PET Image Reconstruction and Deformable Motion Correction Using Unorganized Point Clouds.

Ordered Subsets Expectation Maximization (OSEM) has been introduced to greatly reduce reconstruction time compared to Maximum Likelihood Expectation Maximization (MLEM) in Positron Emission Tomography (PET). In case of noise-free data, OSEM converges to a MLEM image, but in presence of noise this might not be true, and also OSEM might not converge at all but cycle between similar but distinct images. Assessing what are the limits of the OSEM in terms of reliable contrast recovery is particularly interesting in situation of very short acquisitions and very sparse data. In this work, we study the convergence value of the contrast recovery as a function of the count statistics (and therefore the noise level) in the PET data, using a NEMA image quality phantom. A comparison between Time-of-Flight (TOF) and non-TOF implementations is performed. The scope of the work is to assess how the count statistics affects the convergence value and the convergence rate for OSEM reconstruction, and then to compare the corresponding convergence rates in conventional PET and in TOF PET reconstructions, by analyzing both experimental and simulated data.

The iterative maximum-likelihood expectation-maximization (ML-EM) algorithm is an excellent algorithm for image reconstruction and usually provides better images than the filtered backprojection (FBP) algorithm. However, a windowed FBP algorithm can outperform the ML-EM in certain occasions, when the least-squared difference from the true image, that is, the least-squared error (LSE), is used as the comparison criterion. Computer simulations were carried out for the two algorithms. For a given data set the best reconstruction (compared to the true image) from each algorithm was first obtained, and the two reconstructions are compared. The stopping iteration number of the ML-EM algorithm and the parameters of the windowed FBP algorithm were determined, so that they produced an image that was closest to the true image. However, to use the LSE criterion to compare algorithms, one must know the true image. How to select the optimal parameters when the true image is unknown is a practical open problem. For noisy Poisson projections, computer simulation results indicate that the ML-EM images are better than the regular FBP images, and the windowed FBP algorithm images are better than the ML-EM images. For the noiseless projections, the FBP algorithms outperform the ML-EM algorithm. The computer simulations reveal that the windowed FBP algorithm can provide a reconstruction that is closer to the true image than the ML-EM algorithm.

In this paper, we explore a novel method for tomographic image reconstruction in the field of SPECT imaging. Deep Learning methodologies and more specifically deep convolutional neural networks (CNN) are employed in the new reconstruction method, which is referred to as "CNN Reconstruction - CNNR". For training of the CNNR Projection data from software phantoms were used. For evaluation of the efficacy of the CNNR method, both software and hardware phantoms were used. The resulting tomographic images are compared to those produced by filtered back projection (FBP) [1], the "Maximum Likelihood Expectation Maximization" (MLEM) [1] and ordered subset expectation maximization (OSEM) [2].

Emission tomography, including single-photon emission computed tomography (SPECT), requires image reconstruction from noisy and incomplete projection data. The maximum-likelihood expectation maximization (MLEM) algorithm is widely used due to its statistical foundation and non-negativity preservation, but it is highly sensitive to noise, particularly in low-count conditions. Although total variation (TV) regularization can reduce noise, it often oversmooths structural details and requires careful parameter tuning. We propose a Graph-Enhanced Expectation Maximization (GREM) algorithm that incorporates graph-based neighborhood information into an MLEM-type multiplicative reconstruction scheme. The method is motivated by a penalized formulation combining a Kullback–Leibler divergence term with a graph Laplacian regularization term, promoting local structural consistency while preserving edges. The resulting update retains the multiplicative structure of MLEM and preserves the non-negativity of the image estimates. Numerical experiments using synthetic phantoms under multiple noise levels, as well as clinical 99mTc-GSA liver SPECT data, demonstrate that GREM consistently outperforms conventional MLEM and TV-regularized MLEM in terms of PSNR and MS-SSIM. These results indicate that GREM provides an effective and practical approach for edge-preserving noise suppression in emission tomography without relying on external training data.

Iterative algorithms such as maximum likelihood expectation maximization (ML-EM) algorithm are rapidly becoming the standard for image reconstruction in emission computed tomography. The maximum likelihood approach provides images with superior noise characteristics compared to conventional filtered backprojection algorithm. A major drawback of the iterative image reconstruction methods is their high computational cost. In this paper, we develop a new algorithm called the improved ordered subset expectation maximization (IOS-EM) algorithm. This algorithm modifies the number of projections in each subset and the step size (i.e., the relaxation factor) for each iteration in order to recover various frequency components in early iteration steps. In the method presented in this paper, the number of projections in a subset increases and the step size decreases after each iteration. In addition, pixel data are grouped into subdivisions to accelerate image reconstruction. Experimental results show that the IOS-EM algorithm can provide high quality reconstructed images at a small number of iterations.

Three-dimensional (3D) iterative maximum likelihood expectation maximization (ML-EM) algorithms for single-photon emission tomography (SPET) are capable of correcting image-degrading effects of non-uniform attenuation, distance-dependent camera response and patient shape-dependent scatter. However, the resulting improvements in quantitation, resolution and signal-to-noise ratio (SNR) are obtained at the cost of a huge computational burden. This paper presents a new acceleration method for ML-EM: dual matrix ordered subsets (DM-OS). DM-OS combines two acceleration methods: (a) different matrices for projection and back-projection and (b) ordered subsets of projections. DM-OS was compared with ML-EM on simulated data and on physical thorax phantom data, for both 180 degrees and 360 degrees orbits. Contrast, normalized standard deviation and mean squared error were calculated for the digital phantom experiment. DM-OS resulted in similar image quality to ML-EM, even for speed-up factors of 200 compared to ML-EM in the case of 120 projections. The thorax phantom data could be reconstructed 50 times faster (60 projections) using DM-OS with preservation of image quality. ML-EM and DM-OS with scatter compensation showed significant improvement of SNR compared to ML-EM without scatter compensation. Furthermore, inclusion of complex image formation models in the computer code is simplified in the case of DM-OS. It is thus shown that DM-OS is a fast and relatively simple algorithm for 3D iterative scatter compensation, with similar results to conventional ML-EM, for both 180 degrees and 360 degrees acquired data.

Iterative image reconstruction algorithms for positron emission tomography (PET) require a sophisticated system matrix (model) of the scanner. Our aim is to set up such a model offline for the YAP-(S)PET II small animal imaging tomograph in order to use it subsequently with standard ML-EM (maximum-likelihood expectation maximization) and OSEM (ordered subset expectation maximization) for fully three-dimensional image reconstruction. In general, the system model can be obtained analytically, via measurements or via Monte Carlo simulations. In this paper, we present the multi-ray method, which can be considered as a hybrid method to set up the system model offline. It incorporates accurate analytical (geometric) considerations as well as crystal depth and crystal scatter effects. At the same time, it has the potential to model seamlessly other physical aspects such as the positron range. The proposed method is based on multiple rays which are traced from/to the detector crystals through the image volume. Such a ray-tracing approach itself is not new; however, we derive a novel mathematical formulation of the approach and investigate the positioning of the integration (ray-end) points. First, we study single system matrix entries and show that the positioning and weighting of the ray-end points according to Gaussian integration give better results compared to equally spaced integration points (trapezoidal integration), especially if only a small number of integration points (rays) are used. Additionally, we show that, for a given variance of the single matrix entries, the number of rays (events) required to calculate the whole matrix is a factor of 20 larger when using a pure Monte-Carlo-based method. Finally, we analyse the quality of the model by reconstructing phantom data from the YAP-(S)PET II scanner.

Depth-of-interaction enhanced Compton camera using pixelated LYSO(Ce) scintillator arrays and dual-ended SiPMs.

We have developed a three-dimensional (3-D) reconstruction procedure for positron emission tomography (PET) using stochastic sampling techniques-the SS3D algorithm. A forward- and back-projector pair has been developed that eliminates the need to explicitly calculate the system response matrix (SRM). This is advantageous as it eliminates the memory requirements for storing this matrix. As compared to on-the-fly methods, our method is more accurate in its assumptions and can readily incorporate various physical effects of attenuation, scatter, and detector characteristics. This method can be efficiently used with simultaneous or row action algorithms like image space reconstruction algorithm (ISRA), expectation maximization (EM), and ordered subsets expectation maximization (OSEM). We demonstrate the successful implementation of this technique with the maximum likelihood expectation maximization (ML-EM), maximum a posteriori expectation maximization (MAP-EM), and maximum a posteriori ordered subsets expectation maximization (MAP-OS-EM) algorithms by evaluating the images on the basis of uniformity of noise, contrast recovery, signal-to-noise ratio (SNR), point-spread function, structural accuracy, and computational time.

This work is aimed at evaluating the image reconstruction techniques used in single photon emission computed tomography (SPECT/CT) imaging. The reconstruction techniques considered in this work are: the ordered subset expectation maximization (OSEM) and the Filtered Back Projection (FBP). An anthropomorphic torso phantom with lung and liver inserts was injected with 99mTc. The liver and the background were given 0.2 MBq/ml and 0.07 MBq/ml respectively. The lungs inserts were filled with polystyrene beads for humanization. A mimicked 30 ml tumor (27 mm) in the liver insert was given 2 MBq/ml sequential SPECT/CT (step and shot, 10 mins over 180° per head) and CT (120 kVp, 80 mAs) projections were acquired using dual head SPECT/16 slice CT system. The projections were reconstructed using OSEM (10 subsets for 2–10 numbers of iterations, Butterworth post filtering, 10 orders and 0.48 frequencies) and FBP (using Butterworth post filtering at 10 order and cutoff frequencies of 0.38–0.58, 0.05 gaps). Image J software was used for the image analysis. Statistical t-test tested the mean gray values of the tumor and its background. The OSEM and FBP reconstructed images were evaluated from their contrast-to-noise ratio (CNR). The optimal parameter was selected based on 3–5 CNR detection range set by the Rose criterion. The t-test showed the background and the tumors mean values to be statistically significant (P ≪ 0.05). The CNR values for FBP images were all below the detection range, maximum value at the cutoff frequency 0.48 (1.69). In OSEM images at cutoff frequency 0.48, the CNR values were within the detection range for 2–8 numbers of iteration with maximum value (4.89) at 4 numbers of iteration. OSEM was found to be the best for tumor detection and administered activity can be reduced at 4 OSEM’s of iterations (40 MLEM iterations) for patient safety. Keywords: Anthropomorphic torso phantom, 99mTc, SPECT, iterative reconstruction, CNR, P-Value, liver Cite this Article F. Usman, R. Zainon, A. Saidu, A. Bala. Evaluation of image reconstruction techniques in Single photon emission computed tomography (SPECT/CT) imaging. Research & Reviews: Journal of Physics. 2016; 5(2): 13–22p.

We investigated the performance of an ordered-subsets expectation-maximization (OSEM) algorithm for accelerated reconstruction in cone-beam SPECT. SPECT scans were performed using a Defrise phantom filled with 0.9/spl mu/Ci/ml of Tc-99m and a dual-head gamma camera equipped with one cone-beam (CBC, f=70 cm) and one parallel-beam collimator (PBC). Images were reconstructed using a fully-3D approach with resolution and attenuation modeling and an ordered-subsets version of a maximum-likelihood expectation-maximization algorithm (MLEM). Three grouping patterns of subsets were applied: consecutive, orthogonal, and uniform. In contrast to PBC SPECT, we observe that, in CBC SPECT, the reconstruction grouping pattern of the subsets is very important for the image quality obtained. Only when the projection data grouped into a subset were selected as uniformly as possible from all the acquired views, were the image quality and the noise in the images very close to results obtained using MLEM. However, we note that, for both CBC and PBC SPECT, the loglikelihood for a given iteration is practically the same for different grouping patterns of subsets.

The maximum likelihood expectation maximisation (ML-EM) algorithm can be used to reduce reconstruction artefacts produced by filtered backprojection (FBP) methods in pinhole single-photon emission tomography (SPET). However, ML-EM suffers from noise propagation along iterations, which leads to quantitatively unpleasant reconstruction results. To avoid this increase in noise, the median root prior (MRP) algorithm for pinhole SPET was implemented. Projection data of a line source and Picker's thyroid phantom were collected using a single-head gamma camera with a pinhole collimator. MRP was added to existing pinhole ML-EM reconstruction algorithm and the phantom studies were reconstructed using MRP, ML-EM and FBP for comparison. Coefficients of variation, contrasts and full-widths at half-maximum were calculated and showed a clear reduction in noise without significant loss of resolution or decrease in contrast when MRP was applied. MRP also produced visually pleasing images even with high iteration numbers, free of the checkerboard-type noise patterns which are typical of ML-EM images.

Objective To study the effect of the reconstruction method on the semi-quantitative distribution of dopamine transporter (DAT) in the brain, 2β-carbomethoxy-3β-(4-fluorophe-nyl)-(N-11C-methyl)tropane (11C-CFT) PET images of healthy subjects were reconstructed by different PET reconstruction methods. Methods From March 2014 to June 2015, the 11C-CFT PET images of 41 healthy subjects were reconstructed by filtering back projection(FBP) method and ordered subsets expectation maximization (OSEM) iterative method. The brain regions of interest (ROI), namely, caudate nucleus, anterior putamen, and posterior shell nucleus, were automatically sketched with the parietal and occipital cortex lacking of DAT distribution as reference regions. The semi-quantitative value of DAT distribution was calculated using the following formula: radioactivity count of ROI/radioactivity count of parietal and occipital cortex-1. Paired t-test was used to compare the semi-quantitative values of DAT distribution. Correlation analysis was performed using the Pearson correlation analysis. Results The values of DAT distribution based on OSEM were as follows: caudate nucleus (1.77-2.15), anterior putamen (2.17-2.39), and posterior putamen (1.71-2.06). The values of DAT distribution based on FBP were as follows: caudate nucleus (1.68-2.10), anterior putamen (2.07-2.37), and posterior putamen (1.62-1.96). In the bilateral caudate nucleus and anterior and posterior putamen, the 11C-CFT of DAT distribution by OSEM was significantly higher than that by FBP(t=9.658-15.859, all P=0.000). The Pearson correlation analysis showed that the semi-quantitative values of DAT distribution by FBP and OSEM were positively correlated with each other in the bilateral caudate nucleus and anterior and posterior putamen (R2=0.907-0.951, all P=0.000). The DAT distribution by OSEM and FBP decreased with aging in the caudate nucleus and anterior and posterior putamen. Conclusions A significant difference was found in the semi-quantitative value of the DAT distribution in the brain of healthy subjects by different PET reconstruction methods. Therefore, a consistent PET image reconstruction method should be used in a multicenter or longitudinal study. Key words: Dopamine plasma membrane transport proteins; Positron-emission tomography; Filtered backprojection; Iterative

PurposeQ.Clear is a block sequential regularized expectation maximization (BSREM) penalized-likelihood reconstruction algorithm for PET. It tries to improve image quality by controlling noise amplification during image reconstruction. In this study, the noise properties of this BSREM were compared to the ordered-subset expectation maximization (OSEM) algorithm for both phantom and patient data acquired on a state-of-the-art PET/CT.MethodsThe NEMA IQ phantom and a whole-body patient study were acquired on a GE DMI 3-rings system in list mode and different datasets with varying noise levels were generated. Phantom data was evaluated using four different contrast ratios. These were reconstructed using BSREM with different β-factors of 300–3000 and with a clinical setting used for OSEM including point spread function (PSF) and time-of-flight (TOF) information. Contrast recovery (CR), background noise levels (coefficient of variation, COV), and contrast-to-noise ratio (CNR) were used to determine the performance in the phantom data. Findings based on the phantom data were compared with clinical data. For the patient study, the SUV ratio, metabolic active tumor volumes (MATVs), and the signal-to-noise ratio (SNR) were evaluated using the liver as the background region.ResultsBased on the phantom data for the same count statistics, BSREM resulted in higher CR and CNR and lower COV than OSEM. The CR of OSEM matches to the CR of BSREM with β = 750 at high count statistics for 8:1. A similar trend was observed for the ratios 6:1 and 4:1. A dependence on sphere size, counting statistics, and contrast ratio was confirmed by the CNR of the ratio 2:1. BSREM with β = 750 for 2.5 and 1.0 min acquisition has comparable COV to the 10 and 5.0 min acquisitions using OSEM. This resulted in a noise reduction by a factor of 2–4 when using BSREM instead of OSEM. For the patient data, a similar trend was observed, and SNR was reduced by at least a factor of 2 while preserving contrast.ConclusionThe BSREM reconstruction algorithm allowed a noise reduction without a loss of contrast by a factor of 2–4 compared to OSEM reconstructions for all data evaluated. This reduction can be used to lower the injected dose or shorten the acquisition time.

This work explores the feasibility and impact of including both the motion correction and the image registration transformation parameters from positron emission tomography (PET) image space to magnetic resonance (MR), or stereotaxic, image space within the system matrix of PET image reconstruction. This approach is motivated by the fields of neuroscience and psychiatry, where PET is used to investigate differences in activation patterns between different groups of participants, requiring all images to be registered to a common spatial atlas. Currently, image registration is performed after image reconstruction which introduces interpolation effects into the final image. Furthermore, motion correction (also requiring registration) introduces a further level of interpolation, and the overall result of these operations can lead to resolution degradation and possibly artifacts. It is important to note that performing such operations on a post-reconstruction basis means, strictly speaking, that the final images are not ones which maximize the desired objective function (e.g. maximum likelihood (ML), or maximum a posteriori reconstruction (MAP)). To correctly seek parameter estimates in the desired spatial atlas which are in accordance with the chosen reconstruction objective function, it is necessary to include the transformation parameters for both motion correction and registration within the system modeling stage of image reconstruction. Such an approach not only respects the statistically chosen objective function (e.g. ML or MAP), but furthermore should serve to reduce the interpolation effects. To evaluate the proposed method, this work investigates registration (including motion correction) using 2D and 3D simulations based on the high resolution research tomograph (HRRT) PET scanner geometry, with and without resolution modeling, using the ML expectation maximization (MLEM) reconstruction algorithm. The quality of reconstruction was assessed using bias-variance and root mean squared error analyses, comparing the proposed method to conventional post-reconstruction registration methods. An overall reduction in bias (for a cold region: from 41% down to 31% (2D) and 97% down to 65% (3D), and for a hot region: from 11% down to 8% (2D) and from 16% down to 14% (3D)) and in root mean squared error analyses (for a cold region: from 43% to 37% (2D) and from 97% to 65% (3D), and for a hot region: from 11% to 9% (2D) and from 16% down to 14% (3D)) in reconstructed regional mean activities (full regions of interest; all with statistical significance: p < 5 × 10−10) is found when including the motion correction and registration in the system matrix of the MLEM reconstruction, with resolution modeling. However, this improvement in performance comes with an extra computational cost of about 40 min. In this context, this work constitutes an important step toward the goal of estimating parameters of interest directly from the raw Poisson-distributed PET data, and hence toward the complete elimination of post-processing steps.