Data analysis in emission tomography using emission-count posteriors

Hybrid PET/Compton-camera imaging: an imager for the next generation

Compton cameras can offer advantages over gamma cameras for some applications, since they are well suited for multitracer imaging and for imaging high-energy radiotracers, such as those employed in radionuclide therapy. While in conventional clinical settings state-of-the-art Compton cameras cannot compete with well-established methods such as PET and SPECT, there are specific scenarios in which they can constitute an advantageous alternative. The combination of PET and Compton imaging can benefit from the improved resolution and sensitivity of current PET technology and, at the same time, overcome PET limitations in the use of multiple radiotracers. Such a system can provide simultaneous assessment of different radiotracers under identical conditions and reduce errors associated with physical factors that can change between acquisitions. Advances are being made both in instrumentation developments combining PET and Compton cameras for multimodal or three-gamma imaging systems, and in image reconstruction, addressing the challenges imposed by the combination of the two modalities or the new techniques. This review article summarizes the advances made in Compton cameras for medical imaging and their combination with PET.

Artificial Intelligence in PET: An Industry Perspective

Artificial intelligence (AI) has significant potential to positively impact and advance medical imaging, including positron emission tomography (PET) imaging applications. AI has the ability to enhance and optimize all aspects of the PET imaging chain from patient scheduling, patient setup, protocoling, data acquisition, detector signal processing, reconstruction, image processing, and interpretation. AI poses industry-specific challenges which will need to be addressed and overcome to maximize the future potentials of AI in PET. This article provides an overview of these industry-specific challenges for the development, standardization, commercialization, and clinical adoption of AI and explores the potential enhancements to PET imaging brought on by AI in the near future. In particular, the combination of on-demand image reconstruction, AI, and custom-designed data-processing workflows may open new possibilities for innovation which would positively impact the industry and ultimately patients.

Reconstruction, analysis and interpretation of posterior probability distributions of PET images, using the posterior bootstrap

The uncertainty of reconstructed PET images remains difficult to assess and to interpret for the use in diagnostic and quantification tasks. Here we provide (1) an easy-to-use methodology for uncertainty assessment for almost any Bayesian model in PET reconstruction from single datasets and (2) a detailed analysis and interpretation of produced posterior image distributions. We apply a recent posterior bootstrap framework to the PET image reconstruction inverse problem and obtain simple parallelizable algorithms based on random weights and on existing maximuma posteriori(MAP) (posterior maximum) optimization-based algorithms. Posterior distributions are produced, analyzed and interpreted for several common Bayesian models. Their relationship with the distribution of the MAP image estimate over multiple dataset realizations is exposed. The coverage properties of posterior distributions are validated. More insight is obtained for the interpretation of posterior distributions in order to open the way for including uncertainty information into diagnostic and quantification tasks.

Uncertainty analysis of MR-PET image registration for precision neuro-PET imaging

Accurate regional brain quantitative PET measurements, particularly when using partial volume correction, rely on robust image registration between PET and MR images. We argue here that the precision, and hence the uncertainty, of MR-PET image registration is mainly driven by the registration implementation and the quality of PET images due to their lower resolution and higher noise compared to the structural MR images. We propose a dedicated uncertainty analysis for quantifying the precision of MR-PET registration, centred around the bootstrap resampling of PET list-mode events to generate multiple PET image realisations with different noise (count) levels. The effects of PET image reconstruction parameters, such as the use of attenuation and scatter corrections and different number of iterations, on the precision and accuracy of MR-PET registration were investigated. In addition, the performance of four software packages with their default settings for rigid inter-modality image registration were considered: NiftyReg, Vinci, FSL and SPM. Four distinct PET image distributions made of two early time frames (similar to cortical FDG) and two late frames using two amyloid PET dynamic acquisitions of one amyloid positive and one amyloid negative participants were investigated. For the investigated four PET frames, the biggest impact on the uncertainty was observed between registration software packages (up to 10-fold difference in precision) followed by the reconstruction parameters. On average, the lowest uncertainty for different PET frames and brain regions was observed with SPM and two iterations of fully quantitative image reconstruction. The observed uncertainty for the varying PET count-level (from 5% to 60%) was slightly lower than for the reconstruction parameters. We also observed that the registration uncertainty in quantitative PET analysis depends on amyloid status of the considered PET frames, with increased uncertainty (up to three times) when using post-reconstruction partial volume correction. This analysis is applicable for PET data obtained from either PET/MR or PET/CT scanners.

A noise smoothing origin ensemble algorithm based on local filtering

An origin ensemble (OE) image reconstruction algorithm can be used for the fast reconstruction of unconventional geometrical images, e.g. in a Compton camera (CC) system. Due to the low-count rate in the emission data, the reconstructed image is often noisy and inhomogeneous in density. In this study, we propose a way to smooth out the noise in the OE algorithm. During the OE reconstruction, the algorithm stochastically modifies the current location to a random new voxel along the probable corresponding curve of each event depending on the relative event density of the new and old locations. In the original OE technique, the event density is simply the number of events in the voxel. In the proposed method, the event density is estimated from the filtering of a kernel window centered on the voxel. Incorporating the regional filtering is similar to performing an OE algorithm on a smoothed image at each iteration and enables the reconstruction of a smoother image. A Flangeless Esser PET phantom and a multi-activity phantom are used to study the property of the new reconstruction algorithm. The results indicate that the proposed method performs better than a conventional OE algorithm in terms of normalized mean square error (NMSE) and structural similarity (SSIM). Both contrast noise ratio (CNR) and reconstruction accuracy of the new method are better than the conventional OE algorithm and their performances improve with the increase of object size. The median-OE possesses the highest overall image quality and recovery rate among the three filter-OE algorithms and is the method of choice for image reconstruction. Comparing to conventional post-smoothing OEs, the NMSE of median-OE improves 57.6% (46.9%) and the SSIM increased by 73.2% (51.1%) for the Esser (multi-activity) phantom. The proposed OE algorithm is simple and efficient for noise smoothing without complex calculations and highly suited for low-count cases.

PET Reconstruction of the Posterior Image Probability, Including Multimodal Images

In PET image reconstruction, it would be useful to obtain the entire posterior probability distribution of the image, because it allows for both estimating image intensity and assessing the uncertainty of the estimation, thus leading to more reliable interpretation. We propose a new entirely probabilistic model: the prior is a distribution over possible smooth regions (distance-driven Chinese restaurant process), and the posterior distribution is estimated using a Gibbs Markov chain Monte Carlo sampler. Data from other modalities (here one or several MR images) are introduced into the model as additional observed data, providing side information about likely smooth regions in the image. The reconstructed image is the posterior mean, and the uncertainty is presented as an image of the size of 95% posterior intervals. The reconstruction was compared with the maximum-likelihood expectation-maximization and OSEM algorithms, with and without post-smoothing, and with a penalized ML or MAP method that also uses additional images from other modalities. Qualitative and quantitative tests were performed on realistic simulated data with statistical replicates and on several clinical examinations presenting pathologies. The proposed method presents appealing properties in terms of obtained bias, variance, spatial regularization, and use of multimodal data, and produces, in addition, potentially valuable uncertainty information.

Resolution recovery for Compton camera using origin ensemble algorithm

PURPOSE

Compton cameras (CCs) use electronic collimation to reconstruct the images of activity distribution. Although this approach can greatly improve imaging efficiency, due to complex geometry of the CC principle, image reconstruction with the standard iterative algorithms, such as ordered subset expectation maximization (OSEM), can be very time-consuming, even more so if resolution recovery (RR) is implemented. We have previously shown that the origin ensemble (OE) algorithm can be used for the reconstruction of the CC data. Here we propose a method of extending our OE algorithm to include RR.

METHODS

To validate the proposed algorithm we used Monte Carlo simulations of a CC composed of multiple layers of pixelated CZT detectors and designed for imaging small animals. A series of CC acquisitions of small hot spheres and the Derenzo phantom placed in air were simulated. Images obtained from (a) the exact data, (b) blurred data but reconstructed without resolution recovery, and (c) blurred and reconstructed with resolution recovery were compared. Furthermore, the reconstructed contrast-to-background ratios were investigated using the phantom with nine spheres placed in a hot background.

RESULTS

Our simulations demonstrate that the proposed method allows for the recovery of the resolution loss that is due to imperfect accuracy of event detection. Additionally, tests of camera sensitivity corresponding to different detector configurations demonstrate that the proposed CC design has sensitivity comparable to PET. When the same number of events were considered, the computation time per iteration increased only by a factor of 2 when OE reconstruction with the resolution recovery correction was performed relative to the original OE algorithm. We estimate that the addition of resolution recovery to the OSEM would increase reconstruction times by 2-3 orders of magnitude per iteration.

CONCLUSIONS

The results of our tests demonstrate the improvement of image resolution provided by the OE reconstructions with resolution recovery. The quality of images and their contrast are similar to those obtained from the OE reconstructions from scans simulated with perfect energy and spatial resolutions.

Motion compensation using origin ensembles in awake small animal positron emission tomography

In emission tomographic imaging, the stochastic origin ensembles algorithm provides unique information regarding the detected counts given the measured data. Precision in both voxel and region-wise parameters may be determined for a single data set based on the posterior distribution of the count density allowing uncertainty estimates to be allocated to quantitative measures. Uncertainty estimates are of particular importance in awake animal neurological and behavioral studies for which head motion, unique for each acquired data set, perturbs the measured data. Motion compensation can be conducted when rigid head pose is measured during the scan. However, errors in pose measurements used for compensation can degrade the data and hence quantitative outcomes. In this investigation motion compensation and detector resolution models were incorporated into the basic origin ensembles algorithm and an efficient approach to computation was developed. The approach was validated against maximum liklihood-expectation maximisation and tested using simulated data. The resultant algorithm was then used to analyse quantitative uncertainty in regional activity estimates arising from changes in pose measurement precision. Finally, the posterior covariance acquired from a single data set was used to describe correlations between regions of interest providing information about pose measurement precision that may be useful in system analysis and design. The investigation demonstrates the use of origin ensembles as a powerful framework for evaluating statistical uncertainty of voxel and regional estimates. While in this investigation rigid motion was considered in the context of awake animal PET, the extension to arbitrary motion may provide clinical utility where respiratory or cardiac motion perturb the measured data.

Comment on 'Imaging of prompt gamma rays emitted during delivery of clinical proton beams with a Compton camera: feasibility studies for range verification'

The origin ensemble (OE) algorithm is a new method used for image reconstruction from nuclear tomographic data. The main advantage of this algorithm is the ease of implementation for complex tomographic models and the sound statistical theory. In this comment, the author provides the basics of the statistical interpretation of OE and gives suggestions for the improvement of the algorithm in the application to prompt gamma imaging as described in Polf et al (2015 Phys. Med. Biol. 60 7085).

Reconstruction of multiple-pinhole micro-SPECT data using origin ensembles

PURPOSE

The authors are currently developing a dual-resolution multiple-pinhole microSPECT imaging system based on three large NaI(Tl) gamma cameras. Two multiple-pinhole tungsten collimator tubes will be used sequentially for whole-body "scout" imaging of a mouse, followed by high-resolution (hi-res) imaging of an organ of interest, such as the heart or brain. Ideally, the whole-body image will be reconstructed in real time such that data need only be acquired until the area of interest can be visualized well-enough to determine positioning for the hi-res scan. The authors investigated the utility of the origin ensemble (OE) algorithm for online and offline reconstructions of the scout data. This algorithm operates directly in image space, and can provide estimates of image uncertainty, along with reconstructed images. Techniques for accelerating the OE reconstruction were also introduced and evaluated.

METHODS

System matrices were calculated for our 39-pinhole scout collimator design. SPECT projections were simulated for a range of count levels using the MOBY digital mouse phantom. Simulated data were used for a comparison of OE and maximum-likelihood expectation maximization (MLEM) reconstructions. The OE algorithm convergence was evaluated by calculating the total-image entropy and by measuring the counts in a volume-of-interest (VOI) containing the heart. Total-image entropy was also calculated for simulated MOBY data reconstructed using OE with various levels of parallelization.

RESULTS

For VOI measurements in the heart, liver, bladder, and soft-tissue, MLEM and OE reconstructed images agreed within 6%. Image entropy converged after ∼2000 iterations of OE, while the counts in the heart converged earlier at ∼200 iterations of OE. An accelerated version of OE completed 1000 iterations in <9 min for a 6.8M count data set, with some loss of image entropy performance, whereas the same dataset required ∼79 min to complete 1000 iterations of conventional OE. A combination of the two methods showed decreased reconstruction time and no loss of performance when compared to conventional OE alone.

CONCLUSIONS

OE-reconstructed images were found to be quantitatively and qualitatively similar to MLEM, yet OE also provided estimates of image uncertainty. Some acceleration of the reconstruction can be gained through the use of parallel computing. The OE algorithm is useful for reconstructing multiple-pinhole SPECT data and can be easily modified for real-time reconstruction.

Rapid processing of PET list-mode data for efficient uncertainty estimation and data analysis

In this technical note we propose a rapid and scalable software solution for the processing of PET list-mode data, which allows the efficient integration of list mode data processing into the workflow of image reconstruction and analysis. All processing is performed on the graphics processing unit (GPU), making use of streamed and concurrent kernel execution together with data transfers between disk and CPU memory as well as CPU and GPU memory. This approach leads to fast generation of multiple bootstrap realisations, and when combined with fast image reconstruction and analysis, it enables assessment of uncertainties of any image statistic and of any component of the image generation process (e.g. random correction, image processing) within reasonable time frames (e.g. within five minutes per realisation). This is of particular value when handling complex chains of image generation and processing. The software outputs the following: (1) estimate of expected random event data for noise reduction; (2) dynamic prompt and random sinograms of span-1 and span-11 and (3) variance estimates based on multiple bootstrap realisations of (1) and (2) assuming reasonable count levels for acceptable accuracy. In addition, the software produces statistics and visualisations for immediate quality control and crude motion detection, such as: (1) count rate curves; (2) centre of mass plots of the radiodistribution for motion detection; (3) video of dynamic projection views for fast visual list-mode skimming and inspection; (4) full normalisation factor sinograms. To demonstrate the software, we present an example of the above processing for fast uncertainty estimation of regional SUVR (standard uptake value ratio) calculation for a single PET scan of (18)F-florbetapir using the Siemens Biograph mMR scanner.

Sensitivity estimation in time-of-flight list-mode positron emission tomography

PURPOSE

An accurate quantification of the images in positron emission tomography (PET) requires knowing the actual sensitivity at each voxel, which represents the probability that a positron emitted in that voxel is finally detected as a coincidence of two gamma rays in a pair of detectors in the PET scanner. This sensitivity depends on the characteristics of the acquisition, as it is affected by the attenuation of the annihilation gamma rays in the body, and possible variations of the sensitivity of the scanner detectors. In this work, the authors propose a new approach to handle time-of-flight (TOF) list-mode PET data, which allows performing either or both, a self-attenuation correction, and self-normalization correction based on emission data only.

METHODS

The authors derive the theory using a fully Bayesian statistical model of complete data. The authors perform an initial evaluation of algorithms derived from that theory and proposed in this work using numerical 2D list-mode simulations with different TOF resolutions and total number of detected coincidences. Effects of randoms and scatter are not simulated.

RESULTS

The authors found that proposed algorithms successfully correct for unknown attenuation and scanner normalization for simulated 2D list-mode TOF-PET data.

CONCLUSIONS

A new method is presented that can be used for corrections for attenuation and normalization (sensitivity) using TOF list-mode data.

Advances in SPECT and PET Hardware

There have been significant recent advances in single photon emission computed tomography (SPECT) and positron emission tomography (PET) hardware. Novel collimator designs, such as multi-pinhole and locally focusing collimators arranged in geometries that are optimized for cardiac imaging have been implemented to reduce imaging time and radiation dose. These new collimators have been coupled with solid state photon detectors to further improve image quality and reduce scanner size. The new SPECT scanners demonstrate up to a 7-fold increase in photon sensitivity and up to 2 times improvement in image resolution. Although PET scanners are used primarily for oncological imaging, cardiac imaging can benefit from the improved PET sensitivity of 3D systems without inter-plane septa and implementation of the time-of-flight reconstruction. Additionally, resolution recovery techniques are now implemented by all major PET vendors. These new methods improve image contrast, image resolution, and reduce image noise. Simultaneous PET/magnetic resonance (MR) hybrid systems have been developed. Solid state detectors with avalanche photodiodes or digital silicon photomultipliers have also been utilized in PET. These new detectors allow improved image resolution, higher count rate, as well as a reduced sensitivity to electromagnetic MR fields.

Time-of-flight PET image reconstruction using origin ensembles

The origin ensemble (OE) algorithm is a novel statistical method for minimum-mean-square-error (MMSE) reconstruction of emission tomography data. This method allows one to perform reconstruction entirely in the image domain, i.e. without the use of forward and backprojection operations. We have investigated the OE algorithm in the context of list-mode (LM) time-of-flight (TOF) PET reconstruction. In this paper, we provide a general introduction to MMSE reconstruction, and a statistically rigorous derivation of the OE algorithm. We show how to efficiently incorporate TOF information into the reconstruction process, and how to correct for random coincidences and scattered events. To examine the feasibility of LM-TOF MMSE reconstruction with the OE algorithm, we applied MMSE-OE and standard maximum-likelihood expectation-maximization (ML-EM) reconstruction to LM-TOF phantom data with a count number typically registered in clinical PET examinations. We analyzed the convergence behavior of the OE algorithm, and compared reconstruction time and image quality to that of the EM algorithm. In summary, during the reconstruction process, MMSE-OE contrast recovery (CRV) remained approximately the same, while background variability (BV) gradually decreased with an increasing number of OE iterations. The final MMSE-OE images exhibited lower BV and a slightly lower CRV than the corresponding ML-EM images. The reconstruction time of the OE algorithm was approximately 1.3 times longer. At the same time, the OE algorithm can inherently provide a comprehensive statistical characterization of the acquired data. This characterization can be utilized for further data processing, e.g. in kinetic analysis and image registration, making the OE algorithm a promising approach in a variety of applications.

Evaluation of imaging systems using the posterior variance of emission counts

We investigate an approach to evaluation of emission-tomography (ET) imaging systems used for region-of-interest (ROI) estimation tasks. In the evaluation we employ the concept of "emission counts" (EC), which are the number of events per voxel emitted during a scan. We use the reduction in posterior variance of ROI EC, compared to the prior ROI EC variance, as the metric of primary interest, which we call the "posterior variance reduction index" (PVRI). Systems that achieve a higher PVRI are considered superior to systems with lower PVRI. The approach is independent of the reconstruction method and is applicable to all photon-limited data types including list-mode data. We analyzed this approach using a model of 2-D tomography, and compared our results to the classical theory of tomographic sampling. We found that performance evaluations using the PVRI index were consistent with the classical theory. System evaluation based on EC posterior variance is an intuitively appealing and physically meaningful method that is useful for evaluation of system performance in ROI quantitation tasks.