Statistical Reconstruction Algorithm Research Articles

SU‐DD‐A4‐06: Tradeoff Between Noise and Resolution in CT Images — Comparison of Filtered Backprojection and the Penalized Alternating Minimization Algorithm

Purpose: Relative to linear reconstructions, statistical image reconstruction algorithms have been shown to produce images with less error, artifacts and noise for similar high‐contrast resolution as measured with the MTF. This study compares the noise and resolution, using the edge blur, of images reconstructed using filtered backprojection (FBP) and a new statistical algorithm, Alternating Minimization (AM) [O'Sullivan IEEE TMI vol: 26, ♯3]. Method and Materials: Monoenergetic projection data were simulated for two phantoms, each with a high and low‐contrast insert. Two levels of simple Poisson noise were added to simulate low and clinical‐dose protocols. To study image noise and resolution, FBP was performed with a Gaussian blurred ramp filter of varying FWHM. The penalized AM algorithm was run with a range of penalty strengths. Reconstructed pixel size was also varied. Image noise was quantified as the percent standard deviation in the phantom background. Resolution was evaluated by measuring edge blur at contrast boundaries. Blur was quantified as the FWHM of the Gaussian that, when convolved with the known truth image, gives the highest correlation between reconstructed and convolved images for pixels surrounding the edge. Blur was calculated independently around each contrast boundary. AM and FBP image noise is compared as a function of edge blur. Results: For high resolution images (small edge blur), the AM algorithm reconstructs images with up to 50% less noise than FBP for similar resolution. For all conditions (varying pixel size, projection noise, and contrast inserts), AM exhibits an advantage. Conclusion: Edge blur is used as a metric of CT image resolution for both high and low contrast inserts. The penalized AM algorithm is shown to reduce image noise with less edge blurring than FBP. Future work will extend the use of edge blur to compare AM performance in experimentally acquired CT data.

TU-D-304A-07: Reconstruction From Experimentally Acquired Transmission CT Sinograms with the Polyenergetic Alternating Minimization Algorithm Using An Equivalent X-Ray Spectrum Estimated From Transmission Measurements

Purpose: Polyenergetic Alternating Minimization (AM) is a statistical image reconstruction (SIR) algorithm that uses a precomputed estimated x‐ray spectrum to directly model beam hardening effects in the course of iteratively reconstructingCTimages. We hypothesize that SIR reconstructions, based upon a rigorous physical model of the CT signal formation process, are of better quality than filtered‐backprojection images using conventional preprocessing beam‐hardening corrections. This presentation focuses on the accuracy and magnitude of artifacts in polyenergetic Alternating Minimization (AM) images of homogeneous phantoms. Method and Materials: The x‐ray spectrum of a Brilliance CT scanner was estimated from transmission measurements through varying thicknesses of aluminum and polymethyl methacrylate (PMMA) filters. An exhaustive search was used to find the semi‐empirical Birch‐Marshall x‐ray spectrum that most closely reproduced the transmission measurements. The polyenergetic AM algorithm was used to reconstructimages of 4 homogeneous PMMA disks of varying diameters using the estimated spectrum and measured scatter corrections. A simple test of the algorithm is performed: reconstructing PMMA disks using a PMMA basis in the AM algorithm should reconstruct an image intensity of 1.0 for all disk diameters. Mean intensity and noise are evaluated for disk center and periphery. Results: Our estimated spectrum fits the PMMA transmission measurements to within 1.5%. The AM algorithm reconstructs uniform images of the PMMA disks with mean intensity within 0.8% of the expected relative PMMA density for all disk sizes and locations. Relative standard deviations of the reconstructed intensities about the mean vary between 1.9% and 0.6% (center and periphery) for the 30 cm disk and 0.15% and 0.14% for the 5 cm disk. Conclusion: The polyenergetic AM algorithm can reconstruct accurate images from experimentally acquired CT data. However, great care must be taken in the processing of the raw CT data and the x‐ray spectrum estimation.

SU‐FF‐I‐44: Iterative Image Reconstruction for CBCT Using Edge‐Preserving Prior

Purpose: To improve the image quality of low‐dose cone‐beam CT (CBCT) using an iterative image reconstruction algorithm with an edge‐preserving prior. Method and Materials: We reconstructed CBCT image by minimizing the objective function based on the penalized weighted least‐squares (PWLS) criterion with an anisotropic quadratic penalty. The penalty or the prior constraint is applied on neighboring voxels in the image domain, where the gradient of image intensity controls the degree of smoothness in the reconstructed image. For neighbors associated with large gradient, such as the region around sharp edges, equivalence between them will be discouraged. CBCT projection data of a quality assurance phantom was acquired by a Varian Acuity simulator (Varian Medical Systems, Palo Alto, CA). Contrast‐to‐noise ratio (CNR) and modulation transfer function (MTF), which characterizes the spatial resolution of the reconstructed image, are used to quantitatively evaluate the proposed algorithm. Results: At matched spatial resolution, CNR of a low‐contrast region‐of‐interest in the image reconstructed by the proposed algorithm is 2 times higher than that in the corresponding image reconstructed by the analytical FDK algorithm. Compared with the projection domain smoothing algorithm, the iterative image reconstruction algorithm based on the image domain PWLS criterion produces higher resolution image at matched noise level. Comparison studies with conventional isotropic quadratic penalty and Huber penalty also show that the proposed anisotropic penalty generates images of better spatial resolution at matched noise level. Conclusion: CNR in the low‐dose CBCT image can be significantly improved without loss of spatial resolution by using the proposed iterative image reconstruction algorithm. Imaging dose of CBCT can be lowered using statistical image reconstruction algorithms.

Sci-Sat AM(1): Imaging-05: Analytical scatter estimation for cone-beam computed tomography.

A significant challenge to the implementation of cone-beam computed tomography (CBCT) for high-resolution imaging is the high scatter to primary ratio. Scatter causes cupping and shading artifacts, increased noise and decreased contrast in reconstructed images. Methods to reduce the impact of scatter in CBCT are thus very desirable. We are investigating methods for computational scatter estimation and compensation for CBCT, with the goal of incorporating a scatter estimator within a statistical reconstruction algorithm. We have developed an analytical method for estimating single scatter, based on Klein-Nishina cross-sections. We have compared scatter estimates generated with this method with the results of high-count EGSnrc Monte Carlo simulations. The analytical estimates compare favorably with the Monte Carlo estimates. The paper will discuss our method for analytical estimation of single scatter, including the assumptions and simplifications required to render it computationally tractable, along with the results of the comparison between the analytical method and Monte Carlo simulations. The paper will extend previous results obtained with small (40 × 40 × 40 voxel) homogeneous computational phantoms to include results for larger, more clinically relevant phantoms (128 × 128 × 128 voxels, simulated 50/50 breast tissue with inserts of varying contrast). The paper will also discuss computational acceleration obtained through the use of parallel processing via the WestGrid High-Performance Computing network.

Development of novel statistical reconstruction algorithms for poly-energetic X-ray computed tomography

A beam-hardening effect is a common problem affecting the quantitative aspects of X-ray computed tomography (CT). We have developed two statistical reconstruction algorithms for poly-energetic X-ray CT that can effectively reduce the beam-hardening effect. Phantom tests were used to evaluate our approach in comparison with traditional correction methods. Unlike previous methods, our algorithm utilizes multiple energy-corresponding blank scans to estimate the attenuation map for a particular energy spectrum. Therefore, our algorithm is an energy-selective reconstruction. In addition to benefits over other statistical algorithms for poly-energetic reconstruction, our algorithm has the advantage of not requiring prior knowledge of the object material, the energy spectrum of the source and the energy sensitivity of the detector. The results showed an improvement in coefficient of variation, uniformity and signal-to-noise ratio; overall, this novel approach produces a better beam-hardening correction.

Haplotype reconstruction for scnp DNA: a consensus vote approach with extensive sequence data from populations of the migratory locust (Locusta migratoria)

Single copy nuclear polymorphic (scnp) DNA is potentially a powerful molecular marker for evolutionary studies of populations. However, a practical obstacle to its employment is the general problem of haplotype determination due to the common occurrence of heterozygosity in diploid organisms. We explore here a 'consensus vote' (CV) approach to this question, combining statistical haplotype reconstruction and experimental verification using as an example an indel-free scnp DNA marker from the flanking region of a microsatellite locus of the migratory locust. The raw data comprise 251-bp sequences from 526 locust individuals (1052 chromosomes), with 71 (28.3%) polymorphic nucleotide sites (including seven triallelic sites) and 141 distinct genotypes (with frequencies ranging from 0.2 to 25.5%). Six representative statistical haplotype reconstruction algorithms are employed in our CV approach, including one parsimony method, two expectation-maximization (EM) methods and three Bayesian methods. The phases of 116 ambiguous individuals inferred by this approach are verified by molecular cloning experiments. We demonstrate the effectiveness of the CV approach compared to inferences based on individual statistical algorithms. First, it has the unique power to partition the inferrals into a reliable group and an uncertain group, thereby allowing the identification of the inferrals with greater uncertainty (12.7% of the total sample in this case). This considerably reduces subsequent efforts of experimental verification. Second, this approach is capable of handling genotype data pooled from many geographical populations, thus tolerating heterogeneity of genetic diversity among populations. Third, the performance of the CV approach is not influenced by the number of heterozygous sites in the ambiguous genotypes. Therefore, the CV approach is potentially a reliable strategy for effective haplotype determination of nuclear DNA markers. Our results also show that rare variations and rare inferrals tend to be more vulnerable to inference error, and hence deserve extra surveillance.

Statistical image reconstruction from correlated data with applications to PET

Most statistical reconstruction methods for emission tomography are designed for data modeled as conditionally independent Poisson variates. In reality, due to scanner detectors, electronics and data processing, correlations are introduced into the data resulting in dependent variates. In general, these correlations are ignored because they are difficult to measure and lead to computationally challenging statistical reconstruction algorithms. This work addresses the second concern, seeking to simplify the reconstruction of correlated data and provide a more precise image estimate than the conventional independent methods. In general, correlated variates have a large non-diagonal covariance matrix that is computationally challenging to use as a weighting term in a reconstruction algorithm. This work proposes two methods to simplify the use of a non-diagonal covariance matrix as the weighting term by (a) limiting the number of dimensions in which the correlations are modeled and (b) adopting flexible, yet computationally tractable, models for correlation structure. We apply and test these methods with simple simulated PET data and data processed with the Fourier rebinning algorithm which include the one-dimensional correlations in the axial direction and the two-dimensional correlations in the transaxial directions. The methods are incorporated into a penalized weighted least-squares 2D reconstruction and compared with a conventional maximum a posteriori approach.

TU-FF-A4-02: Impact of Sinogram Modeling Inaccuracies On Image Quality in X-Ray CT Imaging Using the Alternating Minimization Algorithm

Purpose: To provide a scientific basis for setting sinogram modeling accuracy targets based on impact of such errors on image quality. Modeling inaccuracies in photon spectrum and scatter distribution assumed by statistical image reconstruction (SIR) algorithms lead to systematic image artifacts. Methods and Materials: A synthetic two-dimensional phantom (25×35 cm) was used to generate both noiseless and noisy sinogram data, based upon a 120 kVp spectrum filtered by 12 mm Al (66.6 keV mean energy)and variable scatter levels (4%, 20%, and 100% of the minimum primary transmission through the phantom). A third generation Siemens Somatom Plus 4 scanner geometry was assumed. The SIR algorithm was the alternating minimization (AM) algorithm [IEEE TMI 26:283]. 500 AM iterations using 22 ordered subsets were applied to the data. Various mismatches between the assumptions in the algorithm and the truth were studied, including erroneous spectra (110kVp to 130kVp, filtration from 6 mm to 18 mm Al, or 62.2 to 69.7 keV mean energy) and erroneous scatter levels (0.25 to 4.0 times the actual sinogram scatter). Result: AM image quality was evaluated in terms of bias, noise, contrast ratio, etc. To assure +/−2% accuracy in the reconstructed attenuation image, photon spectrum uncertainties corresponding to 2 keV shifts in mean energy can be tolerated. For a 30 cm thick subject, this corresponds to errors in primary transmission of 6%–8%. For 20% scatter levels, the maximum tolerated discrepancy in scatter-to-primary ratio (SPR) is about 5% to 8%and 30%–50% for typical MSCT scatter levels. Conclusions: This work indicates AM and other SIR algorithm image estimates are sensitive to errors in the detector response models assumed by the algorithms. For thick patients, a sinogram modeling accuracy of 6% is needed to support reconstructed images of 2% accuracy. Supported in part by NIH grant R01 CA 075371.

SU‐FF‐I‐36: Improving Noise‐Resolution Tradeoffs in X‐Ray CT Imaging by Statistical Image Reconstruction

Purpose: To assess the potential of a statistical image reconstruction (SIR) algorithm, penalized alternating minimization (AM) [IEEE TMI 26: 283] for improving image quality, relative to filtered back projection (FBP), for a given imaging dose. Minimizing the x‐ray CT imaging dose is an important goal both for CT‐guided radiotherapy and for imaging of pediatric patients and screening healthy populations. Method and Materials: Synthetic datasets with Poisson noise were formed from cylindrical phantoms with a variety of simulated high and low contrast features. A penalized AM algorithm based on separable surrogate penalty functions was implemented and investigated for Good's roughness penalty, an edge‐preserving log‐cosh penalty, and a novel penalty on local transmission fluctuations, all of which were applied only to adjacent pixels. Simulations were performed for a Somatom Plus 4 third generation geometry. Image blur (resolution) was specified in terms of the FWHM (σ) of the Gaussian, which when convolved with the truth image, best matched the estimated image. Resolution was varied by adjusting the filter cutoff frequency for FBP and the Lagrange multiplier for AM. Noise was quantified by image intensity variance in a uniform region. Results: For a fixed photon fluence, penalized AM images had smaller variances than FBP at all image blur levels, although the differences were not significant for low spatial resolution and low contrast features. However, for clinically relevant σ < 2 mm, the advantage of AM increased with increasing spatial resolution and contrast. For example, at σ = 1 mm, FBP had 48% and 24% larger variances for 75% contrast inserts with 0.5 mm pixels and 10% contrast with 1 mm pixels. The three penalty functions had comparable performance. Conclusion: Regularized AM SIR has the potential to realize signal‐to‐noise ratio gains equivalent to 30% imaging dose increases.Supported in part by R01 CA075371.

Statistical reconstruction for x-ray computed tomography using energy-integrating detectors

Statistical image reconstruction (SR) algorithms have the potential to significantly reduce x-ray CT image artefacts because they use a more accurate model than conventional filtered backprojection and can incorporate effects such as noise, incomplete data and nonlinear detector response. Most SR algorithms assume that the CT detectors are photon-counting devices and generate Poisson-distributed signals. However, actual CT detectors integrate energy from the x-ray beam and exhibit compound Poisson-distributed signal statistics. This study presents the first assessment of the impact on image quality of the resultant mismatch between the detector and signal statistics models assumed by the sinogram data model and the reconstruction algorithm. A 2D CT projection simulator was created to generate synthetic polyenergetic transmission data assuming (i) photon-counting with simple Poisson-distributed signals and (ii) energy-weighted detection with compound Poisson-distributed signals. An alternating minimization (AM) algorithm was used to reconstruct images from the data models (i) and (ii) for a typical abdominal scan protocol with incident particle fluence levels ranging from 105 to 1.6 × 106 photons/detector. The images reconstructed from data models (i) and (ii) were compared by visual inspection and image-quality figures of merit. The reconstructed image quality degraded significantly when the means were mismatched from the assumed model. However, if the signal means are appropriately modified, images from data models (i) and (ii) did not differ significantly even when SNR is very low. While data-mean mismatches characteristic of the difference between particle-fluence and energy-fluence transmission can cause significant streaking and cupping artefacts, the mismatch between the actual and assumed CT detector signal statistics did not significantly degrade image quality once systematic data means mismatches were corrected.

Evaluation of 3D Monte Carlo-Based Scatter Correction for 201Tl Cardiac Perfusion SPECT

(201)Tl-Chloride ((201)Tl) is a myocardial perfusion SPECT agent with excellent biochemical properties commonly used for assessing tissue viability. However, cardiac (201)Tl SPECT images are severely degraded by photons scattered in the thorax. Accurate correction for this scatter is complicated by the nonuniform density and varied sizes of thoraxes, by the additional attenuation and scatter caused by female patients' breasts, and by the energy spectrum of (201)Tl. Monte Carlo simulation is a general and accurate method well suited to modeling this scatter. Statistical reconstruction that includes Monte Carlo modeling of scatter was compared with statistical reconstruction algorithms not corrected for scatter. In the ADS method, corrections for attenuation, detector response, and scatter (Monte Carlo-based) were implemented simultaneously via the dual-matrix ordered-subset expectation maximization algorithm with a Monte Carlo simulator as part of the forward projector. The ADS method was compared with the A method (ordered-subset expectation maximization with attenuation correction) and with the AD method (a method like the A method but with detector response modeling added). A dual-head SPECT system equipped with two (153)Gd scanning line sources was used for simultaneously acquiring transmission and emission data. Four clinically realistic phantom configurations (a large thorax and a small thorax, each with and without breasts) with a cardiac insert containing 2 cold defects were used to evaluate the proposed reconstruction algorithms. We compared the performance of the different algorithms in terms of noise properties, contrast-to-noise ratios, the contrast separability of perfusion defects, uniformity, and robustness to anatomic variations. The ADS method provided images with clearly better visual defect contrast than did the other methods. The contrasts achieved with the ADS method were 10%-24% higher than those achieved with the AD method and 11%-37% higher than those achieved with the A method. For a typical contrast level, the ADS method exhibited noise levels around 27% lower than the AD method and 34% lower than the A method. Compared with the other 2 algorithms, the ADS reconstructions were less sensitive to anatomic variations and had better image uniformity in the homogeneously perfused myocardium. Finally, we found that the improvements that can be achieved with Monte Carlo-based scatter correction are stronger for (201)Tl than for (99m)Tc imaging. Our results indicate that Monte Carlo-based scatter correction is suitable for (201)Tl cardiac imaging and that such correction simultaneously improves several image-quality metrics.

Improved quantitation for PET/CT image reconstruction with system modeling and anatomical priors

Accurate quantitation of positron emission tomography (PET) tracer uptake levels in tumors is important for staging and monitoring response to treatment. Quantitative accuracy in PET is particularly poor for small tumors because of system partial volume errors and smoothing operations. This work proposes a reconstruction algorithm to reduce the quantitative errors due to limited system resolution and due to necessary image noise reduction. We propose a method for finding and using the detection system response in the projection matrix of a statistical reconstruction algorithm. In addition, we use aligned anatomical information, available in PET/CT scanners, to govern the penalty term applied during each image update. These improvements are combined with Fourier rebinning in a clinically feasible algorithm for reconstructing fully three-dimensional PET data. Results from simulation and measured studies show improved quantitation of tumor values in terms of bias and variance across multiple tumor sizes and activity levels with the proposed method. At common clinical image noise levels for the detection task, the proposed method reduces the error in maximum tumor values by 11% compared to filtered back-projection and 5% compared to conventional iterative methods.

Properties of preprocessed sinogram data in x-ray computed tomography

The accurate determination of x-ray signal properties is important to several computed tomography (CT) research and development areas, notably for statistical reconstruction algorithms and dose-reduction simulation. The most commonly used model of CT signal formation, assuming monoenergetic x-ray sources with quantum counting detectors obeying simple Poisson statistics, does not reflect the actual physics of CT acquisition. This paper describes a more accurate model, taking into account the energy-integrating detection process, nonuniform flux profiles, and data-conditioning processes. Methods are developed to experimentally measure and theoretically calculate statistical distributions, as well as techniques to analyze CT signal properties. Results indicate the limitations of current models and suggest improvements for the description of CT signal properties.

An inter-crystal scatter correction method for DOI PET image reconstruction.

New PET scanners utilize depth-of-interaction (DOI) information to improve image resolution, particularly at the edge of field-of-view while maintaining high detector sensitivity. However, the inter-crystal scatter (ICS) effect cannot be neglected in DOI scanners due to the use of smaller crystals. ICS is the phenomenon wherein there are multiple scintillations for irradiation of a gamma photon due to Compton scatter in detecting crystals. In the case of ICS, only one scintillation position is approximated for detectors with Anger-type logic calculation. This causes an error in position detection and ICS worsens the image contrast, particularly for smaller hotspots. In this study, we propose to model an ICS probability by using a Monte Carlo simulator. The probability is given as a statistical relationship between the gamma photon first interaction crystal pair and the detected crystal pair. It is then used to improve the system matrix of a statistical image reconstruction algorithm, such as ML-EM in order to correct for the position error caused by ICS. We apply the proposed method to simulated data of the jPET-D4, which is a four-layer DOI PET being developed at the National Institute of Radiological Sciences. Our computer simulations show that image contrast is recovered successfully by the proposed method.

The effects of positron binding and annihilation mechanisms in biomolecules on PET resolution

The angular correlation distribution of electron-positron annihilation photons is presented for polar biological molecules, and the associated noncollinearity effect on resolution in positron emission tomography (PET) is discussed. The image resolution in PET is known to be limited by a number of factors such as radioactive decay statistics, attenuation, scatter, or random coincidence of annihilation photons. This paper deals with the resolution limits on the side of the measured system. Our calculated distribution of annihilation momentum belongs to the intrinsic resolution factors together with the positron range in biological tissue; the other factors are due to the interactions along the photon path from the tissue to the detector. Here we demonstrate that the angular distribution of annihilation trajectories is not necessarily Gaussian, especially when the positron temporarily binds in a molecular dipole moment field before annihilation. The theoretical framework treats the electron and positron on the same footing by using the multireference single- and double-excitation configuration interaction algorithms applicable also to other bound-state systems. Our results form a subset of parameters relevant to the statistical image reconstruction algorithms, which may eventually increase the sensitivity of PET imaging in clinical setting

MO-D-I-611-08: Statistical Reconstruction of X-Ray CT Images From Energy-Integrated Signals: A Simulation Study

Purpose: Statistical reconstruction (SR) algorithms have the potential to significantly reduce X-ray CT image artifacts due to a more realistic model of the detector signal acquisition process. Most SR algorithms assume that the CT detectors are photon-counting devices and generate Poisson-distributed signals. However, actual CT detectors integrate energy and exhibit compound Poisson distributed signal statistics. The goal of this study is to assess the impact on image quality of the resultant mismatch between the detector and signal statistics models assumed by the sinogram and the reconstruction algorithm. Method and Materials: A 2D CT projection simulator software was created to generate synthetic polyenergetic transmission data assuming i) photon-count signals with simple Poisson distribution and ii) energy-weighted compound Poisson distributed signals. An Alternating Minimization (AM) algorithm was used to reconstruct images from the data models i) and ii) for a typical abdominal scan protocol and for incident particle fluence levels ranging from 105 to 1.6×106 photons/detector. The phantoms simulated included normal soft tissue, bone, and metal inserts. The images reconstructed from data models i) and ii) were compared by visual inspection and quantitative image-quality measures. Results: Substantial streaking artifacts appear in images formed from energy-integrated data when the AM algorithm assumes a particle-fluence spectrum Φ̄0(E). Once AM's spectrum is replaced by the energy-fluence spectrum E ⋅Φ̄ (E), AM correctly predicts the data means and eliminates the artifacts. With the energy-weighted spectrum, the reconstructed image quality from data models i) and ii) does not differ significantly even when SNR is very low. Conclusion: Mismatch between the actual and assumed CT detector signal statistics does not significantly degrade image quality once systematic data means mismatches are corrected. Within the context of statistical image reconstruction, there appears to be no benefit to develop more complex statistical reconstruction algorithms based upon energy-integrating detector signal statistics models.

Parallel statistical image reconstruction for cone-beam x-ray CT on a shared memory computation platform

Statistical reconstruction methods offer possibilities of improving image quality as compared to analytical methods, but current reconstruction times prohibit routine clinical applications. To reduce reconstruction times we have parallelized a statistical reconstruction algorithm for cone-beam x-ray CT, the ordered subset convex algorithm (OSC), and evaluated it on a shared memory computer. Two different parallelization strategies were developed: one that employs parallelism by computing the work for all projections within a subset in parallel, and one that divides the total volume into parts and processes the work for each sub-volume in parallel. Both methods are used to reconstruct a three-dimensional mathematical phantom on two different grid densities. The reconstructed images are binary identical to the result of the serial (non-parallelized) algorithm. The speed-up factor equals approximately 30 when using 32 to 40 processors, and scales almost linearly with the number of cpus for both methods. The huge reduction in computation time allows us to apply statistical reconstruction to clinically relevant studies for the first time.

Optimization and performance evaluation of the microPET II scanner for in vivo small-animal imaging

MicroPET II is a newly developed PET (positron emission tomography) scanner designed for high-resolution imaging of small animals. It consists of 17 640 LSO crystals each measuring 0.975 × 0.975 × 12.5 mm3, which are arranged in 42 contiguous rings, with 420 crystals per ring. The scanner has an axial field of view (FOV) of 4.9 cm and a transaxial FOV of 8.5 cm. The purpose of this study was to carefully evaluate the performance of the system and to optimize settings for in vivo mouse and rat imaging studies. The volumetric image resolution was found to depend strongly on the reconstruction algorithm employed and averaged 1.1 mm (1.4 µl) across the central 3 cm of the transaxial FOV when using a statistical reconstruction algorithm with accurate system modelling. The sensitivity, scatter fraction and noise-equivalent count (NEC) rate for mouse- and rat-sized phantoms were measured for different energy and timing windows. Mouse imaging was optimized with a wide open energy window (150–750 keV) and a 10 ns timing window, leading to a sensitivity of 3.3% at the centre of the FOV and a peak NEC rate of 235 000 cps for a total activity of 80 MBq (2.2 mCi) in the phantom. Rat imaging, due to the higher scatter fraction, and the activity that lies outside of the field of view, achieved a maximum NEC rate of 24 600 cps for a total activity of 80 MBq (2.2 mCi) in the phantom, with an energy window of 250–750 keV and a 6 ns timing window. The sensitivity at the centre of the FOV for these settings is 2.1%. This work demonstrates that different scanner settings are necessary to optimize the NEC count rate for different-sized animals and different injected doses. Finally, phantom and in vivo animal studies are presented to demonstrate the capabilities of microPET II for small-animal imaging studies.

A fast, cache-aware algorithm for the calculation of radiological paths exploiting subword parallelism

Abstract The calculation of radiological paths is the most important part in statistical positron emission tomography image reconstruction algorithms. We present a new, faster algorithm which replaces Siddon's. Further code transformations on this algorithm prove to be beneficial in a Maximum Likelihood–Expectation Maximization reconstruction algorithm and the result is perfectly suitable for an implementation that exploits the VISual instruction set from Sun or other modern architectural extensions providing subword parallelism. The final speed-up achieved with this new algorithm and its subword parallel implementation is 13. Though smaller data formats are used in subword parallelism, the resulting images are as good as the original ones.

Noise properties of the EM algorithm. II. Monte Carlo simulations

For pt.I see ibid., vol.39, no.5, p.833-46 (1994). In pt.I the authors derived a theoretical formulation for estimating the statistical properties of images reconstructed using the iterative maximum-likelihood expectation-maximization (ML-EM) algorithm. To gain insight into this complex problem, two levels of approximation were considered in the theory. These techniques revealed the dependence of the variance and covariance of the reconstructed image noise on the source distribution, imaging system transfer function, and iteration number. Here, a Monte Carlo approach was taken to study the noise properties of the ML-EM algorithm and to test the predictions of the theory. The study also served to evaluate the approximations used in the theory. Simulated data from phantoms were used in the Monte Carlo experiments. The ML-EM statistical properties were calculated from sample averages of a large number of images with different noise realizations. The agreement between the more exact form of the theoretical formulation and the Monte Carlo formulation was better than 10% in most cases examined, and for many situations the agreement was within the expected error of the Monte Carlo experiments. Results from the studies provide valuable information about the noise characteristics of ML-EM reconstructed images. Furthermore, the studies demonstrate the power of the theoretical and Monte Carlo approaches for investigating noise properties of statistical reconstruction algorithms.