Maximum Likelihood Expectation Maximization Reconstruction Research Articles

Anatomy-guided multi-resolution image reconstruction in PET

Objective. In this paper, we propose positron emission tomography image reconstruction using a multi-resolution triangular mesh. The mesh can be adapted based on patient specific anatomical information that can be in the form of a computed tomography or magnetic resonance imaging image in the hybrid imaging systems. The triangular mesh can be adapted to high resolution in localized anatomical regions of interest (ROI) and made coarser in other regions, leading to an imaging model with high resolution in the ROI with clearly reduced number of degrees of freedom compared to a conventional uniformly dense imaging model. Approach. We compare maximum likelihood expectation maximization reconstructions with the multi-resolution model to reconstructions using a uniformly dense mesh, a sparse mesh and regular rectangular pixel mesh. Two simulated cases are used in the comparison, with the first one using the NEMA image quality phantom and the second the XCAT human phantom. Main results. When compared to the results with the uniform imaging models, the locally refined multi-resolution mesh retains the accuracy of the dense mesh reconstruction in the ROI while being faster to compute than the reconstructions with the uniformly dense mesh. The locally dense multi-resolution model leads also to more accurate reconstruction than the pixel-based mesh or the sparse triangular mesh. Significance. The findings suggest that triangular multi-resolution mesh, which can be made patient and application specific, is a potential alternative for pixel-based reconstruction.

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.

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.

Dual gating myocardial perfusion SPECT denoising using a conditional generative adversarial network.

Dual respiratory-cardiac gating reduces respiratory and cardiac motion blur in myocardial perfusion single-photon emission computed tomography (MP-SPECT). However, image noise is increased as detected counts are reduced in each dual gate (DG). We aim to develop a denoising method for dual gating MP-SPECT images using a 3D conditional generative adversarial network (cGAN). Twenty extended cardiac-torso phantoms with various 99m Tc-sestamibi distributions, defect characteristics, and body and organ sizes were used in the simulation, modeling six respiratory and eight cardiac gates (CGs), that is, 48 DGs for ordered subset expectation maximization reconstruction. Twenty clinical 99m Tc-sestamibi SPECT/CT datasets were re-binned into 7 respiratory gates and 8 CGs, that is, 56 DGs for maximum likelihood expectation maximization reconstruction. We evaluated the use of (i) phantoms' own datasets (patient-specific denoising [PD]) or other phantoms' datasets (cross-patient denoising) for training; (ii) the CG or the static (non-gated [NG]) data as the training references for cGAN; and (iii) cGAN as compared to conventional 3D post-reconstruction filtering, cardiac gating methods, and convolutional neural network. Normalized mean squared error, noise as assessed by normalized standard deviation, spatial blurring measured as the full-width-at-half-maximum of left ventricular wall, ejection fraction, joint correlation histogram, and defect size were analyzed as metrics of image quality. Training using patients' own dataset is superior to conventional training based on other patients' data. Using CG image as training reference provides a better trade-off in terms of noise and image blur as compared to the use of NG. cGAN-CG-PD provides superior performance as compared to other denoising methods for all physical and diagnostic indices evaluated in both simulation and clinical studies. cGAN denoising is promising for dual gating MP-SPECT based on the metrics mentioned earlier.

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.

Estimate of the 225Ac Radioactive Isotope Distribution by Means of DOI Compton Imaging in Targeted Alpha Radiotherapy: A Monte Carlo Simulation

For successful targeted alpha radiotherapy (TAT), verifying the accurate position and distribution of a targeted radiotherapeutic agent in a patient or phantom is important. This paper, describes our investigation of depth-of-interaction (DOI) Compton imaging for the two γ-rays emitted during TAT with the 225Ac radioactive isotope. We optimized the design parameters of the DOI Compton camera, for example, the inter-detector distance, based on the figure of merit (FOM). The performance of DOI Compton imaging for TAT was improved because Doppler broadening and the energy uncertainty are inversely proportional to the radiation energy and the position uncertainty of the depth information is decreased. After the contrast phantom and the resolution phantom had been designed, two reconstruction algorithms, the filtered back-projection (FBP) algorithm and the maximum-likelihood expectation maximization (MLEM) algorithm, were applied to each reconstructed phantom image, and the qualities of the reconstructed images for the two γ-rays (218 keV and 440 keV) were compared. In the quantitative evaluation of the reconstructed images, the MLEM reconstruction algorithm performed better than the FBP algorithm. Based on Monte Carlo simulation studies, the DOI Compton images of the 225Ac radioactive isotope emitting two γ-rays demonstrated the capability of imaging a targeted radiotherapeutic agent in TAT.

Computationally Efficient System Matrix Calculation Techniques in Computed Tomography Iterative Reconstruction.

Background:Relative to classical methods in computed tomography, iterative reconstruction techniques enable significantly improved image qualities and/or lowered patient doses. However, the computational speed is a major concern for these iterative techniques. In the present study, we present a method for fast system matrix calculation based on the line integral model (LIM) to speed up the computations without compromising the image quality. In addition, we develop a hybrid line–area integral model (AIM) that highlights the advantages of both LIM and AIMs.Methods:The contributing detectors for a given pixel and a given projection view, and the length of corresponding intersection lines with pixels, are calculated using our proposed algorithm. For the hybrid method, the respective narrow-angle fan beam was modeled by multiple equally spaced lines. The computed system matrix was evaluated in the context of reconstruction using the simultaneous algebraic reconstruction technique (SART) as well as maximum likelihood expectation maximization (MLEM).Results:The proposed LIM offers a considerable reduction in calculation times compared to the standard Siddon algorithm: 2.9 times faster. Differences in root mean square error and peak signal-to-noise ratio were not significant between the proposed LIM and the Siddon algorithm for both SART and MLEM reconstruction methods (P > 0.05). Meanwhile, the proposed hybrid method resulted in significantly improved image qualities relative to LIM and the Siddon algorithm (P < 0.05), though computations were 4.9 times more intensive than the proposed LIM.Conclusion:We have proposed two fast algorithms to calculate the system matrix. The first is based on LIM and was faster than the Siddon algorithm, with matched image quality, whereas the second method is a hybrid LIM–AIM that achieves significantly improved images though with its computational requirements.

MLEM reconstruction method applied to partial defect verification using simulated data

Gamma emission tomography (GET) using the maximum likelihood-expectation maximization (MLEM) algorithm was developed to detect fuel rods emitting gamma-rays for potential use as a verification tool in nuclear safeguards. To examine the feasibility of the method, scenarios of partial fuel rod defects in a General Electric 7 × 7 boiling water reactor assembly were modeled. Thereafter, ORIGEN-ARP was used to generate the gamma-ray emission spectrum from the fuel, MCNP was used to simulate the measurements using the source term obtained from ORIGEN-ARP. GET was performed using MLEM with passive gamma ray projection profiles provided by MCNP5. As a result, we concluded that GET using MLEM functions is an effective visualization technique of gamma ray emitters for verification. The reconstruction, however, featured minor activities in the center zone of fuel assemblies due to unconsidered attenuation effect, which interferes with the quantitative analysis of rod-wise gamma emitter activities.

Modeling the primary source intensity distribution: reconstruction and inter-comparison of six Varian TrueBeam sources

The primary source size is one of the most important beam model parameters in small photon fields. In this work we apply a recently suggested reconstruction technique to characterize the primary source of 6 Varian TrueBeam (TB) linacs. A series of photon fluence profile measurements were performed on 6 Varian TB linacs in the crossplane and inplane orientation using radiochromic film in air and a 2 mm Pb foil as a build-up layer. An image reconstruction algorithm was then applied, based on the maximum likelihood expectation-maximization (MLEM) algorithm, to estimate the source distribution. The method iteratively ray-traces photons from the source plane to the measurement plane to extract source profile corrections. The technique was first benchmarked using a Monte Carlo (MC) model of a Varian TrueBeam with known input Gaussian source sizes. The robustness of the suggested technique was also tested by randomly sampling different combinations of source and field size values and repeating the reconstruction. At the MC benchmarking stage the MLEM reconstruction algorithm was capable of reproducing the Gaussian shape with a RMSE less than 4.0%, while the reconstructed source size (FWHM) and field size were determined with an accuracy level of 0.14 mm and 0.10 mm respectively. Experimentally, the reconstructed TB sources presented FWHM values between 1.02–1.5 mm (–0.18 mm) and 1.08–1.42 mm (–0.13 mm) in the crossplane and inplane orientations respectively. All TB sources studied in this work can be considered symmetric within uncertainties with the exception of one. The source distribution presented systematic deviations from a Gaussian distribution mostly in the lower tail region. Multi-parameter functional forms, such as Pearson VII or double Gaussian presented improvements in modeling the source in this region, but increase the model complexity. The reconstructed sources measured in this work can serve as reference values for commissioning beam models in small fields and set upper and lower thresholds values of the expected source size for a TB linac.

Muography of different structures using muon scattering and absorption algorithms.

In recent decades, muon imaging has found a plethora of applications in many fields. This technique succeeds to infer the density distribution of big inaccessible structures where conventional techniques cannot be used. The requirements of different applications demand specific implementations of image reconstruction algorithms for either multiple scattering or absorption-transmission data analysis, as well as noise-suppression filters and muon momentum estimators. This paper presents successful results of image reconstruction techniques applied to simulated data of some representative applications. In addition to well-known reconstruction methods, a novel approach, the so-called μCT, is proposed for the inspection of spent nuclear fuel canisters. Results obtained based on both μCT and the maximum-likelihood expectation maximization reconstruction algorithms are presented.This article is part of the Theo Murphy meeting issue 'Cosmic-ray muography'.

Penalized maximum likelihood simultaneous longitudinal PET image reconstruction with difference‐image priors

Many clinical contexts require the acquisition of multiple positron emission tomography (PET) scans of a single subject, for example, to observe and quantitate changes in functional behaviour in tumors after treatment in oncology. Typically, the datasets from each of these scans are reconstructed individually, without exploiting the similarities between them. We have recently shown that sharing information between longitudinal PET datasets by penalizing voxel-wise differences during image reconstruction can improve reconstructed images by reducing background noise and increasing the contrast-to-noise ratio of high-activity lesions. Here, we present two additional novel longitudinal difference-image priors and evaluate their performance using two-dimesional (2D) simulation studies and a three-dimensional (3D) real dataset case study. We have previously proposed a simultaneous difference-image-based penalized maximum likelihood (PML) longitudinal image reconstruction method that encourages sparse difference images (DS-PML), and in this work we propose two further novel prior terms. The priors are designed to encourage longitudinal images with corresponding differences which have (a) low entropy (DE-PML), and (b) high sparsity in their spatial gradients (DTV-PML). These two new priors and the originally proposed longitudinal prior were applied to 2D-simulated treatment response [18 F]fluorodeoxyglucose (FDG) brain tumor datasets and compared to standard maximum likelihood expectation-maximization (MLEM) reconstructions. These 2D simulation studies explored the effects of penalty strengths, tumor behaviour, and interscan coupling on reconstructed images. Finally, a real two-scan longitudinal data series acquired from a head and neck cancer patient was reconstructed with the proposed methods and the results compared to standard reconstruction methods. Using any of the three priors with an appropriate penalty strength produced images with noise levels equivalent to those seen when using standard reconstructions with increased counts levels. In tumor regions, each method produces subtly different results in terms of preservation of tumor quantitation and reconstruction root mean-squared error (RMSE). In particular, in the two-scan simulations, the DE-PML method produced tumor means in close agreement with MLEM reconstructions, while the DTV-PML method produced the lowest errors due to noise reduction within the tumor. Across a range of tumor responses and different numbers of scans, similar results were observed, with DTV-PML producing the lowest errors of the three priors and DE-PML producing the lowest bias. Similar improvements were observed in the reconstructions of the real longitudinal datasets, although imperfect alignment of the two PET images resulted in additional changes in the difference image that affected the performance of the proposed methods. Reconstruction of longitudinal datasets by penalizing difference images between pairs of scans from a data series allows for noise reduction in all reconstructed images. An appropriate choice of penalty term and penalty strength allows for this noise reduction to be achieved while maintaining reconstruction performance in regions of change, either in terms of quantitation of mean intensity via DE-PML, or in terms of tumor RMSE via DTV-PML. Overall, improving the image quality of longitudinal datasets via simultaneous reconstruction has the potential to improve upon currently used methods, allow dose reduction, or reduce scan time while maintaining image quality at current levels.

Design and Performance of a 1 mm3 Resolution Clinical PET System Comprising 3-D Position Sensitive Scintillation Detectors.

We are developing a 1-mm3 resolution, high-sensitivity positron emission tomography (PET) system for loco-regional cancer imaging. The completed system will comprise two cm detector panels and contain 4 608 position sensitive avalanche photodiodes (PSAPDs) coupled to arrays of mm3 LYSO crystal elements for a total of 294 912 crystal elements. For the first time, this paper summarizes the design and reports the performance of a significant portion of the final clinical PET system, comprising 1 536 PSAPDs, 98 304 crystal elements, and an active field-of-view (FOV) of cm. The sub-system performance parameters, such as energy, time, and spatial resolutions are predictive of the performance of the final system due to the modular design. Analysis of the multiplexed crystal flood histograms shows 84% of the crystal elements have>99% crystal identification accuracy. The 511 keV photopeak energy resolution was 11.34±0.06% full-width half maximum (FWHM), and coincidence timing resolution was 13.92 ± 0.01 ns FWHM at 511 keV. The spatial resolution was measured using maximum likelihood expectation maximization reconstruction of a grid of point sources suspended in warm background. The averaged resolution over the central 6 cm of the FOV is 1.01 ± 0.13 mm in the X-direction, 1.84 ± 0.20 mm in the Y-direction, and 0.84 ± 0.11 mm in the Z-direction. Quantitative analysis of acquired micro-Derenzo phantom images shows better than 1.2 mm resolution at the center of the FOV, with subsequent resolution degradation in the y-direction toward the edge of the FOV caused by limited angle tomography effects.

Singular value decomposition analysis of back projection operator of maximum likelihood expectation maximization PET image reconstruction.

BackgroundIn emission tomography maximum likelihood expectation maximization reconstruction technique has replaced the analytical approaches in several applications. The most important drawback of this iterative method is its linear rate of convergence and the corresponding computational burden. Therefore, simplifications are usually required in the Monte Carlo simulation of the back projection step. In order to overcome these problems, a reconstruction code has been developed with graphical processing unit based Monte Carlo engine which enabled full physical modelling in the back projection.Materials and methodsCode performance was evaluated with simulations on two geometries. One is a sophisticated scanner geometry which consists of a dodecagon with inscribed circle radius of 8.7 cm, packed on each side with an array of 39 × 81 LYSO detector pixels of 1.17 mm sided squares, similar to a Mediso nanoScan PET/CT scanner. The other, simplified geometry contains a 38,4mm long interval as a voxel space, detector pixels are assigned in two parallel sections each containing 81 crystals of a size 1.17×1.17 mm.ResultsWe have demonstrated that full Monte Carlo modelling in the back projection step leads to material dependent inhomogeneities in the reconstructed image. The reasons behind this apparently anomalous behaviour was analysed in the simplified system by means of singular value decomposition and explained by different speed of convergence.ConclusionsTo still take advantage of the higher noise stability of the full physical modelling, a new filtering technique is proposed for convergence acceleration. Some theoretical considerations for the practical implementation and for further development are also presented.

Maximum-Likelihood Expectation-Maximization Algorithm Versus Windowed Filtered Backprojection Algorithm: A Case Study

Filtered backprojection (FBP) algorithms reduce image noise by smoothing the image. Iterative algorithms reduce image noise by noise weighting and regularization. It is believed that iterative algorithms are able to reduce noise without sacrificing image resolution, and thus iterative algorithms, especially maximum-likelihood expectation maximization (MLEM), are used in nuclear medicine to replace FBP algorithms. Methods: This short paper uses counter examples to show that this belief is not true. We compare image noise variance for FBP and MLEM reconstructions having the same spatial resolution. Results: The truth is that although MLEM suppresses image noise, it does so by sacrificing image resolution as well; the performance of windowed FBP may be better than that of MLEM in our case study. Conclusion: The myth of the superiority of iterative algorithms is caused by comparing them with conventional FBP instead of with windowed FBP. However, we do not intend to generalize the comparison results to imply which algorithm is more favorable.

Development of image reconstruction algorithm with iterative method using maximum-likelihood expectation-maximization (MLEM) for chest digital tomosynthesis (CDT) X-ray system

Digital tomosynthesis system (DTS) has been increasingly used in chest X-ray imaging with a limited-projection angle image reconstruction method. Image reconstruction methods in chest digital tomosynthesis (CDT) have fundamental impacts on image characteristics. Among these methods, iterative algorithm provides the additional benefits of chest X-ray imaging. However, there is almost no research that maximum-likelihood expectation-maximization (MLEM) method in CDT system. Thus, the purpose of this study was (1) to develop MLEM reconstruction algorithm based on CDT system and (2) to quantitatively compare the image characteristics with respect to the total angular range and iteration number as applied this system. For that purpose, we performed both simulation using MATLAB program and experimental studies. Tomography was performed linearly with a maximum ±30° total angular range and then we acquired Shepp-Logan and PMMA-Aluminum (Al) phantom images using 120 kVp X-ray source for simulation and experiment, respectively. We evaluated and compared the MLEM reconstructed image characteristics using root-mean-square error (RMSE) and signal difference-to-noise ratio (SDNR) with various total angular ranges and iteration numbers. According to the results, we can acquire improved image characteristics as the number of iterations and the number of projections increased. Also, we found optimized iteration number for 20 iteration numbers in our CDT system geometry because there were few changes of image characteristics over 20 iteration numbers. In conclusion, we have presented usefulness and effectiveness of developed CDT image reconstruction algorithm.

Performance evaluation of a multiple-scattering Compton imager for distribution of prompt gamma-rays in proton therapy

The purpose of this study is to compare and evaluate the performance of a multiple-scattering Compton imager (MSCI) to measure prompt gamma-rays emitted during proton therapy. Because prompt gamma-rays are generated simultaneously during the proton beam delivery, the falloff position of the Bragg peak of the proton beam can be determined from the distribution of prompt gamma-rays. The detection system was designed using three CdZnTe detector layers that can track radiation of unknown energy on the basis of effective Compton scattering events. The simple back-projection, filtered back-projection, and maximum likelihood expectation maximization (MLEM) algorithms were applied for the reconstructed Compton images. The falloff positions of the Bragg peaks determined from individual MSCIs were compared with the theoretical values calculated using the Monte Carlo N-Particle eXtended code. Moreover, the performance of the MSCI was compared with that of a previously developed system based on a slit collimator gamma camera. In summary, the MSCI with the MLEM reconstruction algorithm was better than the other reconstruction methods in terms of the falloff position of the Bragg peak, the angular resolution, and the signal-to-noise ratio.

A Prototype High-Resolution Small-Animal PET Scanner Dedicated to Mouse Brain Imaging.

We developed a prototype small-animal PET scanner based on depth-encoding detectors using dual-ended readout of small scintillator elements to produce high and uniform spatial resolution suitable for imaging the mouse brain. The scanner consists of 16 tapered dual-ended-readout detectors arranged in a 61-mm-diameter ring. The axial field of view (FOV) is 7 mm, and the transaxial FOV is 30 mm. The scintillator arrays consist of 14 × 14 lutetium oxyorthosilicate elements, with a crystal size of 0.43 × 0.43 mm at the front end and 0.80 × 0.43 mm at the back end, and the crystal elements are 13 mm long. The arrays are read out by 8 × 8 mm and 13 × 8 mm position-sensitive avalanche photodiodes (PSAPDs) placed at opposite ends of the array. Standard nuclear-instrumentation-module electronics and a custom-designed multiplexer are used for signal processing. The detector performance was measured, and all but the crystals at the very edge could be clearly resolved. The average intrinsic spatial resolution in the axial direction was 0.61 mm. A depth-of-interaction resolution of 1.7 mm was achieved. The sensitivity of the scanner at the center of the FOV was 1.02% for a lower energy threshold of 150 keV and 0.68% for a lower energy threshold of 250 keV. The spatial resolution within a FOV that can accommodate the entire mouse brain was approximately 0.6 mm using a 3-dimensional maximum-likelihood expectation maximization reconstruction. Images of a hot-rod microphantom showed that rods with a diameter of as low as 0.5 mm could be resolved. The first in vivo studies were performed using (18)F-fluoride and confirmed that a 0.6-mm resolution can be achieved in the mouse head in vivo. Brain imaging studies with (18)F-FDG were also performed. We developed a prototype PET scanner that can achieve a spatial resolution approaching the physical limits of a small-bore PET scanner set by positron range and detector interaction. We plan to add more detector rings to extend the axial FOV of the scanner and increase sensitivity.

Wobbling and LSF-based maximum likelihood expectation maximization reconstruction for wobbling PET

Abstract Positron emission tomography (PET) is a widely used imaging modality; however, the PET spatial resolution is not yet satisfactory for precise anatomical localization of molecular activities. Detector size is the most important factor because it determines the intrinsic resolution, which is approximately half of the detector size and determines the ultimate PET resolution. Detector size, however, cannot be made too small because both the decreased detection efficiency and the increased septal penetration effect degrade the image quality. A wobbling and line spread function (LSF)-based maximum likelihood expectation maximization (WL-MLEM) algorithm, which combined the MLEM iterative reconstruction algorithm with wobbled sampling and LSF-based deconvolution using the system matrix, was proposed for improving the spatial resolution of PET without reducing the scintillator or detector size. The new algorithm was evaluated using a simulation, and its performance was compared with that of the existing algorithms, such as conventional MLEM and LSF-based MLEM. Simulations demonstrated that the WL-MLEM algorithm yielded higher spatial resolution and image quality than the existing algorithms. The WL-MLEM algorithm with wobbling PET yielded substantially improved resolution compared with conventional algorithms with stationary PET. The algorithm can be easily extended to other iterative reconstruction algorithms, such as maximum a priori (MAP) and ordered subset expectation maximization (OSEM). The WL-MLEM algorithm with wobbling PET may offer improvements in both sensitivity and resolution, the two most sought-after features in PET design.

Ray-tracing-based reconstruction algorithms for digital breast tomosynthesis

As a breast-imaging technique, digital breast tomosynthesis has great potential to improve the diagnosis of early breast cancer over mammography. Ray-tracing-based reconstruction algorithms, such as ray-tracing back projection, maximum-likelihood expectation maximization (MLEM), ordered-subset MLEM (OS-MLEM), and simultaneous algebraic reconstruction technique (SART), have been developed as reconstruction methods for different breast tomosynthesis systems. This paper provides a comparative study to investigate these algorithms by computer simulation and phantom study. Experimental results suggested that, among the four investigated reconstruction algorithms, OS-MLEM and SART performed better in interplane artifact removal with a fast speed convergence.

Research of the system response of neutron double scatter imaging for MLEM reconstruction

A Maximum Likelihood image reconstruction technique has been applied to neutron scatter imaging. The response function of the imaging system can be obtained by Monte Carlo simulation, which is very time-consuming if the number of image pixels and particles is large. In this work, to improve time efficiency, an analytical approach based on the probability of neutron interaction and transport in the detector is developed to calculate the system response function. The response function was applied to calculate the relative efficiency of the neutron scatter imaging system as a function of the incident neutron energy. The calculated results agreed with simulations by the MCNP5 software. Then the maximum likelihood expectation maximization (MLEM) reconstruction method with the system response function was used to reconstruct data simulated by Monte Carlo method. The results showed that there was good consistency between the reconstruction position and true position. Compared with back-projection reconstruction, the improvement in image quality was obvious, and the locations could be discerned easily for multiple radiation point sources.