fast-neutron spectrometer for nuclear emergency response applications

We have developed a Compact Fast Neutron Spectrometer (CFNS) for passive assay of special nuclear material (SNM) through the observation of fast neutrons. The CFNS consists of eight organic glass scintillators (OGS) coupled to silicon photomultipliers and a waveform digitizer, which are integrated within a human-portable box. The CFNS determines the neutron energy profile by spectrum unfolding using the Maximum-Likelihood Expectation Maximization method. The detector acquisition system was optimized to have a dynamic range of up to 10 MeV neutron energy. Bulk special nuclear material (SNM) measurements from the National Criticality Experiments Research Center were analyzed for SNM validation/examination. The results show that the CFNS can be used to distinguish between fission and (α, n) neutron emitters, regardless of intervening material type (Cu and polyethylene) and thickness, by taking the ratio of neutron counts at different regions in the unfolded energy spectrum. Additionally, by fitting an exponential curve to the unfolded energy spectrum of PuO2 and Pu neutron emitters, the CFNS showed the ability of distinguishing between pure Pu oxide, pure Pu metal and mixed oxide-metal configurations.

PET Image Reconstruction with Kernel and Kernel Space Composite Regularizer.

Led by the kernelized expectation maximization (KEM) method, the kernelized maximum-likelihood (ML) expectation maximization (EM) methods have recently gained prominence in PET image reconstruction, outperforming many previous state-of-the-art methods. But they are not immune to the problems of non-kernelized MLEM methods in potentially large reconstruction variance and high sensitivity to iteration numbers, and the difficulty in preserving image details and suppressing image variance simultaneously. To solve these problems, this paper derives, using the ideas of data manifold and graph regularization, a novel regularized KEM (RKEM) method with a kernel space composite regularizer for PET image reconstruction. The composite regularizer consists of a convex kernel space graph regularizer that smooths the kernel coefficients, a concave kernel space energy regularizer that enhances the coefficients' energy, and a composition constant that is analytically set to guarantee the convexity of composite regularizer. The composite regularizer renders easy use of PET-only image priors to overcome KEM's difficulty caused by the mismatch of MR prior and underlying PET images. Using this kernel space composite regularizer and the technique of optimization transfer, a globally convergent iterative algorithm is derived for RKEM reconstruction. Tests and comparisons on the simulated and in vivo data are presented to validate and evaluate the proposed algorithm, and demonstrate its better performance and advantages over KEM and other conventional methods.

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.

Location and Activity Characterization of Gamma-Ray Point Sources Concealed in Shipping Containers Using Iterative Reconstruction and Modeling Cargo-Specific Attenuation

Simulated measurements of traditional shipping container screening infrastructure based on large-area polyvinyl-toluene (PVT) or sodium-iodide detectors (NaI) are used alongside an iterative reconstruction algorithm to characterize the activity and location of a radioactive point source concealed within a shipping container loaded with cargo. A maximum likelihood expectation maximization reconstruction method is employed to reconstruct the source distribution under the assumption that there exists a single point source in the scenario. To account for shielding by the cargo, it is assumed that the encompassing cargo, which was chosen to represent iron cargo, such as scrap metal or machine parts, is homogeneously distributed throughout the 32.2-m3 container at realistic loaded container densities of 0.0, 0.2, or 0.6 gcm−3. When the material properties of the cargo are assumed known and provided to the algorithm, the method is capable of localizing the source to within 40.5 cm and estimating the activity to the correct order of magnitude for cases with no cargo and 0.2 gcm−3 iron cargo completely filling the 32.2-m3 volume. With iron cargo at a density of 0.6 gcm−3, the localization and activity estimation is significantly worse, which is attributed to the method of accounting for attenuation in the cargo, a decreased signal-to-noise ratio, and the use of gross-count data that include the effect of buildup radiation. Using 662-keV photopeak data from a NaI-based radiation portal monitor (RPM) achieves better results than gross-count data from a PVT- or NaI-based RPM with the correct order of magnitude activity estimates for all cargo densities. For scenarios where the material of the cargo is unknown, but its density and distribution are known, a brute-force search is performed to find the optimum mass attenuation coefficient that describes the cargo. From the range of mass attenuation coefficients obtained, the method is not capable of differentiating between different types of common cargo, but demonstrates the principle of the method for characterizing shipping container cargo. Ultimately, the largest limiting factor in this method is the use of a simple average to estimate the path length traveled from a point in the container through the cargo in the direction of a detector. The large area detectors result in a high variance in this path length, and the degree of attenuation is exponentially dependent on this value. Despite the simple method of accounting for attenuation in the cargo, the maximum likelihood expectation maximization point source (MLEM PS) method is able to characterize a concealed point source well in the case with a PVT-based RPM and 0.2 gcm−3, which is cargo above the average density of a shipping container, drastically reducing the search area in secondary screening processes. The MLEM PS algorithm, therefore, represents a means of enhancing shipping container screening procedures without requiring significant changes in infrastructure and hardware.

TOF MLEM Adaptation for the Total-Body J-PET With a Realistic Analytical System Response Matrix

We report a study of the original image reconstruction algorithm based on the time-of-flight maximum likelihood expectation maximisation (TOF MLEM), developed for the total-body (TB) Jagiellonian PET (J-PET) scanners. The method is applicable to generic cylindrical or modular multi-layer layouts and is extendable to multi-photon imaging. The system response matrix (SRM) is represented as a set of analytical functions, uniquely defined for each pair of plastic scintillator strips used for the detection. A realistic resolution model (RM) in detector space is derived from fitting the Monte Carlo simulated emissions and detections of annihilation photons on oblique transverse planes. Additional kernels embedded in SRM account for TOF, parallax effect and axial smearing. The algorithm was tested on datasets, simulated in GATE for the NEMA IEC and static XCAT phantoms inside a 24-module 2-layer TB J-PET. Compared to the reference TOF MLEM with none or a shift-invariant RM, an improvement was observed, as evaluated by the analysis of image quality, difference images and ground truth metrics. We also reconstructed the data with additive contributions, pre-filtered geometrically and with non-TOF scatter correction applied. Despite some deterioration, the obtained results still capitalise on the realistic RM with better edge preservation and superior ground truth metrics. The envisioned prospects of the TOF MLEM with analytical SRM include its application in multi-photon imaging and further upgrade to account for the non-collinearity, positron range and other factors.

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.

The study of a neutron spectrum unfolding method based on particle swarm optimization combined with maximum likelihood expectation maximization

The study of a neutron spectrum unfolding method based on particle swarm optimization combined with maximum likelihood expectation maximization

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.