Advances in PET Image Reconstruction

An iterative reconstruction algorithm for unsupervised PET image

Objective.In recent years, convolutional neural networks (CNNs) have shown great potential in positron emission tomography (PET) image reconstruction. However, most of them rely on many low-quality and high-quality reference PET image pairs for training, which are not always feasible in clinical practice. On the other hand, many works improve the quality of PET image reconstruction by adding explicit regularization or optimizing the network structure, which may lead to complex optimization problems.Approach.In this paper, we develop a novel iterative reconstruction algorithm by integrating the deep image prior (DIP) framework, which only needs the prior information (e.g. MRI) and sinogram data of patients. To be specific, we construct the objective function as a constrained optimization problem and utilize the existing PET image reconstruction packages to streamline calculations. Moreover, to further improve both the reconstruction quality and speed, we introduce the Nesterov's acceleration part and the restart mechanism in each iteration.Main results.2D experiments on PET data sets based on computer simulations and real patients demonstrate that our proposed algorithm can outperform existing MLEM-GF, KEM and DIPRecon methods.Significance.Unlike traditional CNN methods, the proposed algorithm does not rely on large data sets, but only leverages inter-patient information. Furthermore, we enhance reconstruction performance by optimizing the iterative algorithm. Notably, the proposed method does not require much modification of the basic algorithm, allowing for easy integration into standard implementations.

The Past, Present, and Future Role of Artificial Intelligence in Ventilation/Perfusion Scintigraphy: A Systematic Review

Ventilation-perfusion (V/Q) lung scans constitute one of the oldest nuclear medicine procedures, remain one of the few studies performed in the acute setting, and are amongst the few performed in the emergency setting. V/Q studies have witnessed a long fluctuation in adoption rates in parallel to continuous advances in image processing and computer vision techniques. This review provides an overview on the status of artificial intelligence (AI) in V/Q scintigraphy. To clearly assess the past, current, and future role of AI in V/Q scans, we conducted a systematic Ovid MEDLINE(R) literature search from 1946 to August 5, 2022 in addition to a manual search. The literature was reviewed and summarized in terms of methodologies and results for the various applications of AI to V/Q scans. The PRISMA guidelines were followed. Thirty-one publications fulfilled our search criteria and were grouped into two distinct categories: (1) disease diagnosis/detection (N = 22, 71.0%) and (2) cross-modality image translation into V/Q images (N = 9, 29.0%). Studies on disease diagnosis and detection relied heavily on shallow artificial neural networks for acute pulmonary embolism (PE) diagnosis and were primarily published between the mid-1990s and early 2000s. Recent applications almost exclusively regard image translation tasks from CT to ventilation or perfusion images with modern algorithms, such as convolutional neural networks, and were published between 2019 and 2022. AI research in V/Q scintigraphy for acute PE diagnosis in the mid-90s to early 2000s yielded promising results but has since been largely neglected and thus have yet to benefit from today's state-of-the art machine-learning techniques, such as deep neural networks. Recently, the main application of AI for V/Q has shifted towards generating synthetic ventilation and perfusion images from CT. There is therefore considerable potential to expand and modernize the use of real V/Q studies with state-of-the-art deep learning approaches, especially for workflow optimization and PE detection at both acute and chronic stages. We discuss future challenges and potential directions to compensate for the lag in this domain and enhance the value of this traditional nuclear medicine scan.

AI for PET image reconstruction

Image reconstruction for positron emission tomography (PET) has been developed over many decades, with advances coming from improved modelling of the data statistics and improved modelling of the imaging physics. However, high noise and limited spatial resolution have remained issues in PET imaging, and state-of-the-art PET reconstruction has started to exploit other medical imaging modalities (such as MRI) to assist in noise reduction and enhancement of PET's spatial resolution. Nonetheless, there is an ongoing drive towards not only improving image quality, but also reducing the injected radiation dose and reducing scanning times. While the arrival of new PET scanners (such as total body PET) is helping, there is always a need to improve reconstructed image quality due to the time and count limited imaging conditions. Artificial intelligence (AI) methods are now at the frontier of research for PET image reconstruction. While AI can learn the imaging physics as well as the noise in the data (when given sufficient examples), one of the most common uses of AI arises from exploiting databases of high-quality reference examples, to provide advanced noise compensation and resolution recovery. There are three main AI reconstruction approaches: (i) direct data-driven AI methods which rely on supervised learning from reference data, (ii) iterative (unrolled) methods which combine our physics and statistical models with AI learning from data, and (iii) methods which exploit AI with our known models, but crucially can offer benefits even in the absence of any example training data whatsoever. This article reviews these methods, considering opportunities and challenges of AI for PET reconstruction.

Fully 3D implementation of the end-to-end deep image prior-based PET image reconstruction using block iterative algorithm

Objective. Deep image prior (DIP) has recently attracted attention owing to its unsupervised positron emission tomography (PET) image reconstruction method, which does not require any prior training dataset. In this paper, we present the first attempt to implement an end-to-end DIP-based fully 3D PET image reconstruction method that incorporates a forward-projection model into a loss function.Approach. A practical implementation of a fully 3D PET image reconstruction could not be performed at present because of a graphics processing unit memory limitation. Consequently, we modify the DIP optimization to a block iteration and sequential learning of an ordered sequence of block sinograms. Furthermore, the relative difference penalty (RDP) term is added to the loss function to enhance the quantitative accuracy of the PET image.Main results. We evaluated our proposed method using Monte Carlo simulation with [18F]FDG PET data of a human brain and a preclinical study on monkey-brain [18F]FDG PET data. The proposed method was compared with the maximum-likelihood expectation maximization (EM), maximuma posterioriEM with RDP, and hybrid DIP-based PET reconstruction methods. The simulation results showed that, compared with other algorithms, the proposed method improved the PET image quality by reducing statistical noise and better preserved the contrast of brain structures and inserted tumors. In the preclinical experiment, finer structures and better contrast recovery were obtained with the proposed method.Significance.The results indicated that the proposed method could produce high-quality images without a prior training dataset. Thus, the proposed method could be a key enabling technology for the straightforward and practical implementation of end-to-end DIP-based fully 3D PET image reconstruction.

Similarity-Driven Fine-Tuning Methods for Regularization Parameter Optimization in PET Image Reconstruction

We present an adaptive method for fine-tuning hyperparameters in edge-preserving regularization for PET image reconstruction. For edge-preserving regularization, in addition to the smoothing parameter that balances data fidelity and regularization, one or more control parameters are typically incorporated to adjust the sensitivity of edge preservation by modifying the shape of the penalty function. Although there have been efforts to develop automated methods for tuning the hyperparameters in regularized PET reconstruction, the majority of these methods primarily focus on the smoothing parameter. However, it is challenging to obtain high-quality images without appropriately selecting the control parameters that adjust the edge preservation sensitivity. In this work, we propose a method to precisely tune the hyperparameters, which are initially set with a fixed value for the entire image, either manually or using an automated approach. Our core strategy involves adaptively adjusting the control parameter at each pixel, taking into account the degree of patch similarities calculated from the previous iteration within the pixel's neighborhood that is being updated. This approach allows our new method to integrate with a wide range of existing parameter-tuning techniques for edge-preserving regularization. Experimental results demonstrate that our proposed method effectively enhances the overall reconstruction accuracy across multiple image quality metrics, including peak signal-to-noise ratio, structural similarity, visual information fidelity, mean absolute error, root-mean-square error, and mean percentage error.

Q.Clear reconstruction for reducing the scanning time for 68 Ga-DOTA-FAPI-04 PET/MR imaging

PURPOSE

This study aims to determine whether Q.Clear positron emission tomography (PET) reconstruction may reduce tracer injection dose or shorten scanning time in 68Gallium-labelled fibroblast activation protein inhibitor (68 Ga-FAPI) PET/magnetic resonance (MR) imaging.

METHODS

We retrospectively collected cases of 68 Ga-FAPI whole-body imaging performed on integrated PET/MR. PET images were reconstructed using three different methods: ordered subset expectation maximization (OSEM) reconstruction with full scanning time, OSEM reconstruction with half scanning time, and Q.Clear reconstruction with half scanning time. We then measured standardized uptake values (SUVs) within and around lesions, alongside their volumes. We also evaluated image quality using lesion-to-background (L/B) ratio and signal-to-noise ratio (SNR). We then compared these metrics across the three reconstruction techniques using statistical methods.

RESULTS

Q.Clear reconstruction significantly increased SUVmax and SUVmean within lesions (more than 30%) and reduced their volumes in comparison with OSEM reconstruction. Background SUVmax also increased significantly, while background SUVmean showed no difference. Average L/B values for Q.Clear reconstruction were only marginally higher than those from OSME reconstruction with half-time. SNR decreased significantly in Q.Clear reconstruction compared with OSEM reconstruction with full time (but not half time). Differences between Q.Clear and OSEM reconstructions in SUVmax and SUVmean values within lesions were significantly correlated with SUVs within lesions.

CONCLUSIONS

Q.Clear reconstruction was useful for reducing PET injection dose or scanning time while maintaining the image quality. Q.Clear may affect PET quantification, and it is necessary to establish diagnostic recommendations based on Q.Clear results for Q.Clear application.

Comparison of the performances of machine learning and deep learning in improving the quality of low dose lung cancer PET images

PURPOSE

To compare the performances of machine learning (ML) and deep learning (DL) in improving the quality of low dose (LD) lung cancer PET images and the minimum counts required.

MATERIALS AND METHODS

33 standard dose (SD) PET images, were used to simulate LD PET images at seven-count levels of 0.25, 0.5, 1, 2, 5, 7.5 and 10 million (M) counts. Image quality transfer (IQT), a ML algorithm that uses decision tree and patch-sampling was compared to two DL networks-HighResNet (HRN) and deep-boosted regression (DBR). Supervised training was performed by training the ML and DL algorithms with matched-pair SD and LD images. Image quality evaluation and clinical lesion detection tasks were performed by three readers. Bias in 53 radiomic features, including mean SUV, was evaluated for all lesions.

RESULTS

ML- and DL-estimated images showed higher signal and smaller error than LD images with optimal image quality recovery achieved using LD down to 5 M counts. True positive rate and false discovery rate were fairly stable beyond 5 M counts for the detection of small and large true lesions. Readers rated average or higher ratings to images estimated from LD images of count levels above 5 M only, with higher confidence in detecting true lesions.

CONCLUSION

LD images with a minimum of 5 M counts (8.72 MBq for 10 min scan or 25 MBq for 3 min scan) are required for optimal clinical use of ML and DL, with slightly better but more varied performance shown by DL.

Evaluation of the spline reconstruction technique for preclinical PET imaging

BACKGROUND AND OBJECTIVE

The Spline Reconstruction Technique (SRT) is a fast algorithm based on a novel numerical implementation of an analytic representation of the inverse Radon transform. The purpose of this study is to provide a comparison between SRT, Filtered Back-Projection (FBP), Ordered Subset Expectation Maximization 2D (2D-OSEM), and the Tera-Tomo 3D algorithm, using phantom data at various acquisition durations as well as small-animal data obtained from the Mediso nanoScan® PET/CT scanner.

METHODS

For this purpose, the "NEMA NU 4-2008 standards" protocol was employed at five different realizations and acquisition durations. In addition to the image quality metrics described by the NEMA protocol, Cold Region Contrast was also considered as a figure-of-merit. Furthermore, Cold Region Contrast was measured in the myocardial infarction region of six male Wistar rats. The volumetric defect quantification was assessed with dedicated computer software. Lastly, plots of Recovery Coefficient and Spill-Over Ratio as a function of the Percentage Standard Deviation were generated, after smoothing the phantom reconstructions with four different Gaussian filters. Statistical significance was determined by employing the Kruskal-Wallis test or One-way Analysis of Variance depending on the normality of the variable's distribution.

RESULTS

The present study revealed that, at the expense of slightly increased noise in the reconstructed images, SRT resulted in higher Recovery Coefficient values for small hot regions of interest, when compared with FBP and 2D-OSEM at all acquisition durations. Furthermore, SRT reconstructed images exhibit higher Recovery Coefficient values, for all hot regions of interest, when compared to the other 2D algorithms at short acquisition durations. In both phantom and animal studies, SRT achieved a significant improvement over 2D-OSEM for the Spill-Over Ratio and the Cold Region Contrast. These advantages were maintained even after comparing the algorithms at equal noise levels. The Tera-Tomo 3D algorithm (4 subsets, iterations≥ 13) performed significantly better compared to the other algorithms for all figures-of-merit. No statistically significant differences regarding the myocardial defect size were observed between the algorithms investigated.

CONCLUSIONS

Overall, SRT appears that could be useful for the quantification of small hot regions of interest, cold regions of interest, as well as in low-count imaging applications.

Penalized-Likelihood PET Image Reconstruction Using Similarity-Driven Median Regularization

In this paper, we present a new regularized image reconstruction method for positron emission tomography (PET), where an adaptive weighted median regularizer is used in the context of a penalized-likelihood framework. The motivation of our work is to overcome the limitation of the conventional median regularizer, which has proven useful for tomographic reconstruction but suffers from the negative effect of removing fine details in the underlying image when the edges occupy less than half of the window elements. The crux of our method is inspired by the well-known non-local means denoising approach, which exploits the measure of similarity between the image patches for weighted smoothing. However, our method is different from the non-local means denoising approach in that the similarity measure between the patches is used for the median weights rather than for the smoothing weights. As the median weights, in this case, are spatially variant, they provide adaptive median regularization achieving high-quality reconstructions. The experimental results indicate that our similarity-driven median regularization method not only improves the reconstruction accuracy, but also has great potential for super-resolution reconstruction for PET.

Leveraging deep neural networks to improve numerical and perceptual image quality in low-dose preclinical PET imaging

The amount of radiotracer injected into laboratory animals is still the most daunting challenge facing translational PET studies. Since low-dose imaging is characterized by a higher level of noise, the quality of the reconstructed images leaves much to be desired. Being the most ubiquitous techniques in denoising applications, edge-aware denoising filters, and reconstruction-based techniques have drawn significant attention in low-count applications. However, for the last few years, much of the credit has gone to deep-learning (DL) methods, which provide more robust solutions to handle various conditions. Albeit being extensively explored in clinical studies, to the best of our knowledge, there is a lack of studies exploring the feasibility of DL-based image denoising in low-count small animal PET imaging. Therefore, herein, we investigated different DL frameworks to map low-dose small animal PET images to their full-dose equivalent with quality and visual similarity on a par with those of standard acquisition. The performance of the DL model was also compared to other well-established filters, including Gaussian smoothing, nonlocal means, and anisotropic diffusion. Visual inspection and quantitative assessment based on quality metrics proved the superior performance of the DL methods in low-count small animal PET studies, paving the way for a more detailed exploration of DL-assisted algorithms in this domain.

The Evolution of Image Reconstruction in PET: From Filtered Back-Projection to Artificial Intelligence

PET can provide functional images revealing physiologic processes in vivo. Although PET has many applications, there are still some limitations that compromise its precision: the absorption of photons in the body causes signal attenuation; the dead-time limit of system components leads to the loss of the count rate; the scattered and random events received by the detector introduce additional noise; the characteristics of the detector limit the spatial resolution; and the low signal-to-noise ratio caused by the scan-time limit (eg, dynamic scans) and dose concern. The early PET reconstruction methods are analytical approaches based on an idealized mathematical model.

Artificial intelligence in molecular imaging

AI has, to varying degrees, affected all aspects of molecular imaging, from image acquisition to diagnosis. During the last decade, the advent of deep learning in particular has transformed medical image analysis. Although the majority of recent advances have resulted from neural-network models applied to image segmentation, a broad range of techniques has shown promise for image reconstruction, image synthesis, differential-diagnosis generation, and treatment guidance. Applications of AI for drug design indicate the way forward for using AI to facilitate molecular-probe design, which is still in its early stages. Deep-learning models have demonstrated increased efficiency and image quality for PET reconstruction from sinogram data. Generative adversarial networks (GANs), which are paired neural networks that are jointly trained to generate and classify images, have found applications in modality transformation, artifact reduction, and synthetic-PET-image generation. Some AI applications, based either partly or completely on neural-network approaches, have demonstrated superior differential-diagnosis generation relative to radiologists. However, AI models have a history of brittleness, and physicians and patients may not trust AI applications that cannot explain their reasoning. To date, the majority of molecular-imaging applications of AI have been confined to research projects, and are only beginning to find their ways into routine clinical workflows via commercialization and, in some cases, integration into scanner hardware. Evaluation of actual clinical products will yield more realistic assessments of AI’s utility in molecular imaging.

Quantitative Molecular Positron Emission Tomography Imaging Using Advanced Deep Learning Techniques

The widespread availability of high-performance computing and the popularity of artificial intelligence (AI) with machine learning and deep learning (ML/DL) algorithms at the helm have stimulated the development of many applications involving the use of AI-based techniques in molecular imaging research. Applications reported in the literature encompass various areas, including innovative design concepts in positron emission tomography (PET) instrumentation, quantitative image reconstruction and analysis techniques, computer-aided detection and diagnosis, as well as modeling and prediction of outcomes. This review reflects the tremendous interest in quantitative molecular imaging using ML/DL techniques during the past decade, ranging from the basic principles of ML/DL techniques to the various steps required for obtaining quantitatively accurate PET data, including algorithms used to denoise or correct for physical degrading factors as well as to quantify tracer uptake and metabolic tumor volume for treatment monitoring or radiation therapy treatment planning and response prediction.This review also addresses future opportunities and current challenges facing the adoption of ML/DL approaches and their role in multimodality imaging.

OMEGA-open-source emission tomography software

In this paper we present OMEGA, an open-source software, for efficient and fast image reconstruction in positron emission tomography (PET). OMEGA uses the scripting language of MATLAB and GNU Octave allowing reconstruction of PET data with a MATLAB or GNU Octave interface. The goal of OMEGA is to allow easy and fast reconstruction of any PET data, and to provide a computationally efficient, easy-access platform for development of new PET algorithms with built-in forward and backward projection operations available to the user as a MATLAB/Octave class. OMEGA also includes direct support for GATE simulated data, facilitating easy evaluation of the new algorithms using Monte Carlo simulated PET data. OMEGA supports parallel computing by utilizing OpenMP for CPU implementations and OpenCL for GPU allowing any hardware to be used. OMEGA includes built-in function for the computation of normalization correction and allows several other corrections to be applied such as attenuation, randoms or scatter. OMEGA includes several different maximum-likelihood and maximum a posteriori (MAP) algorithms with several different priors. The user can also input their own priors to the built-in MAP functions. The image reconstruction in OMEGA can be computed either by using an explicitly computed system matrix or with a matrix-free formalism, where the latter can be accelerated with OpenCL. We provide an overview on the software and present some examples utilizing the different features of the software.

Non-local mean denoising using multiple PET reconstructions

OBJECTIVES

Non-local mean (NLM) filtering has been broadly used for denoising of natural and medical images. The NLM filter relies on the redundant information, in the form of repeated patterns/textures, in the target image to discriminate the underlying structures/signals from noise. In PET (or SPECT) imaging, the raw data could be reconstructed using different parameters and settings, leading to different representations of the target image, which contain highly similar structures/signals to the target image contaminated with different noise levels (or properties). In this light, multiple-reconstruction NLM filtering (MR-NLM) is proposed, which relies on the redundant information provided by the different reconstructions of the same PET data (referred to as auxiliary images) to conduct the denoising process.

METHODS

Implementation of the MR-NLM approach involved the use of twelve auxiliary PET images (in addition to the target image) reconstructed using the same iterative reconstruction algorithm with different numbers of iterations and subsets. For each target voxel, the patches of voxels at the same location are extracted from the auxiliary PET images based on which the NLM denoising process is conducted. Through this, the exhaustive search scheme performed in the conventional NLM method to find similar patches of voxels is bypassed. The performance evaluation of the MR-NLM filter was carried out against the conventional NLM, Gaussian and bilateral post-reconstruction approaches using the experimental Jaszczak phantom and 25 whole-body PET/CT clinical studies.

RESULTS

The signal-to-noise ratio (SNR) in the experimental Jaszczak phantom study improved from 25.1 when using Gaussian filtering to 27.9 and 28.8 when the conventional NLM and MR-NLM methods were applied (p value < 0.05), respectively. Conversely, the Gaussian filter led to quantification bias of 35.4%, while NLM and MR-NLM approaches resulted in a bias of 32.0% and 31.1% (p value < 0.05), respectively. The clinical studies further confirm the superior performance of the MR-NLM method, wherein the quantitative bias measured in malignant lesions (hot spots) decreased from - 12.3 ± 2.3% when using the Gaussian filter to - 3.5 ± 1.3% and - 2.2 ± 1.2% when using the NLM and MR-NLM approaches (p value < 0.05), respectively.

CONCLUSION

The MR-NLM approach exhibited promising performance in terms of noise suppression and signal preservation for PET images, thus translating into higher SNR compared to the conventional NLM approach. Despite the promising performance of the MR-NLM approach, the additional computational burden owing to the requirement of multiple PET reconstruction still needs to be addressed.

Depth of Interaction Estimation in a Preclinical PET Scanner Equipped with Monolithic Crystals Coupled to SiPMs Using a Deep Neural Network

The scintillation light distribution produced by photodetectors in positron emission tomography (PET) provides the depth of interaction (DOI) information required for high-resolution imaging. The goal of positioning techniques is to reverse the photodetector signal’s pattern map to the coordinates of the incident photon energy position. By considering the DOI information, monolithic crystals offer good spatial, energy, and timing resolution along with high sensitivity. In this work, a supervised deep neural network was used for the approximation of DOI and to assess through Monte Carlo (MC) simulations the performance on a small-animal PET scanner consisting of ten 50 × 50 × 10 mm3 continuous Lutetium-Yttrium Oxyorthosilicate doped with Cerium (LYSO: Ce) crystals and 12 × 12 silicon photomultiplier (SiPM) arrays. The scintillation position was predicted by a multilayer perceptron neural network with 256 units and 4 layers whose inputs were the number of fired pixels on the SiPM plane and the total deposited energy. A GEANT4 MC code was used to generate training and test datasets by altering the photons’ incident position, energy, and direction, as well as readout of the photodetector output. The calculated spatial resolutions in the X-Y plane and along the Z-axis were 0.96 and 1.02 mm, respectively. Our results demonstrated that using a multilayer perceptron (MLP)-based positioning algorithm in the detector modules, constituting the PET scanner, enhances the spatial resolution by approximately 18% while the absolute sensitivity remains constant. The proposed algorithm proved its ability to predict the DOI for depth under 7 mm with an error below 8.7%.

Non-invasive in vivo imaging of acute thrombosis: development of a novel factor XIIIa radiotracer

AIMS

Cardiovascular thrombosis is responsible a quarter of deaths annually worldwide. Current imaging methods for cardiovascular thrombosis focus on anatomical identification of thrombus but cannot determine thrombus age or activity. Molecular imaging techniques hold promise for identification and quantification of thrombosis in vivo. Our objective was to assess a novel optical and positron-emitting probe targeting Factor XIIIa (ENC2015) as biomarker of active thrombus formation.

METHODS AND RESULTS

Optical and positron-emitting ENC2015 probes were assessed ex vivo using blood drawn from human volunteers and passed through perfusion chambers containing denuded porcine aorta as a model of arterial injury. Specificity of ENC2015 was established with co-infusion of a factor XIIIa inhibitor. In vivo18F-ENC2015 biodistribution, kinetics, radiometabolism, and thrombus binding were characterized in rats. Both Cy5 and fluorine-18 labelled ENC2015 rapidly and specifically bound to thrombi. Thrombus uptake was inhibited by a factor XIIIa inhibitor. 18F-ENC2015 remained unmetabolized over 8 h when incubated in ex vivo human blood. In vivo, 42% of parent radiotracer remained in blood 60 min post-administration. Biodistribution studies demonstrated rapid clearance from tissues with elimination via the urinary system. In vivo,18F-ENC2015 uptake was markedly increased in the thrombosed carotid artery compared to the contralateral patent artery (mean standard uptake value ratio of 2.40 vs. 0.74, P < 0.0001).

CONCLUSION

ENC2015 rapidly and selectively binds to acute thrombus in both an ex vivo human translational model and an in vivo rodent model of arterial thrombosis. This probe holds promise for the non-invasive identification of thrombus formation in cardiovascular disease.

Real-Time 3D PET Image with Pseudoinverse Reconstruction

Real-time positron emission tomography (PET) may provide information from first-shot images, enable PET-guided biopsies, and allow awake animal studies. Fully-3D iterative reconstructions yield the best images in PET, but they are too slow for real-time imaging. Analytical methods such as Fourier back projection (FBP) are very fast, but yield images of poor quality with artifacts due to noise or data incompleteness. In this work, an image reconstruction based on the pseudoinverse of the system response matrix (SRM) is presented. w. To implement the pseudoinverse method, the reconstruction problem is separated into two stages. First, the axial part of the SRM is pseudo-inverted (PINV) to rebin the 3D data into 2D datasets. Then, the resulting 2D slices can be reconstructed with analytical methods or by applying the pseudoinverse algorithm again. The proposed two-step PINV reconstruction yielded good-quality images at a rate of several frames per second, compatible with real time applications. Furthermore, extremely fast direct PINV reconstruction of projections of the 3D image collapsed along specific directions can be implemented.

Real-Time 3D PET Image with Pseudoinverse Reconstruction

Real-time positron emission tomography (PET) may provide information from first-shot images, enable PET-guided biopsies, and allow awake animal studies. Fully-3D iterative reconstructions yield the best images in PET, but they are too slow for real-time imaging. Analytical methods such as Fourier back projection (FBP) are very fast, but yield images of poor quality with artifacts due to noise or data incompleteness. In this work, an image reconstruction based on the pseudoinverse of the system response matrix (SRM) is presented. w. To implement the pseudoinverse method, the reconstruction problem is separated into two stages. First, the axial part of the SRM is pseudo-inverted (PINV) to rebin the 3D data into 2D datasets. Then, the resulting 2D slices can be reconstructed with analytical methods or by applying the pseudoinverse algorithm again. The proposed two-step PINV reconstruction yielded good-quality images at a rate of several frames per second, compatible with real time applications. Furthermore, extremely fast direct PINV reconstruction of projections of the 3D image collapsed along specific directions can be implemented.

Projection Space Implementation of Deep Learning-Guided Low-Dose Brain PET Imaging Improves Performance over Implementation in Image Space

Our purpose was to assess the performance of full-dose (FD) PET image synthesis in both image and sinogram space from low-dose (LD) PET images and sinograms without sacrificing diagnostic quality using deep learning techniques. Methods: Clinical brain PET/CT studies of 140 patients were retrospectively used for LD-to-FD PET conversion. Five percent of the events were randomly selected from the FD list-mode PET data to simulate a realistic LD acquisition. A modified 3-dimensional U-Net model was implemented to predict FD sinograms in the projection space (PSS) and FD images in image space (PIS) from their corresponding LD sinograms and images, respectively. The quality of the predicted PET images was assessed by 2 nuclear medicine specialists using a 5-point grading scheme. Quantitative analysis using established metrics including the peak signal-to-noise ratio (PSNR), structural similarity index metric (SSIM), regionwise SUV bias, and first-, second- and high-order texture radiomic features in 83 brain regions for the test and evaluation datasets was also performed. Results: All PSS images were scored 4 or higher (good to excellent) by the nuclear medicine specialists. PSNR and SSIM values of 0.96 ± 0.03 and 0.97 ± 0.02, respectively, were obtained for PIS, and values of 31.70 ± 0.75 and 37.30 ± 0.71, respectively, were obtained for PSS. The average SUV bias calculated over all brain regions was 0.24% ± 0.96% and 1.05% ± 1.44% for PSS and PIS, respectively. The Bland-Altman plots reported the lowest SUV bias (0.02) and variance (95% confidence interval, -0.92 to +0.84) for PSS, compared with the reference FD images. The relative error of the homogeneity radiomic feature belonging to the gray-level cooccurrence matrix category was -1.07 ± 1.77 and 0.28 ± 1.4 for PIS and PSS, respectively. Conclusion: The qualitative assessment and quantitative analysis demonstrated that the FD PET PSS led to superior performance, resulting in higher image quality and lower SUV bias and variance than for FD PET PIS.

Probabilistic Graphical Models for Dynamic PET: A Novel Approach to Direct Parametric Map Estimation and Image Reconstruction

In the context of dynamic emission tomography, the conventional processing pipeline consists of independent image reconstruction of single-time frames, followed by the application of a suitable kinetic model to time-activity curves (TACs) at the voxel or region-of-interest level. Direct 4D positron emission tomography (PET) reconstruction, by contrast, seeks to move beyond this scheme and incorporate information from multiple time frames within the reconstruction task. Established direct methods are based on a deterministic description of voxelwise TACs, captured by the chosen kinetic model, considering the photon counting process the only source of uncertainty. In this paper, we introduce a new probabilistic modeling strategy based on the key assumption that activity time course would be subject to uncertainty even if the parameters of the underlying dynamic process are known. This leads to a hierarchical model that we formulate using the formalism of probabilistic graphical modeling. The inference is addressed using a new iterative algorithm, in which kinetic modeling results are treated as prior expectation of activity time course, rather than as a deterministic match, making it possible to control the trade-off between a data-driven and a model-driven reconstruction. The proposed method is flexible to an arbitrary choice of (linear and nonlinear) kinetic models, it enables the inclusion of arbitrary (sub)differentiable priors for parametric maps, and it is simple to implement. Computer simulations and an application to a real-patient scan show how the proposed method is able to generalize over conventional indirect and direct approaches, providing a bridge between them by properly tuning the impact of the kinetic modeling step on image reconstruction.

Implementation of cylindrical PET scanners with block detector geometry in STIR

BACKGROUND

Software for Tomographic Image Reconstruction (STIR) is an open-source library for PET and SPECT image reconstruction, implementing iterative reconstruction as well as 2D- and 3D-filtered back projection. Quantitative reconstruction of PET data requires the knowledge of the scanner geometry. Typical scanners, clinical as well as pre-clinical ones, use a block-type geometry. Several rectangular blocks of crystals are arranged into regular polygons. Multiple of such polygons are arranged along the scanner axis. However, the geometrical representation of a scanner provided by STIR is a cylinder made of rings of individual crystals equally distributed in axial and transaxial directions. The data of realistic scanners are projected onto such virtual scanners prior to image reconstruction. This results in reduced quality of the reconstructed image. In this study, we implemented the above-described block geometry into the STIR library, permitting the image reconstruction without the interpolation step. In order to evaluate the difference in image quality, we performed Monte Carlo simulation studies of three different scanner designs: two scanners with multiple crystals per block and one with a single crystal per block. Simulated data were reconstructed using the standard STIR method and the newly implemented block geometry.

RESULTS

Visual comparison between the images reconstructed by the two models for the block-type scanners shows that the new implementation enhances the image quality to the extent that the results before normalization correction are comparable with those after normalization correction. The simulation result of a uniform cylinder shows that the coefficient of variation decreases from 25.8% to 20.9% by using the new implementation in STIR. Spatial resolution is enhanced resulting in a lower partial loss of intensity in sources of small size, e.g., the spill-over ratio for spherical sources of 1.8 mm diameter is 0.19 in the block and 0.34 in the cylindrical model.

CONCLUSIONS

Results indicate a significant improvement for the new model in comparison with the old one which mapped the polygonal geometry into a cylinder. The new implementation was tested and is available for use via the library of Swiss Federal Institute of Technology in Zurich (ETH).

Improvement of image quality in PET using post-reconstruction hybrid spatial-frequency domain filtering

PET images commonly suffer from the high noise level and poor signal-to-noise ratio (SNR), thus adversely impacting lesion detectability and quantitative accuracy. In this work, a novel hybrid dual-domain PET denoising approach is proposed, which combines the advantages of both spatial and transform domain filtering to preserve image textures while minimizing quantification uncertainty. Spatial domain denoising techniques excel at preserving high-contrast patterns compared to transform domain filters, which perform well in recovering low-contrast details normally smoothed out by spatial domain filters. For spatial domain filtering, the non-local mean algorithm was chosen owing to its performance in denoising high-contrast features whereas multi-scale curvelet denoising was exploited for the transform domain owing to its capability to recover small details. The proposed hybrid method was compared to conventional post-reconstruction Gaussian and edge preserving bilateral filters. Computer simulations of a thorax phantom containing three small lesions, experimental measurements using the Jaszczak phantom and clinical whole-body PET/CT studies were used to evaluate the performance of the proposed PET denoising technique. The proposed hybrid filter increased the SNR from 8.0 (non-filtered PET image) to 39.3 for small lesions in the computerized thorax phantom, while Gaussian and bilateral filtering led to SNRs of 23.3 and 24.4, respectively. For the experimental Jaszczak phantom, the contrast-to-noise ratio (CNR) improved from 10.84 when using Gaussian smoothing to 14.02 and 19.39 using the bilateral and the proposed hybrid filters, respectively. The clinical studies further demonstrated the superior performance of the hybrid method, yielding a quantification change (the original noisy OSEM image was used as reference in the absence of ground truth) in malignant lesions of  -2.4% compared to  -11.9% and  -6.6% achieved using Gaussian and bilateral filters, respectively. In some cases, the visual difference between the bilateral and hybrid filtered images is not substantial; however the improved CNR score from 11.3 by OSEM to 17.1 and 21.8 by bilateral to the hybrid filtering, respectively, demonstrates the overall gain achieved by the hybrid approach. The proposed hybrid algorithm improved the contrast, SNR and quantitative accuracy compared to Gaussian and bilateral approaches, and can be utilized as an alternative post-reconstruction filter in clinical PET/CT imaging.

Novel Quantitative PET Techniques for Clinical Decision Support in Oncology

Quantitative image analysis has deep roots in the usage of positron emission tomography (PET) in clinical and research settings to address a wide variety of diseases. It has been extensively employed to assess molecular and physiological biomarkers in vivo in healthy and disease states, in oncology, cardiology, neurology, and psychiatry. Quantitative PET allows relating the time-varying activity concentration in tissues/organs of interest and the basic functional parameters governing the biological processes being studied. Yet, quantitative PET is challenged by a number of degrading physical factors related to the physics of PET imaging, the limitations of the instrumentation used, and the physiological status of the patient. Moreover, there is no consensus on the most reliable and robust image-derived PET metric(s) that can be used with confidence in clinical oncology owing to the discrepancies between the conclusions reported in the literature. There is also increasing interest in the use of artificial intelligence based techniques, particularly machine learning and deep learning techniques in a variety of applications to extract quantitative features (radiomics) from PET including image segmentation and outcome prediction in clinical oncology. These novel techniques are revolutionizing clinical practice and are now offering unique capabilities to the clinical molecular imaging community and biomedical researchers at large. In this report, we summarize recent developments and future tendencies in quantitative PET imaging and present example applications in clinical decision support to illustrate its potential in the context of clinical oncology.

Enhancement of dynamic myocardial perfusion PET images based on low-rank plus sparse decomposition

BACKGROUND AND OBJECTIVE

The absolute quantification of dynamic myocardial perfusion (MP) PET imaging is challenged by the limited spatial resolution of individual frame images due to division of the data into shorter frames. This study aims to develop a method for restoration and enhancement of dynamic PET images.

METHODS

We propose that the image restoration model should be based on multiple constraints rather than a single constraint, given the fact that the image characteristic is hardly described by a single constraint alone. At the same time, it may be possible, but not optimal, to regularize the image with multiple constraints simultaneously. Fortunately, MP PET images can be decomposed into a superposition of background vs. dynamic components via low-rank plus sparse (L + S) decomposition. Thus, we propose an L + S decomposition based MP PET image restoration model and express it as a convex optimization problem. An iterative soft thresholding algorithm was developed to solve the problem. Using realistic dynamic ⁸²Rb MP PET scan data, we optimized and compared its performance with other restoration methods.

RESULTS

The proposed method resulted in substantial visual as well as quantitative accuracy improvements in terms of noise versus bias performance, as demonstrated in extensive ⁸²Rb MP PET simulations. In particular, the myocardium defect in the MP PET images had improved visual as well as contrast versus noise tradeoff. The proposed algorithm was also applied on an 8-min clinical cardiac ⁸²Rb MP PET study performed on the GE Discovery PET/CT, and demonstrated improved quantitative accuracy (CNR and SNR) compared to other algorithms.

CONCLUSIONS

The proposed method is effective for restoration and enhancement of dynamic PET images.

Advances in PET/MR instrumentation and image reconstruction

The combination of positron emission tomography (PET) and MRI has attracted the attention of researchers in the past approximately 20 years in small-animal imaging and more recently in clinical research. The combination of PET/MRI allows researchers to explore clinical and research questions in a wide number of fields, some of which are briefly mentioned here. An important number of groups have developed different concepts to tackle the problems that PET instrumentation poses to the exposition of electromagnetic fields. We have described most of these research developments in preclinical and clinical experiments, including the few commercial scanners available. From the software perspective, an important number of algorithms have been developed to address the attenuation correction issue and to exploit the possibility that MRI provides for motion correction and quantitative image reconstruction, especially parametric modelling of radiopharmaceutical kinetics. In this work, we give an overview of some exemplar applications of simultaneous PET/MRI, together with technological hardware and software developments.

Towards enhanced PET quantification in clinical oncology

Positron emission tomography (PET) has, since its inception, established itself as the imaging modality of choice for the in vivo quantitative assessment of molecular targets in a wide range of biochemical processes underlying tumour physiology. PET image quantification enables to ascertain a direct link between the time-varying activity concentration in organs/tissues and the fundamental parameters portraying the biological processes at the cellular level being assessed. However, the quantitative potential of PET may be affected by a number of factors related to physical effects, hardware and software system specifications, tracer kinetics, motion, scan protocol design and limitations in current image-derived PET metrics. Given the relatively large number of PET metrics reported in the literature, the selection of the best metric for fulfilling a specific task in a particular application is still a matter of debate. Quantitative PET has advanced elegantly during the last two decades and is now reaching the maturity required for clinical exploitation, particularly in oncology where it has the capability to open many avenues for clinical diagnosis, assessment of response to treatment and therapy planning. Therefore, the preservation and further enhancement of the quantitative features of PET imaging is crucial to ensure that the full clinical value of PET imaging modality is utilized in clinical oncology. Recent advancements in PET technology and methodology have paved the way for faster PET acquisitions of enhanced sensitivity to support the clinical translation of highly quantitative four-dimensional (4D) parametric imaging methods in clinical oncology. In this report, we provide an overview of recent advances and future trends in quantitative PET imaging in the context of clinical oncology. The pros/cons of the various image-derived PET metrics will be discussed and the promise of novel methodologies will be highlighted.

Reproducibility of F18-FDG PET radiomic features for different cervical tumor segmentation methods, gray-level discretization, and reconstruction algorithms

Site‐specific investigations of the role of radiomics in cancer diagnosis and therapy are emerging. We evaluated the reproducibility of radiomic features extracted from ¹⁸Flourine–fluorodeoxyglucose (¹⁸F‐FDG) PET images for three parameters: manual versus computer‐aided segmentation methods, gray‐level discretization, and PET image reconstruction algorithms. Our cohort consisted of pretreatment PET/CT scans from 88 cervical cancer patients. Two board‐certified radiation oncologists manually segmented the metabolic tumor volume (MTV₁ and MTV₂) for each patient. For comparison, we used a graphical‐based method to generate semiautomated segmented volumes (GBSV). To address any perturbations in radiomic feature values, we down‐sampled the tumor volumes into three gray‐levels: 32, 64, and 128 from the original gray‐level of 256. Finally, we analyzed the effect on radiomic features on PET images of eight patients due to four PET 3D‐reconstruction algorithms: maximum likelihood‐ordered subset expectation maximization (OSEM) iterative reconstruction (IR) method, fourier rebinning‐ML‐OSEM (FOREIR), FORE‐filtered back projection (FOREFBP), and 3D‐Reprojection (3DRP) analytical method. We extracted 79 features from all segmentation method, gray‐levels of down‐sampled volumes, and PET reconstruction algorithms. The features were extracted using gray‐level co‐occurrence matrices (GLCM), gray‐level size zone matrices (GLSZM), gray‐level run‐length matrices (GLRLM), neighborhood gray‐tone difference matrices (NGTDM), shape‐based features (SF), and intensity histogram features (IHF). We computed the Dice coefficient between each MTV and GBSV to measure segmentation accuracy. Coefficient values close to one indicate high agreement, and values close to zero indicate low agreement. We evaluated the effect on radiomic features by calculating the mean percentage differences (d¯) between feature values measured from each pair of parameter elements (i.e. segmentation methods: MTV₁‐MTV₂, MTV₁‐GBSV, MTV₂‐GBSV; gray‐levels: 64‐32, 64‐128, and 64‐256; reconstruction algorithms: OSEM‐FORE‐OSEM, OSEM‐FOREFBP, and OSEM‐3DRP). We used |d¯| as a measure of radiomic feature reproducibility level, where any feature scored |d¯| ±SD ≤ |25|% ± 35% was considered reproducible. We used Bland–Altman analysis to evaluate the mean, standard deviation (SD), and upper/lower reproducibility limits (U/LRL) for radiomic features in response to variation in each testing parameter. Furthermore, we proposed U/LRL as a method to classify the level of reproducibility: High— ±1% ≤ U/LRL ≤ ±30%; Intermediate— ±30% < U/LRL ≤ ±45%; Low— ±45 < U/LRL ≤ ±50%. We considered any feature below the low level as nonreproducible (NR). Finally, we calculated the interclass correlation coefficient (ICC) to evaluate the reliability of radiomic feature measurements for each parameter. The segmented volumes of 65 patients (81.3%) scored Dice coefficient >0.75 for all three volumes. The result outcomes revealed a tendency of higher radiomic feature reproducibility among segmentation pair MTV₁‐GBSV than MTV₂‐GBSV, gray‐level pairs of 64‐32 and 64‐128 than 64‐256, and reconstruction algorithm pairs of OSEM‐FOREIR and OSEM‐FOREFBP than OSEM‐3DRP. Although the choice of cervical tumor segmentation method, gray‐level value, and reconstruction algorithm may affect radiomic features, some features were characterized by high reproducibility through all testing parameters. The number of radiomic features that showed insensitivity to variations in segmentation methods, gray‐level discretization, and reconstruction algorithms was 10 (13%), 4 (5%), and 1 (1%), respectively. These results suggest that a careful analysis of the effects of these parameters is essential prior to any radiomics clinical application.

Time-invariant component-based normalization for a simultaneous PET-MR scanner

Component-based normalization is a method used to compensate for the sensitivity of each of the lines of response acquired in positron emission tomography. This method consists of modelling the sensitivity of each line of response as a product of multiple factors, which can be classified as time-invariant, time-variant and acquisition-dependent components. Typical time-variant factors are the intrinsic crystal efficiencies, which are needed to be updated by a regular normalization scan. Failure to do so would in principle generate artifacts in the reconstructed images due to the use of out of date time-variant factors. For this reason, an assessment of the variability and the impact of the crystal efficiencies in the reconstructed images is important to determine the frequency needed for the normalization scans, as well as to estimate the error obtained when an inappropriate normalization is used. Furthermore, if the fluctuations of these components are low enough, they could be neglected and nearly artifact-free reconstructions become achievable without performing a regular normalization scan. In this work, we analyse the impact of the time-variant factors in the component-based normalization used in the Biograph mMR scanner, but the work is applicable to other PET scanners. These factors are the intrinsic crystal efficiencies and the axial factors. For the latter, we propose a new method to obtain fixed axial factors that was validated with simulated data. Regarding the crystal efficiencies, we assessed their fluctuations during a period of 230 d and we found that they had good stability and low dispersion. We studied the impact of not including the intrinsic crystal efficiencies in the normalization when reconstructing simulated and real data. Based on this assessment and using the fixed axial factors, we propose the use of a time-invariant normalization that is able to achieve comparable results to the standard, daily updated, normalization factors used in this scanner. Moreover, to extend the analysis to other scanners, we generated distributions of crystal efficiencies with greater fluctuations than those found in the Biograph mMR scanner and evaluated their impact in simulations with a wide variety of noise levels. An important finding of this work is that a regular normalization scan is not needed in scanners with photodetectors with relatively low dispersion in their efficiencies.

Singular value decomposition for photon-processing nuclear imaging systems and applications for reconstruction and computing null functions

Recent advances in technology are enabling a new class of nuclear imaging systems consisting of detectors that use real-time maximum-likelihood (ML) methods to estimate the interaction position, deposited energy, and other attributes of each photon-interaction event and store these attributes in a list format. This class of systems, which we refer to as photon-processing (PP) nuclear imaging systems, can be described by a fundamentally different mathematical imaging operator that allows processing of the continuous-valued photon attributes on a per-photon basis. Unlike conventional photon-counting (PC) systems that bin the data into images, PP systems do not have any binning-related information loss. Mathematically, while PC systems have an infinite-dimensional null space due to dimensionality considerations, PP systems do not necessarily suffer from this issue. Therefore, PP systems have the potential to provide improved performance in comparison to PC systems. To study these advantages, we propose a framework to perform the singular-value decomposition (SVD) of the PP imaging operator. We use this framework to perform the SVD of operators that describe a general two-dimensional (2D) planar linear shift-invariant (LSIV) PP system and a hypothetical continuously rotating 2D single-photon emission computed tomography (SPECT) PP system. We then discuss two applications of the SVD framework. The first application is to decompose the object being imaged by the PP imaging system into measurement and null components. We compare these components to the measurement and null components obtained with PC systems. In the process, we also present a procedure to compute the null functions for a PC system. The second application is designing analytical reconstruction algorithms for PP systems. The proposed analytical approach exploits the fact that PP systems acquire data in a continuous domain to estimate a continuous object function. The approach is parallelizable and implemented for graphics processing units (GPUs). Further, this approach leverages another important advantage of PP systems, namely the possibility to perform photon-by-photon real-time reconstruction. We demonstrate the application of the approach to perform reconstruction in a simulated 2D SPECT system. The results help to validate and demonstrate the utility of the proposed method and show that PP systems can help overcome the aliasing artifacts that are otherwise intrinsically present in PC systems.

Applications of the line-of-response probability density function resolution model in PET list mode reconstruction

Resolution degradation in PET image reconstruction can be caused by inaccurate modeling of the physical factors in the acquisition process. Resolution modeling (RM) is a common technique that takes into account the resolution degrading factors in the system matrix. Our previous work has introduced a probability density function (PDF) method of deriving the resolution kernels from Monte Carlo simulation and parameterizing the LORs to reduce the number of kernels needed for image reconstruction. In addition, LOR-PDF allows different PDFs to be applied to LORs from different crystal layer pairs of the HRRT. In this study, a thorough test was performed with this new model (LOR-PDF) applied to two PET scanners-the HRRT and Focus-220. A more uniform resolution distribution was observed in point source reconstructions by replacing the spatially-invariant kernels with the spatially-variant LOR-PDF. Specifically, from the center to the edge of radial field of view (FOV) of the HRRT, the measured in-plane FWHMs of point sources in a warm background varied slightly from 1.7 mm to 1.9 mm in LOR-PDF reconstructions. In Minihot and contrast phantom reconstructions, LOR-PDF resulted in up to 9% higher contrast at any given noise level than image-space resolution model. LOR-PDF also has the advantage in performing crystal-layer-dependent resolution modeling. The contrast improvement by using LOR-PDF was verified statistically by replicate reconstructions. In addition, [(11)C]AFM rats imaged on the HRRT and [(11)C]PHNO rats imaged on the Focus-220 were utilized to demonstrated the advantage of the new model. Higher contrast between high-uptake regions of only a few millimeter diameter and the background was observed in LOR-PDF reconstruction than in other methods.

An update on novel quantitative techniques in the context of evolving whole-body PET imaging

Since its foundation PET has established itself as one of the standard imaging modalities enabling the quantitative assessment of molecular targets in vivo. In the past two decades, quantitative PET has become a necessity in clinical oncology. Despite introduction of various measures for quantification and correction of PET parameters, there is debate on the selection of the appropriate methodology in specific diseases and conditions. In this review, we have focused on these techniques with special attention to topics such as static and dynamic whole body PET imaging, tracer kinetic modeling, global disease burden, texture analysis and radiomics, dual time point imaging and partial volume correction.

Multiple importance sampling for PET

This paper proposes the application of multiple importance sampling in fully 3-D positron emission tomography to speed up the iterative reconstruction process. The proposed method combines the results of lines of responses (LOR) driven and voxel driven projections keeping their advantages, like importance sampling, performance and parallel execution on graphics processing units. Voxel driven methods can focus on point like features while LOR driven approaches are efficient in reconstructing homogeneous regions. The theoretical basis of the combination is the application of the mixture of the samples generated by the individual importance sampling methods, emphasizing a particular method where it is better than others. The proposed algorithms are built into the Tera-tomo system.

Averaging and Metropolis iterations for positron emission tomography

Iterative positron emission tomography (PET) reconstruction computes projections between the voxel space and the lines of response (LOR) space, which are mathematically equivalent to the evaluation of multi-dimensional integrals. The dimension of the integration domain can be very high if scattering needs to be compensated. Monte Carlo (MC) quadrature is a straightforward method to approximate high-dimensional integrals. As the numbers of voxels and LORs can be in the order of hundred millions and the projection also depends on the measured object, the quadratures cannot be precomputed, but Monte Carlo simulation should take place on-the-fly during the iterative reconstruction process. This paper presents modifications of the maximum likelihood, expectation maximization (ML-EM) iteration scheme to reduce the reconstruction error due to the on-the-fly MC approximations of forward and back projections. If the MC sample locations are the same in every iteration step of the ML-EM scheme, then the approximation error will lead to a modified reconstruction result. However, when random estimates are statistically independent in different iteration steps, then the iteration may either diverge or fluctuate around the solution. Our goal is to increase the accuracy and the stability of the iterative solution while keeping the number of random samples and therefore the reconstruction time low. We first analyze the error behavior of ML-EM iteration with on-the-fly MC projections, then propose two solutions: averaging iteration and Metropolis iteration. Averaging iteration averages forward projection estimates during the iteration sequence. Metropolis iteration rejects those forward projection estimates that would compromise the reconstruction and also guarantees the unbiasedness of the tracer density estimate. We demonstrate that these techniques allow a significant reduction of the required number of samples and thus the reconstruction time. The proposed methods are built into the Teratomo system.

Novel Quantitative Techniques in Hybrid (PET-MR) Imaging of Brain Tumors

Brain tumors are a collection of heterogeneous intracranial neoplasms. Molecular PET and anatomic MR imaging together can provide reliable quantitative information on tumor characterization, and help in treatment planning and monitoring therapeutic evaluation, noninvasively. Coregistration of MRI and PET images have been successfully used to improve diagnostic accuracy and in evaluating treatment response. Whole-body PET-MR scanners capable of assessing morphologic, metabolic, and functional information simultaneously are now commercially available. Early clinical studies speculate that PET-MR will be useful in several clinical specialties. In this report, we highlight the advances and applications of hybrid PET-MR in quantitative brain tumor imaging.

3.5D dynamic PET image reconstruction incorporating kinetics-based clusters

Standard 3D dynamic positron emission tomographic (PET) imaging consists of independent image reconstructions of individual frames followed by application of appropriate kinetic model to the time activity curves at the voxel or region-of-interest (ROI). The emerging field of 4D PET reconstruction, by contrast, seeks to move beyond this scheme and incorporate information from multiple frames within the image reconstruction task. Here we propose a novel reconstruction framework aiming to enhance quantitative accuracy of parametric images via introduction of priors based on voxel kinetics, as generated via clustering of preliminary reconstructed dynamic images to define clustered neighborhoods of voxels with similar kinetics. This is then followed by straightforward maximum a posteriori (MAP) 3D PET reconstruction as applied to individual frames; and as such the method is labeled '3.5D' image reconstruction. The use of cluster-based priors has the advantage of further enhancing quantitative performance in dynamic PET imaging, because: (a) there are typically more voxels in clusters than in conventional local neighborhoods, and (b) neighboring voxels with distinct kinetics are less likely to be clustered together. Using realistic simulated (11)C-raclopride dynamic PET data, the quantitative performance of the proposed method was investigated. Parametric distribution-volume (DV) and DV ratio (DVR) images were estimated from dynamic image reconstructions using (a) maximum-likelihood expectation maximization (MLEM), and MAP reconstructions using (b) the quadratic prior (QP-MAP), (c) the Green prior (GP-MAP) and (d, e) two proposed cluster-based priors (CP-U-MAP and CP-W-MAP), followed by graphical modeling, and were qualitatively and quantitatively compared for 11 ROIs. Overall, the proposed dynamic PET reconstruction methodology resulted in substantial visual as well as quantitative accuracy improvements (in terms of noise versus bias performance) for parametric DV and DVR images. The method was also tested on a 90 min (11)C-raclopride patient study performed on the high-resolution research tomography. The proposed method was shown to outperform the conventional method in visual as well as quantitative accuracy improvements (in terms of noise versus regional DVR value performance).