Statistical Image Reconstruction Methods Research Articles

SPLIT: Statistical Positronium Lifetime Image Reconstruction via Time-Thresholding.

Positron emission tomography (PET) is a widely utilized medical imaging modality that uses positron-emitting radiotracers to visualize biochemical processes in a living body. The spatiotemporal distribution of a radiotracer is estimated by detecting the coincidence photon pairs generated through positron annihilations. In human tissue, about 40% of the positrons form positroniums prior to the annihilation. The lifetime of these positroniums is influenced by the microenvironment in the tissue and could provide valuable information for better understanding of disease progression and treatment response. Currently, there are few methods available for reconstructing high-resolution lifetime images in practical applications. This paper presents an efficient statistical image reconstruction method for positronium lifetime imaging (PLI). We also analyze the random triple-coincidence events in PLI and propose a correction method for random events, which is essential for real applications. Both simulation and experimental studies demonstrate that the proposed method can produce lifetime images with high numerical accuracy, low variance, and resolution comparable to that of the activity images generated by a PET scanner with currently available time-of-flight resolution.

Towards subpercentage uncertainty proton stopping-power mapping via dual-energy CT: Direct experimental validation and uncertainty analysis of a statistical iterative image reconstruction method.

To assess the potential of a joint dual-energy computerized tomography (CT) reconstruction process (statistical image reconstruction method built on a basis vector model (JSIR-BVM)) implemented on a 16-slice commercial CT scanner to measure high spatial resolution stopping-power ratio (SPR) maps with uncertainties of less than 1%. JSIR-BVM was used to reconstruct images of effective electron density and mean excitation energy from dual-energy CT (DECT) sinograms for 10 high-purity samples of known density and atomic composition inserted into head and body phantoms. The measured DECT data consisted of 90 and 140 kVp axial sinograms serially acquired on a Philips Brilliance Big Bore CT scanner without beam-hardening corrections. The corresponding SPRs were subsequently measured directly via ion chamber measurements on a MEVION S250 superconducting synchrocyclotron and evaluated theoretically from the known sample compositions and densities. Deviations of JSIR-BVM SPR values from their theoretically calculated and directly measured ground-truth values were evaluated for our JSIR-BVM method and our implementation of the Hünemohr-Saito (H-S) DECT image-domain decomposition technique for SPR imaging. A thorough uncertainty analysis was then performed for five different scenarios (comparison of JSIR-BVM stopping-power ratio/stopping power (SPR/SP) to International Commission on Radiation Measurements and Units benchmarks; comparison of JSIR-BVM SPR to measured benchmarks; and uncertainties in JSIR-BVM SPR/SP maps for patients of unknown composition) per the Joint Committee for Guides in Metrology and the Guide to Expression of Uncertainty in Measurement, including the impact of uncertainties in measured photon spectra, sample composition and density, photon cross section and I-value models, and random measurement uncertainty. Estimated SPR uncertainty for three main tissue groups in patients of unknown composition and the weighted proportion of each tissue type for three proton treatment sites were then used to derive a composite range uncertainty for our method. Mean JSIR-BVM SPR estimates deviated by less than 1% from their theoretical and directly measured ground-truth values for most inserts and phantom geometries except for high-density Delrin and Teflon samples with SPR error relative to proton measurements of 1.1% and -1.0% (head phantom) and 1.1% and -1.1% (body phantom). The overall root-mean-square (RMS) deviations over all samples were 0.39% and 0.52% (head phantom) and 0.43% and 0.57% (body phantom) relative to theoretical and directly measured ground-truth SPRs, respectively. The corresponding RMS (maximum) errors for the image-domain decomposition method were 2.68% and 2.73% (4.68% and 4.99%) for the head phantom and 0.71% and 0.87% (1.37% and 1.66%) for the body phantom. Compared to H-S SPR maps, JSIR-BVM yielded 30% sharper and twofold sharper images for soft tissues and bone-like surrogates, respectively, while reducing noise by factors of 6 and 3, respectively. The uncertainty (coverage factor k=1) of the DECT-to-benchmark values comparison ranged from 0.5% to 1.5% and is dominated by scanning-beam photon-spectra uncertainties. An analysis of the SPR uncertainty for patients of unknown composition showed a JSIR-BVM uncertainty of 0.65%, 1.21%, and 0.77% for soft-, lung-, and bony-tissue groups which led to a composite range uncertainty of 0.6-0.9%. Observed JSIR-BVM SPR estimation errors were all less than 50% of the estimated k=1 total uncertainty of our benchmarking experiment, demonstrating that JSIR-BVM high spatial resolution, low-noise SPR mapping is feasible and is robust to variations in the geometry of the scanned object. In contrast, the much larger H-S SPR estimation errors are dominated by imaging noise and residual beam-hardening artifacts. While the uncertainties characteristic of our current JSIR-BVM implementation can be as large as 1.5%, achieving<1% total uncertainty is feasible by improving the accuracy of scanner-specific scatter-profile and photon-spectrum estimates. With its robustness to beam-hardening artifact, image noise, and variations in phantom size and geometry, JSIR-BVM has the potential to achieve high spatial-resolution SPR mapping with subpercentage accuracy and estimated uncertainty in the clinical setting.

Primer and Historical Review on Rapid Cardiac CINE MRI.

Acceleration is an important consideration when imaging moving organs such as the heart. Not only does acceleration enable motion-free scans but, more importantly, it lies at the heart of capturing the dynamics of cardiac motion. For over three decades, various ingenious approaches have been devised and implemented for rapid CINE MRI suitable for dynamic cardiac imaging. Virtually all techniques relied on acquiring less data to reduce acquisition times. Parallel imaging was among the first of these innovations, using multiple receiver coils and mathematical algorithms for reconstruction; acceleration factors of 2 to 3 were readily achieved in clinical practice. However, in the context of imaging dynamic events, further decreases in scan time beyond those provided by parallel imaging were possible by exploiting temporal coherencies. This recognition ushered in the era of k-t accelerated MRI, which utilized predominantly statistical methods for image reconstruction from highly undersampled k-space. Despite the successes of k-t acceleration methods, however, the accuracy of reconstruction was not always guaranteed. To address this gap, MR physicists and mathematicians applied compressed sensing theory to ensure reconstruction accuracy. Reconstruction was, indeed, more robust, but it required optimizing regularization parameters and long reconstruction times. To solve the limitations of all previous methods, researchers have turned to artificial intelligence and deep neural networks for the better part of the past decade, with recent results showing rapid, robust reconstruction. This review provides a comprehensive overview of key developments in the history of CINE MRI acceleration, and offers a unique and intuitive explanation behind the techniques and underlying mathematics.Level of Evidence: 5Technical Efficacy Stage: 1.

Computed tomography reconstruction on distributed storage using hybrid regularization approach

Computed Tomography (CT) is considered as a significant imaging tool for clinical diagnoses. Due to low-dose radiation in CT, the projection data is highly affected by Gaussian noise which may lead to blurred images, staircase effect, loss of basic fine structure and detailed information. Therefore, there is a demand for an approach that can eliminate noise and can provide high-quality images. To achieve this objective, this paper presents a new statistical image reconstruction method by proposing a suitable regularization approach. The proposed regularization is a hybrid approach of Complex Diffusion and Shock filter as a prior term. To handle the problem of prominent Gaussian noise as well as ill-posedness, the proposed hybrid regularization is further combined with the standard Maximum Likelihood Expectation Maximization (MLEM) reconstruction algorithm in an iterative manner and has been referred to as the proposed CT-Reconstruction (CT-R) algorithm here after. Besides, considering the large sizes of image data sets for medical imaging, distributed storage for images have been employed on Hadoop Distributed File System (HDFS) and the proposed MLEM algorithms have been deployed for improved performance.The proposed method has been evaluated on both the simulated and real test phantoms. The final results are compared with the other standard methods and it is observed that the proposed method has many desirable properties such as better noise robustness, less computational cost and enhanced denoising effect.

Experimental implementation of a joint statistical image reconstruction method for proton stopping power mapping from dual-energy CT data.

To experimentally commission a dual-energy CT (DECT) joint statistical image reconstruction (JSIR) method, which is built on a linear basis vector model (BVM) of material characterization, for proton stopping power ratio (SPR) estimation. The JSIR-BVM method builds on the relationship between the energy-dependent photon attenuation coefficients and the proton stopping power via a pair of BVM component weights. The two BVM component images are simultaneously reconstructed from the acquired DECT sinograms and then used to predict the electron density and mean excitation energy (I-value), which are required by the Bethe equationfor SPR computation. A post-reconstruction image-based DECT method, which utilizes the two separate CT images reconstructed via the scanner's software, was implemented for comparison. The DECT measurement data were acquired on a Philips Brilliance scanner at 90 and 140kVp for two phantoms of different sizes. Each phantom contains 12 different soft and bony tissue surrogates with known compositions. The SPR estimation results were compared to the reference values computed from the known compositions. The difference of the computed water equivalent path lengths (WEPL) across the phantoms between the two methods was also compared. The overall root-mean-square (RMS) of SPR estimation error of the JSIR-BVM method are 0.33% and 0.37% for the head- and body-sized phantoms, respectively, and all SPR estimates of the test samples are within 0.7% of the reference ground truth. The image-based method achieves overall RMS errors of 2.35% and 2.50% for the head- and body-sized phantoms, respectively. The JSIR-BVM method also reduces the pixel-wise random variation by 4-fold to 6-fold within homogeneous regions compared to the image-based method. The average differences between the JSIR-BVM method and the image-based method are 0.54% and 1.02% for the head- and body-sized phantoms, respectively. By taking advantage of an accurate polychromatic CT data model and a model-based DECT statistical reconstruction algorithm, the JSIR-BVM method accounts for both systematic bias and random noise in the acquired DECT measurement data. Therefore, the JSIR-BVM method achieves good accuracy and precision on proton SPR estimation for various tissue surrogates and object sizes. In contrast, the experimentally achievable accuracy of the image-based method may be limited by the uncertainties in the image formation process. The result suggests that the JSIR-BVM method has the potential for more accurate SPR prediction compared to post-reconstruction image-based methods in clinical settings.

Regularization strategies in statistical image reconstruction of low-dose x-ray CT: A review.

Statistical image reconstruction (SIR) methods have shown potential to substantially improve the image quality of low-dose x-ray computed tomography (CT) as compared to the conventional filtered back-projection (FBP) method. According to the maximum a posteriori (MAP) estimation, the SIR methods are typically formulated by an objective function consisting of two terms: (a) a data-fidelity term that models imaging geometry and physical detection processes in projection data acquisition, and (b) a regularization term that reflects prior knowledge or expectations of the characteristics of the to-be-reconstructed image. SIR desires accurate system modeling of data acquisition, while the regularization term also has a strong influence on the quality of reconstructed images. A variety of regularization strategies have been proposed for SIR in the past decades, based on different assumptions, models, and prior knowledge. In this paper, we review the conceptual and mathematical bases of these regularization strategies and briefly illustrate their efficacies in SIR of low-dose CT.

Extended depth-of-field in holographic imaging using deep-learning-based autofocusing and phase recovery

Holography encodes the three dimensional (3D) information of a sample in the form of an intensity-only recording. However, to decode the original sample image from its hologram(s), auto-focusing and phase-recovery are needed, which are in general cumbersome and time-consuming to digitally perform. Here we demonstrate a convolutional neural network (CNN) based approach that simultaneously performs auto-focusing and phase-recovery to significantly extend the depth-of-field (DOF) in holographic image reconstruction. For this, a CNN is trained by using pairs of randomly de-focused back-propagated holograms and their corresponding in-focus phase-recovered images. After this training phase, the CNN takes a single back-propagated hologram of a 3D sample as input to rapidly achieve phase-recovery and reconstruct an in focus image of the sample over a significantly extended DOF. This deep learning based DOF extension method is non-iterative, and significantly improves the algorithm time-complexity of holographic image reconstruction from O(nm) to O(1), where n refers to the number of individual object points or particles within the sample volume, and m represents the focusing search space within which each object point or particle needs to be individually focused. These results highlight some of the unique opportunities created by data-enabled statistical image reconstruction methods powered by machine learning, and we believe that the presented approach can be broadly applicable to computationally extend the DOF of other imaging modalities.

Reduced anatomical clutter in digital breast tomosynthesis with statistical iterative reconstruction.

Digital breast tomosynthesis (DBT) has been shown to somewhat alleviate the breast tissue overlapping issues of two-dimensional (2D) mammography. However, the improvement in current DBT systems over mammography is still limited. Statistical image reconstruction (SIR) methods have the potential to reduce through-plane artifacts in DBT, and thus may be used to further reduce anatomical clutter. The purpose of this work was to study the impact of SIR on anatomical clutter in the reconstructed DBT image volumes. An SIR with a slice-wise total variation (TV) regularizer was implemented to reconstruct DBT images which were compared with the clinical reconstruction method (filtered backprojection). The artifact spread function (ASF) was measured to quantify the reduction of the through-plane artifacts level in phantom studies and microcalcifications in clinical cases. The anatomical clutter was quantified by the anatomical noise power spectrum with a power law fitting model: NPSa ( f) = α f-β . The β values were measured from the reconstructed image slices when the two reconstruction methods were applied to a cohort of clinical breast exams (N = 101) acquired using Hologic Selenia Dimensions DBT systems. The full width half maximum (FWHM) of the measured ASF was reduced from 8.7 ± 0.1 mm for clinical reconstruction to 6.5 ± 0.1 mm for SIR which yields a 25% reduction in FWHM in phantom studies and the same amount of ASF reduction was also found in clinical measurements from microcalcifications. The measured β values for the two reconstruction methods were 3.17 ± 0.36 and 2.14 ± 0.39 for the clinical reconstruction method and the SIR method, respectively. This difference was statistically significant (P << 0.001). The dependence of β on slice location using either method was negligible. Statistical image reconstruction enabled a significant reduction of both the through-plane artifacts level and anatomical clutter in the DBT reconstructions. The β value was found to be β≈2.14 with the SIR method. This value stays in the middle between the β≈1.8 for cone beam CT and β≈3.2 for mammography. In contrast, the measured β value in the clinical reconstructions (β≈3.17) remains close to that of mammography.

Relaxed Linearized Algorithms for Faster X-Ray CT Image Reconstruction.

Statistical image reconstruction (SIR) methods are studied extensively for X-ray computed tomography (CT) due to the potential of acquiring CT scans with reduced X-ray dose while maintaining image quality. However, the longer reconstruction time of SIR methods hinders their use in X-ray CT in practice. To accelerate statistical methods, many optimization techniques have been investigated. Over-relaxation is a common technique to speed up convergence of iterative algorithms. For instance, using a relaxation parameter that is close to two in alternating direction method of multipliers (ADMM) has been shown to speed up convergence significantly. This paper proposes a relaxed linearized augmented Lagrangian (AL) method that shows theoretical faster convergence rate with over-relaxation and applies the proposed relaxed linearized AL method to X-ray CT image reconstruction problems. Experimental results with both simulated and real CT scan data show that the proposed relaxed algorithm (with ordered-subsets [OS] acceleration) is about twice as fast as the existing unrelaxed fast algorithms, with negligible computation and memory overhead.

Statistical image reconstruction for low-dose CT using nonlocal means-based regularization. Part II: An adaptive approach

To reduce radiation dose in X-ray computed tomography (CT) imaging, one common strategy is to lower the tube current and exposure time settings during projection data acquisition. However, this strategy would inevitably increase the projection data noise, and the resulting image by the conventional filtered back-projection (FBP) method may suffer from excessive noise and streak artifacts. The well-known edge-preserving nonlocal means (NLM) filtering can reduce the noise-induced artifacts in the FBP reconstructed image, but it sometimes cannot completely eliminate the artifacts, especially under the very low-dose circumstance when the image is severely degraded. Instead of taking NLM filtering, we proposed a NLM-regularized statistical image reconstruction scheme, which can effectively suppress the noise-induced artifacts and significantly improve the reconstructed image quality. From our previous investigation on NLM-based strategy, we noted that using a spatially invariant filtering parameter in the regularization was rarely optimal for the entire field of view (FOV). Therefore, in this study we developed a novel strategy for designing spatially variant filtering parameters which are adaptive to the local characteristics of the image to be reconstructed. This adaptive NLM-regularized statistical image reconstruction method was evaluated with low-contrast phantoms and clinical patient data to show (1) the necessity in introducing the spatial adaptivity and (2) the efficacy of the adaptivity in achieving superiority in reconstructing CT images from low-dose acquisitions.

Regularization designs for uniform spatial resolution and noise properties in statistical image reconstruction for 3-D X-ray CT.

Statistical image reconstruction methods for X-ray computed tomography (CT) provide improved spatial resolution and noise properties over conventional filtered back-projection (FBP) reconstruction, along with other potential advantages such as reduced patient dose and artifacts. Conventional regularized image reconstruction leads to spatially variant spatial resolution and noise characteristics because of interactions between the system models and the regularization. Previous regularization design methods aiming to solve such issues mostly rely on circulant approximations of the Fisher information matrix that are very inaccurate for undersampled geometries like short-scan cone-beam CT. This paper extends the regularization method proposed in to 3-D cone-beam CT by introducing a hypothetical scanning geometry that helps address the sampling properties. The proposed regularization designs were compared with the original method in with both phantom simulation and clinical reconstruction in 3-D axial X-ray CT. The proposed regularization methods yield improved spatial resolution or noise uniformity in statistical image reconstruction for short-scan axial cone-beam CT.

Statistical image reconstruction for low-dose CT using nonlocal means-based regularization

Low-dose computed tomography (CT) imaging without sacrifice of clinical tasks is desirable due to the growing concerns about excessive radiation exposure to the patients. One common strategy to achieve low-dose CT imaging is to lower the milliampere-second (mAs) setting in data scanning protocol. However, the reconstructed CT images by the conventional filtered back-projection (FBP) method from the low-mAs acquisitions may be severely degraded due to the excessive noise. Statistical image reconstruction (SIR) methods have shown potentials to significantly improve the reconstructed image quality from the low-mAs acquisitions, wherein the regularization plays a critical role and an established family of regularizations is based on the Markov random field (MRF) model. Inspired by the success of nonlocal means (NLM) in image processing applications, in this work, we propose to explore the NLM-based regularization for SIR to reconstruct low-dose CT images from low-mAs acquisitions. Experimental results with both digital and physical phantoms consistently demonstrated that SIR with the NLM-based regularization can achieve more gains than SIR with the well-known Gaussian MRF regularization or the generalized Gaussian MRF regularization and the conventional FBP method, in terms of image noise reduction and resolution preservation.

Soft-tissue imaging with C-arm cone-beam CT using statistical reconstruction

The potential for statistical image reconstruction methods such as penalized-likelihood (PL) to improve C-arm cone-beam CT (CBCT) soft-tissue visualization for intraoperative imaging over conventional filtered backprojection (FBP) is assessed in this work by making a fair comparison in relation to soft-tissue performance. A prototype mobile C-arm was used to scan anthropomorphic head and abdomen phantoms as well as a cadaveric torso at doses substantially lower than typical values in diagnostic CT, and the effects of dose reduction via tube current reduction and sparse sampling were also compared. Matched spatial resolution between PL and FBP was determined by the edge spread function of low-contrast (∼40–80 HU) spheres in the phantoms, which were representative of soft-tissue imaging tasks. PL using the non-quadratic Huber penalty was found to substantially reduce noise relative to FBP, especially at lower spatial resolution where PL provides a contrast-to-noise ratio increase up to 1.4–2.2× over FBP at 50% dose reduction across all objects. Comparison of sampling strategies indicates that soft-tissue imaging benefits from fully sampled acquisitions at dose above ∼1.7 mGy and benefits from 50% sparsity at dose below ∼1.0 mGy. Therefore, an appropriate sampling strategy along with the improved low-contrast visualization offered by statistical reconstruction demonstrates the potential for extending intraoperative C-arm CBCT to applications in soft-tissue interventions in neurosurgery as well as thoracic and abdominal surgeries by overcoming conventional tradeoffs in noise, spatial resolution, and dose.

Ordered subset image reconstruction studied by means of total variation minimization and fast first-order method in low dose computed tomograhpy

Low-dose computed tomography(CT) has an advantage to reduce X-rays that are harmful to the body. This paper considers the issue of reconstructing high-quality low-dose CT images from incomplete projection data. Generally, this can be done by statistical image reconstruction methods. However, the huge number of iterations of the statistical reconstruction algorithms leads to long computing time, making them difficult to be of practical value. To solve this problem, we propose a method to alleviate the issue by using total variation minimization and fast first-order method for the ordered subsets. We use Split Bregman alternating direction method to solve the optimization problem. Then, the projection onto convex sets method is used to speed up the convergence rate of the iterative method. Numerical experiments show that the relative reconstruction error of the proposed method can decrease faster than the first-order method of ordered subsets with the same iterative number.

Quantifying the Importance of the Statistical Assumption in Statistical X-ray CT Image Reconstruction

Statistical image reconstruction (SIR) is a promising approach to reducing radiation dose in clinical computerized tomography (CT) scans. Clinical CT scanners use energy-integrating detectors. The CT signal follows a compound Poisson distribution, its probability density function (PDF) does not have an analytical form hence cannot be used in an SIR method. The goal of this work is to quantify the effects of using an approximate statistical assumption in SIR methods for clinical CT applications. We apply a pseudo-Ideal Observer (pIO) to simulated CT projection data of the fanbeam geometry at different dose levels. The simulation models the polychromatic X-ray tube spectrum, the effects of the bowtie filter, and the energy-integrating detectors. The pIO uses a pseudo likelihood function (pLF) to calculate the pseudo likelihood ratio, which is the decision variable used by the pIO in a binary detection task. The pLF is an approximation to the true LF of the underlying data. The pIO has inferior performance than the IO unless the pLF coincides with the LF; this performance difference quantifies the closeness between the pseudo likelihood and the exact one. Using lesion detectability in a signal known exactly, background known exactly binary detection task as a figure-of-merit, our results show that at down to 0.1% of a reference tube current level I0, the pIO that uses a Poisson approximation, or a matched variance Gaussian approximation in either the transmission or the line integral domain, achieves 99% the performance of the IO. The constant variance Gaussian approximation has only 70%-80% of the IO performance. At tube currents lower than 0.1% I0, the performance difference is more substantial. We conclude that at current clinical dose levels, it is important to account for the mean-dependent variance in CT projection data in SIR problem formulation, the exact PDF of the CT signal is not as important.

TU-A-211-01: Iterative Image Reconstruction for CT

After decades of research efforts, statistical methods for image reconstruction have begun to appear in commercial X‐ray CT systems, offering substantial improvements in image quality and/or substantial reductions in patient X‐ray dose, at the price of increased computation time. This educational talk will give an overview of the principles of statistical/iterative methods for image reconstruction for X‐ray CTimaging along with examples from clinical CT.

Statistical optoacoustic image reconstruction using a-priori knowledge on the location of acoustic distortions

Strong reflection and scattering effects, arising at the boundaries of acoustically mismatched areas in living organisms, such as bones, lungs, and other air cavities, may introduce severe image artifacts into optoacoustic reconstructions. Yet, in many cases, an a priori knowledge on the location of strongly mismatched areas is available, either based on general anatomical knowledge or using other imaging modalities. In this letter, we suggest a statistical optoacoustic image reconstruction method, which uses a priori knowledge on the location of acoustic distortions in order to improve image quality and quantification. Significant improvements are showcased experimentally on tissue mimicking phantoms of different complexities.

Quadratic Regularization Design for 2-D CT

Statistical methods for tomographic image reconstruction have improved noise and spatial resolution properties that may improve image quality in X-ray computed tomography (CT). Penalized weighted least squares (PWLS) methods using conventional quadratic regularization lead to nonuniform and anisotropic spatial resolution due to interactions between the weighting, which is necessary for good noise properties, and the regularizer. Previously, we addressed this problem for parallel-beam emission tomography using matrix algebra methods to design data-dependent, shift-variant regularizers that improve resolution uniformity. This paper develops a fast angular integral mostly analytical (AIMA) regularization design method for 2-D fan-beam X-ray CT imaging, for which parallel-beam tomography is a special case. Simulation results demonstrate that the new method for regularization design requires very modest computation and leads to nearly uniform and isotropic spatial resolution in transmission tomography when using quadratic regularization.

Theoretical study of penalized-likelihood image reconstruction for region of interest quantification

Region of interest (ROI) quantification is an important task in emission tomography (e.g., positron emission tomography and single photon emission computed tomography). It is essential for exploring clinical factors such as tumor activity, growth rate, and the efficacy of therapeutic interventions. Statistical image reconstruction methods based on the penalized maximum-likelihood (PML) or maximum a posteriori principle have been developed for emission tomography to deal with the low signal-to-noise ratio of the emission data. Similar to the filter cut-off frequency in the filtered backprojection method, the regularization parameter in PML reconstruction controls the resolution and noise tradeoff and, hence, affects ROI quantification. In this paper, we theoretically analyze the performance of ROI quantification in PML reconstructions. Building on previous work, we derive simplified theoretical expressions for the bias, variance, and ensemble mean-squared-error (EMSE) of the estimated total activity in an ROI that is surrounded by a uniform background. When the mean and covariance matrix of the activity inside the ROI are known, the theoretical expressions are readily computable and allow for fast evaluation of image quality for ROI quantification with different regularization parameters. The optimum regularization parameter can then be selected to minimize the EMSE. Computer simulations are conducted for small ROIs with variable uniform uptake. The results show that the theoretical predictions match the Monte Carlo results reasonably well.

A new reconstruction algorithm based on ordered projection subset and divided pixel subset

Statistical iterative methods for image reconstruction like maximum likelihood expectation maximization are more vigorous and feasible than analytical inversion methods and allow for accurately modelling the counting statistics and the photon transport during acquisition. The maximum likelihood approach provides images with superior noise characteristics compared to conventional algorithms, but it has huge computation burden. The objection of this paper is to develop a new algorithm, which modifies the number of projections and the step size for each iteration in order to recover various frequency components. In the present method, the number of projections in a subset increases and the step size decreases when all the subsets have been processed. In addition, the pixel data are divided into subsets to accelerate image reconstruction. The experimental results demonstrate that this algorithm converge faster than any other reconstruction algorithms and can provide high quality of reconstructed images.