An Investigation of Stochastic Variance Reduction Algorithms for Relative Difference Penalized 3D PET Image Reconstruction.

Penalised PET image reconstruction algorithms are often accelerated during early iterations with the use of subsets. However, these methods may exhibit limit cycle behaviour at later iterations due to variations between subsets. Desirable converged images can be achieved for a subclass of these algorithms via the implementation of a relaxed step size sequence, but the heuristic selection of parameters will impact the quality of the image sequence and algorithm convergence rates. In this work, we demonstrate the adaption and application of a class of stochastic variance reduction gradient algorithms for PET image reconstruction using the relative difference penalty and numerically compare convergence performance to BSREM. The two investigated algorithms are: SAGA and SVRG. These algorithms require the retention in memory of recently computed subset gradients, which are utilised in subsequent updates. We present several numerical studies based on Monte Carlo simulated data and a patient data set for fully 3D PET acquisitions. The impact of the number of subsets, different preconditioners and step size methods on the convergence of regions of interest values within the reconstructed images is explored. We observe that when using constant preconditioning, SAGA and SVRG demonstrate reduced variations in voxel values between subsequent updates and are less reliant on step size hyper-parameter selection than BSREM reconstructions. Furthermore, SAGA and SVRG can converge significantly faster to the penalised maximum likelihood solution than BSREM, particularly in low count data.

A Fast Convergent Ordered-Subsets Algorithm With Subiteration-Dependent Preconditioners for PET Image Reconstruction.

We investigated the imaging performance of a fast convergent ordered-subsets algorithm with subiteration-dependent preconditioners (SDPs) for positron emission tomography (PET) image reconstruction. In particular, we considered the use of SDP with the block sequential regularized expectation maximization (BSREM) approach with the relative difference prior (RDP) regularizer due to its prior clinical adaptation by vendors. Because the RDP regularization promotes smoothness in the reconstructed image, the directions of the gradients in smooth areas more accurately point toward the objective function's minimizer than those in variable areas. Motivated by this observation, two SDPs have been designed to increase iteration step-sizes in the smooth areas and reduce iteration step-sizes in the variable areas relative to a conventional expectation maximization preconditioner. The momentum technique used for convergence acceleration can be viewed as a special case of SDP. We have proved the global convergence of SDP-BSREM algorithms by assuming certain characteristics of the preconditioner. By means of numerical experiments using both simulated and clinical PET data, we have shown that the SDP-BSREM algorithms substantially improve the convergence rate, as compared to conventional BSREM and a vendor's implementation as Q.Clear. Specifically, SDP-BSREM algorithms converge 35%-50% faster in reaching the same objective function value than conventional BSREM and commercial Q.Clear algorithms. Moreover, we showed in phantoms with hot, cold and background regions that the SDP-BSREM algorithms approached the values of a highly converged reference image faster than conventional BSREM and commercial Q.Clear algorithms.

Benefits of Using a Spatially-Variant Penalty Strength With Anatomical Priors in PET Reconstruction.

In this study, we explore the use of a spatially-variant penalty strength in penalized image reconstruction using anatomical priors to reduce the dependence of lesion contrast on surrounding activity and lesion location. This work builds on a previous method to make the local perturbation response (LPR) approximately spatially invariant. While the dependence of lesion contrast on the local properties introduced by the anatomical penalty is intentional, the method aims to reduce the influence from surroundings lying along the lines of response (LORs) but not in the penalty neighborhood structure. The method is evaluated using simulated data, assuming that the anatomical information is absent or well-aligned with the corresponding activity images. Since the parallel level sets (PLS) penalty is convex and has shown promising results in the literature, it is chosen as the representative anatomical penalty and incorporated into the previously proposed preconditioned algorithm (L-BFGS-B-PC) for achieving good image quality and fast convergence rate. A 2D disc phantom with a feature at the center and a 3D XCAT thorax phantom with lesions inserted in different slices are used to study how surrounding activity and lesion location affect the visual appearance and quantitative consistency. A bias and noise analysis is also performed with the 2D disc phantom. The consistency of the algorithm convergence rate with respect to different data noise and background levels is also investigated using the XCAT phantom. Finally, an example of reconstruction for a patient dataset with inserted pseudo lesions is used as a demonstration in a clinical context. We show that applying the spatially-variant penalization with PLS can reduce the dependence of the lesion contrast on the surrounding activity and lesion location. It does not affect the bias and noise trade-off curves for matched local resolution. Moreover, when using the proposed penalization, significant improvement in algorithm convergence rate and convergence consistency is observed.

Fast Quasi-Newton Algorithms for Penalized Reconstruction in Emission Tomography and Further Improvements via Preconditioning.

This paper reports on the feasibility of using a quasi-Newton optimization algorithm, limited-memory Broyden-Fletcher-Goldfarb-Shanno with boundary constraints (L-BFGS-B), for penalized image reconstruction problems in emission tomography (ET). For further acceleration, an additional preconditioning technique based on a diagonal approximation of the Hessian was introduced. The convergence rate of L-BFGS-B and the proposed preconditioned algorithm (L-BFGS-B-PC) was evaluated with simulated data with various factors, such as the noise level, penalty type, penalty strength and background level. Data of three 18F-FDG patient acquisitions were also reconstructed. Results showed that the proposed L-BFGS-B-PC outperforms L-BFGS-B in convergence rate for all simulated conditions and the patient data. Based on these results, L-BFGS-B-PC shows promise for clinical application.

Sign determination methods for the respiratory signal in data-driven PET gating.

Patient respiratory motion during PET image acquisition leads to blurring in the reconstructed images and may cause significant artifacts, resulting in decreased lesion detectability, inaccurate standard uptake value calculation and incorrect treatment planning in radiation therapy. To reduce these effects data can be regrouped into (nearly) 'motion-free' gates prior to reconstruction by selecting the events with respect to the breathing phase. This gating procedure therefore needs a respiratory signal: on current scanners it is obtained from an external device, whereas with data driven (DD) methods it can be directly obtained from the raw PET data. DD methods thus eliminate the use of external equipment, which is often expensive, needs prior setup and can cause patient discomfort, and they could also potentially provide increased fidelity to the internal movement. DD methods have been recently applied on PET data showing promising results. However, many methods provide signals whose direction with respect to the physical motion is uncertain (i.e. their sign is arbitrary), therefore a maximum in the signal could refer either to the end-inspiration or end-expiration phase, possibly causing inaccurate motion correction. In this work we propose two novel methods, CorrWeights and CorrSino, to detect the correct direction of the motion represented by the DD signal, that is obtained by applying principal component analysis (PCA) on the acquired data. They only require the PET raw data, and they rely on the assumption that one of the major causes of change in the acquired data related to the chest is respiratory motion in the axial direction, that generates a cranio-caudal motion of the internal organs. We also implemented two versions of a published registration-based method, that require image reconstruction. The methods were first applied on XCAT simulations, and later evaluated on cancer patient datasets monitored by the Varian Real-time Position ManagementTM (RPM) device, selecting the lower chest bed positions. For each patient different time intervals were evaluated ranging from 50 to 300 s in duration. The novel methods proved to be generally more accurate than the registration-based ones in detecting the correct sign of the respiratory signal, and their failure rates are lower than 3% when the DD signal is highly correlated with the RPM. They also have the advantage of faster computation time, avoiding reconstruction. Moreover, CorrWeights is not specifically related to PCA and considering its simple implementation, it could easily be applied together with any DD method in clinical practice.

Impact of CT attenuation correction method on quantitative respiratory-correlated (4D) PET/CT imaging.

PURPOSE: Respiratory-correlated positron emission tomography (PET/CT) 4D PET/CT is used to mitigate errors from respiratory motion; however, the optimal CT attenuation correction (CTAC) method for 4D PET/CT is unknown. The authors performed a phantom study to evaluate the quantitative performance of CTAC methods for 4D PET/CT in the ground truth setting. METHODS: A programmable respiratory motion phantom with a custom movable insert designed to emulate a lung lesion and lung tissue was used for this study. The insert was driven by one of five waveforms: two sinusoidal waveforms or three patient-specific respiratory waveforms. 3DPET and 4DPET images of the phantom under motion were acquired and reconstructed with six CTAC methods: helical breath-hold (3DHEL), helical free-breathing (3DMOT), 4D phase-averaged (4DAVG), 4D maximum intensity projection (4DMIP), 4D phase-matched (4DMATCH), and 4D end-exhale (4DEXH) CTAC. Recovery of SUV(max), SUV(mean), SUV(peak), and segmented tumor volume was evaluated as RC(max), RC(mean), RC(peak), and RC(vol), representing percent difference relative to the static ground truth case. Paired Wilcoxon tests and Kruskal-Wallis ANOVA were used to test for significant differences. RESULTS: For 4DPET imaging, the maximum intensity projection CTAC produced significantly more accurate recovery coefficients than all other CTAC methods (p < 0.0001 over all metrics). Over all motion waveforms, ratios of 4DMIP CTAC recovery were 0.2 ± 5.4, -1.8 ± 6.5, -3.2 ± 5.0, and 3.0 ± 5.9 for RC(max), RC(peak), RC(mean), and RC(vol). In comparison, recovery coefficients for phase-matched CTAC were -8.4 ± 5.3, -10.5 ± 6.2, -7.6 ± 5.0, and -13.0 ± 7.7 for RC(max), RC(peak), RC(mean), and RC(vol). When testing differences between phases over all CTAC methods and waveforms, end-exhale phases were significantly more accurate (p = 0.005). However, these differences were driven by the patient-specific respiratory waveforms; when testing patient and sinusoidal waveforms separately, patient waveforms were significantly different between phases (p < 0.0001) while the sinusoidal waveforms were not significantly different (p = 0.98). When considering only the subset of 4DMATCH images that corresponded to the end-exhale image phase, 4DEXH, mean and interquartile range were similar to 4DMATCH but variability was considerably reduced. CONCLUSIONS: Comparative advantages in accuracy and precision of SUV metrics and segmented volumes were demonstrated with the use of the maximum intensity projection and end-exhale CT attenuation correction. While respiratory phase-matched CTAC should in theory provide optimal corrections, image artifacts and differences in implementation of 4DCT and 4DPET sorting can degrade the benefit of this approach. These results may be useful to guide the implementation, analysis, and development of respiratory-correlated thoracic PET/CT in the radiation oncology and diagnostic settings.

Assessment of patient selection criteria for quantitative imaging with respiratory-gated positron emission tomography.

The objective of this investigation was to propose techniques for determining which patients are likely to benefit from quantitative respiratory-gated imaging by correlating respiratory patterns to changes in positron emission tomography (PET) metrics. Twenty-six lung and liver cancer patients underwent PET/computed tomography exams with recorded chest/abdominal displacements. Static and adaptive amplitude-gated [[Formula: see text]]fluoro-D-glucose (FDG) PET images were generated from list-mode acquisitions. Patients were grouped by respiratory pattern, lesion location, or degree of lesion attachment to anatomical structures. Respiratory pattern metrics were calculated during time intervals corresponding to PET field of views over lesions of interest. FDG PET images were quantified by lesion maximum standardized uptake value ([Formula: see text]). Relative changes in [Formula: see text] between static and gated PET images were tested for association to respiratory pattern metrics. Lower lung lesions and liver lesions had significantly higher changes in [Formula: see text] than upper lung lesions (14 versus 3%, [Formula: see text]). Correlation was highest ([Formula: see text], [Formula: see text], [Formula: see text]) between changes in [Formula: see text] and nonstandard respiratory pattern metrics. Lesion location had a significant impact on changes in PET quantification due to respiratory gating. Respiratory pattern metrics were correlated to changes in [Formula: see text], though sample size limited statistical power. Validation in larger cohorts may enable selection of patients prior to acquisition who would benefit from respiratory-gated PET imaging.

Application and evaluation of a measured spatially variant system model for PET image reconstruction.

Accurate system modeling in tomographic image reconstruction has been shown to reduce the spatial variance of resolution and improve quantitative accuracy. System modeling can be improved through analytic calculations, Monte Carlo simulations, and physical measurements. The purpose of this work is to improve clinical fully-3-D reconstruction without substantially increasing computation time. We present a practical method for measuring the detector blurring component of a whole-body positron emission tomography (PET) system to form an approximate system model for use with fully-3-D reconstruction. We employ Monte Carlo simulations to show that a non-collimated point source is acceptable for modeling the radial blurring present in a PET tomograph and we justify the use of a Na22 point source for collecting these measurements. We measure the system response on a whole-body scanner, simplify it to a 2-D function, and incorporate a parameterized version of this response into a modified fully-3-D OSEM algorithm. Empirical testing of the signal versus noise benefits reveal roughly a 15% improvement in spatial resolution and 10% improvement in contrast at matched image noise levels. Convergence analysis demonstrates improved resolution and contrast versus noise properties can be achieved with the proposed method with similar computation time as the conventional approach. Comparison of the measured spatially variant and invariant reconstruction revealed similar performance with conventional image metrics. Edge artifacts, which are a common artifact of resolution-modeled reconstruction methods, were less apparent in the spatially variant method than in the invariant method. With the proposed and other resolution-modeled reconstruction methods, edge artifacts need to be studied in more detail to determine the optimal tradeoff of resolution/contrast enhancement and edge fidelity.

Image Reconstruction for a Partially Collimated Whole Body PET Scanner.

Partially collimated PET systems have less collimation than conventional 2-D systems and have been shown to offer count rate improvements over 2-D and 3-D systems. Despite this potential, previous efforts have not established image-based improvements with partial collimation and have not customized the reconstruction method for partially collimated data. This work presents an image reconstruction method tailored for partially collimated data. Simulated and measured sensitivity patterns are presented and provide a basis for modification of a fully 3-D reconstruction technique. The proposed method uses a measured normalization correction term to account for the unique sensitivity to true events. This work also proposes a modified scatter correction based on simulated data. Measured image quality data supports the use of the normalization correction term for true events, and suggests that the modified scatter correction is unnecessary.

Optimization of noise equivalent count rate performance for a partially collimated PET scanner by varying the number of septa.

We present a simulation study of the global count-rate performance of a positron emission tomography (PET) scanner with different levels of partial collimation to maximize the noise equivalent count rate for whole-body PET imaging. We achieve partial collimation by removing different numbers of septal rings from the standard 2-D septa set for the GE Advance PET scanner. System behavior is studied with a photon tracking simulation package, which we modify to enable the production of random coincidences. The simulations are validated with measured data taken in 2-D and fully 3-D acquisition mode on a GE Advance system using the National Electrical Manufacturers Association NU-2 count-rate phantom with two sets of annular sleeves to expand the diameter to 27 and 35 cm. For all diameters and in 2-D and fully 3-D mode, there is good agreement between measurements and simulations. All studies use the three phantom diameters to evaluate the effect of patient thickness for each amount of collimation. Optimized system parameters, such as maximum ring difference for single slice rebinning, are determined for the five partially collimated systems considered. The resulting global count rates for true, scattered, and random coincidences, the noise equivalent count (NEC) rates, and the scatter fractions for different levels of collimation are compared along with the results from the conventional 2-D and fully 3-D modes. Improved statistical data quality relative to both 2-D and fully 3-D data is found with the partially collimated systems, particularly when one-half or two-thirds of the septal rings are removed. An increase in NEC rates of as much as 50% is found for clinically relevant activities between 5-10 mCi (184-370 MBq). Scatter fractions for the partially collimated systems are intermediate between the 2-D and fully 3-D numbers. Many factors that affect image quality have not been considered in this paper. However, the significant increase in statistical data quality warrants further investigation of the impact of partial collimation on clinical whole-body PET imaging.

Validation of GATE Monte Carlo simulations of the GE Advance/Discovery LS PET scanners.

The recently developed GATE (GEANT4 application for tomographic emission) Monte Carlo package, designed to simulate positron emission tomography (PET) and single photon emission computed tomography (SPECT) scanners, provides the ability to model and account for the effects of photon noncollinearity, off-axis detector penetration, detector size and response, positron range, photon scatter, and patient motion on the resolution and quality of PET images. The objective of this study is to validate a model within GATE of the General Electric (GE) Advance/Discovery Light Speed (LS) PET scanner. Our three-dimensional PET simulation model of the scanner consists of 12 096 detectors grouped into blocks, which are grouped into modules as per the vendor's specifications. The GATE results are compared to experimental data obtained in accordance with the National Electrical Manufactures Association/Society of Nuclear Medicine (NEMA/SNM), NEMA NU 2-1994, and NEMA NU 2-2001 protocols. The respective phantoms are also accurately modeled thus allowing us to simulate the sensitivity, scatter fraction, count rate performance, and spatial resolution. In-house software was developed to produce and analyze sinograms from the simulated data. With our model of the GE Advance/Discovery LS PET scanner, the ratio of the sensitivities with sources radially offset 0 and 10 cm from the scanner's main axis are reproduced to within 1% of measurements. Similarly, the simulated scatter fraction for the NEMA NU 2-2001 phantom agrees to within less than 3% of measured values (the measured scatter fractions are 44.8% and 40.9 +/- 1.4% and the simulated scatter fraction is 43.5 +/- 0.3%). The simulated count rate curves were made to match the experimental curves by using deadtimes as fit parameters. This resulted in deadtime values of 625 and 332 ns at the Block and Coincidence levels, respectively. The experimental peak true count rate of 139.0 kcps and the peak activity concentration of 21.5 kBq/cc were matched by the simulated results to within 0.5% and 0.1% respectively. The simulated count rate curves also resulted in a peak NECR of 35.2 kcps at 10.8 kBq/cc compared to 37.6 kcps at 10.0 kBq/cc from averaged experimental values. The spatial resolution of the simulated scanner matched the experimental results to within 0.2 mm.

Count-Rate Performance of the Discovery STE PET Scanner Using Partial Collimation.

We investigated the use of partial collimation on a clinical PET scanner by removing septa from conventional 2D collimators. The goal is to improve noise equivalent count-rates (NEC) compared to 2D and 3D scans for clinically relevant activity concentrations. We evaluated two cases: removing half of the septa (2.5D); and removing two-thirds of the septa (2.7D). System performance was first modeled using the SimSET simulation package, and then measured with the NEMA NU2-2001 count-rate cylinder (20 cm dia., 70 cm long), and 27 cm and 35 cm diameter cylinders of the same length. An image quality phantom was also imaged with the 2.7D collimator. SimSET predicted the relative NEC curves very well, as confirmed by measurements, with 2.5D and 2.7D NEC greater than 2D and 3D NEC in the range of ~5-20 mCi in the phantom. We successfully reconstructed images of the image quality phantom from measured 2.7D data using custom 2.7D normalization. Partial collimation shows promise for optimized clinical imaging in a fixed-collimator system.

Performance characteristics of a newly developed PET/CT scanner using NEMA standards in 2D and 3D modes.

UNLABELLED: This study evaluates the 2-dimensional (2D) and 3-dimensional (3D) performance characteristics of a newly developed PET/CT scanner using the National Electrical Manufacturers Association (NEMA) NU 2-1994 (NU94) and NEMA NU 2-2001 (NU01) standards. The PET detector array consists of 10,080 individual bismuth germanate crystals arranged in 24 rings of 420 crystals each. The size of each crystal is 6.3 x 6.3 x 30 mm in the axial, transaxial, and radial dimensions, respectively. The PET detector ring diameter is 88.6 cm with axial and transaxial fields of view (FOVs) of 15.7 and 70 cm, respectively. The scanner has a uniform patient port of 70 cm throughout the PET and CT FOV, and the PET scanner is equipped with retractable septa to allow 2D and 3D imaging. METHODS: Spatial resolution, scatter fraction, sensitivity, counting rate, image quality, and accuracy as defined by the NEMA protocols of NU94 and NU01 for 2D and 3D modes are evaluated. The 2D mode data were acquired with a maximum ring difference of 5, whereas the 3D mode acquisition used ring differences of 23. Both 2D and 3D mode data were acquired with an energy window of 375-650 keV. Random estimation from singles counting rate was applied to all relevant analysis. In addition, images from 2 clinical whole-body oncology studies acquired in 2D and 3D modes are shown to demonstrate the image quality obtained from this scanner. RESULTS: The 2D NU94 transaxial resolution is 6.1-mm full width at half maximum (FWHM) 1 cm off center and increases to 6.9 mm tangential and 8.1 mm radial at a radius (R) of 20 cm. NU01 2D average transaxial (axial) FWHM resolution measured 6.1 (5.2) mm at R = 1 cm and 6.7 (6.1) mm at R = 10 cm. The NU94 scatter fraction for 2D (3D) was 13% (29%), whereas the NU01 scatter fraction gave 19% (45%). NU01 peak 2D (3D) noise equivalent counting rate (T(2)/[T + R + S]) was 90.2 (67.8) kilocount per second (kcps) at 52.5 (12) kBq/mL. Total 2D (3D) system sensitivity for true events is 8 (32.9) kcps/kBq/mL for NU94 and 1.95 (9.2) kcps/Bq for NU01. CONCLUSION: The results show excellent system sensitivity with relatively uniform resolution throughout the FOV, making this scanner highly suitable for whole-body studies.

PET performance measurements using the NEMA NU 2-2001 standard.

UNLABELLED: The NU 2-1994 standard document for PET performance measurements has recently been updated. The updated document, NU 2-2001, includes revised measurements for spatial resolution, intrinsic scatter fraction, sensitivity, counting rate performance, and accuracy of count loss and randoms corrections. The revised measurements are designed to allow testing of dedicated PET systems in both 2-dimensional and 3-dimensional modes as well as coincidence gamma cameras, conditions not considered in the original NU 2-1994 standard. In addition, the updated measurements strive toward being more representative of clinical studies, in particular, whole-body imaging. METHODS: Performance measurements following the NU 2-1994 and NU 2-2001 standards were performed on several different PET scanners. Differences between the procedures and resulting performance characteristics, as well as the rationale for these changes, were noted. RESULTS: Spatial resolution is measured with a point source in all 3 directions, rather than a line source, as specified previously. For the measurements of intrinsic scatter fraction, sensitivity, and counting rate performance, a 70-cm line source is now specified, instead of a 19-cm-long cylindric phantom. The longer configuration permits measurement of these performance characteristics over the entire axial field of view of all current PET scanners and incorporates the effects of activity outside the scanner. A measurement of image quality has been added in an effort to measure overall image quality under clinically realistic conditions. This measurement replaces the individual measurements of uniformity and of the accuracy of corrections for attenuation and scatter. CONCLUSION: The changes from the NU 2-1994 standard to the NU 2-2001 standard strive toward establishing relevance with clinical studies. The tests in the updated standard also are, in general, simpler and less time-consuming to perform than those in the NU 2-1994 standard.