PET image reconstruction using kernel method

A kernel-based image denoising method for improving parametric image generation

One of the main challenges in the pixel-wise modeling analysis is the presence of high noise levels. Wang and Qi proposed a kernel-based method for dynamic positron emission tomgraphy reconstruction. Inspired by this method, we propose a kernel-based image denoising method based on the minimization of a kernel-based lp-norm regularized problem. To solve the kernel-based image denoising problem, we used the general-threshold filtering algorithm in combination with total difference. In the present study, we investigated whether diffusion-weighted magnetic resonance imaging (DW-MRI) data denoised using the proposed method can provide improved intravoxel incoherent motion (IVIM) parametric images. We also compared the proposed method with the method using the local principal component analysis (LPCA). The simulated DW-MR magnitude images are assumed to have Rician distributed noise. Computer simulations show that the proposed image denoising method can achieve a better bias-variance trade-off than the LPCA method. Moreover, the proposed method can reduce variance while simultaneously preserving edges in the parametric images. We tested our image denoising method on in vivo DW-MRI data, and the result showed that the denoised DWI-MRI data obtained using the proposed method can substantially improve the quality of IVIM parametric images.

Two novel PET image restoration methods guided by PET-MR kernels: Application to brain imaging

PURPOSE

Post-reconstruction positron emission tomography (PET) image restoration methods that take advantage of available anatomical information can play an important role in accurate quantification of PET images. However, when using anatomical information, the resulting PET image may lose resolution in certain regions where the anatomy does not agree with the change in functional activity. In this work, this problem is addressed by using both magnetic resonance (MR) and filtered PET images to guide the denoising process.

METHODS

In this work, two novel post-reconstruction methods for restoring PET images using the subject's registered T1-weighted MR image are proposed. The first method is based on a representation of the image using basis functions extracted from T1-weighted MR and filtered PET image. The coefficients for these basis functions are estimated using a sparsity-penalized least squares objective function. The second method is a noniterative fast method that uses guided kernel filtering in combination with twicing to restore the noisy PET image. When applied after conventional PVE correction, these methods can be considered as voxel-based MR-guided partial volume effect (PVE) correction methods.

RESULTS

Using simulation analyses of [ 18 F]FDG PET images of the brain with lesions, the proposed methods are compared to other denoising methods through different figures of merit. The results show promising improvements in image quality as well as reduction in bias and variance of the lesions. We also show the application of the proposed methods on real [ 18 F]FDG data.

CONCLUSION

Two methods for restoring PET images were proposed. The methods were evaluated on simulation and real brain images. Most MR-guided PVE correction methods are only based on segmented T1-weighted images and their accuracy is very sensitive to segmentation errors, especially in regions of abnormalities and lesions. However, both proposed methods can use the T1-weighted image without segmentation. The simplicity and the very low computational cost of the second method make it suitable for clinical applications and large data studies. The proposed methods can be naturally extended to PVE correction and denoising of other functional modalities using corresponding anatomical information.

Indirect methods for improving parameter estimation of PET kinetic models

PURPOSE

Parametric images obtained from kinetic modeling of dynamic positron emission tomography (PET) data provide a new way of visualizing quantitative parameters of the tracer kinetics. However, due to the high noise level in pixel-wise image-driven time-activity curves, parametric images often suffer from poor quality and accuracy. In this study, we propose an indirect parameter estimation framework which aims to improve the quality and quantitative accuracy of parametric images.

METHODS

Three different approaches related to noise reduction and advanced curve fitting algorithm are used in the proposed framework. First, dynamic PET images are denoised using a kernel-based denoising method and the highly constrained backprojection technique. Second, gradient-free curve fitting algorithms are exploited to improve the accuracy and precision of parameter estimates. Third, a kernel-based post-filtering method is applied to parametric images to further improve the quality of parametric images. Computer simulations were performed to evaluate the performance of the proposed framework.

RESULTS AND CONCLUSIONS

The simulation results showed that when compared to the Gaussian filtering, the proposed denoising method could provide better PET image quality, and consequentially improve the quality and quantitative accuracy of parametric images. In addition, gradient-free optimization algorithms (i.e., pattern search) can result in better parametric images than the gradient-based curve fitting algorithm (i.e., trust-region-reflective). Finally, our results showed that the proposed kernel-based post-filtering method could further improve the precision of parameter estimates while maintaining the accuracy of parameter estimates.

High Temporal-Resolution Dynamic PET Image Reconstruction Using a New Spatiotemporal Kernel Method

Current clinical dynamic PET has an effective temporal resolution of 5-10 seconds, which can be adequate for traditional compartmental modeling but is inadequate for exploiting the benefit of more advanced tracer kinetic modeling for characterization of diseases (e.g., cancer and heart disease). There is a need to improve dynamic PET to allow fine temporal sampling of 1-2 seconds. However, the reconstruction of these short-time frames from tomographic data is extremely challenging as the count level of each frame is very low and high noise presents in both spatial and temporal domains. Previously, the kernel framework has been developed and demonstrated as a statistically efficient approach to utilizing image prior for low-count PET image reconstruction. Nevertheless, the existing kernel methods mainly explore spatial correlations in the data and only have a limited ability in suppressing temporal noise. In this paper, we propose a new kernel method which extends the previous spatial kernel method to the general spatiotemporal domain. The new kernelized model encodes both spatial and temporal correlations obtained from image prior information and are incorporated into the PET forward projection model to improve themaximumlikelihood(ML) image reconstruction. Computer simulations and an application to real patient scan have shown that the proposed approach can achieve effective noise reduction in both spatial and temporal domains and outperform the spatial kernel method and conventional ML reconstruction method for improving the high temporal-resolution dynamic PET imaging.

Iterative PET Image Reconstruction Using Convolutional Neural Network Representation

PET image reconstruction is challenging due to the ill-poseness of the inverse problem and limited number of detected photons. Recently, the deep neural networks have been widely and successfully used in computer vision tasks and attracted growing interests in medical imaging. In this paper, we trained a deep residual convolutional neural network to improve PET image quality by using the existing inter-patient information. An innovative feature of the proposed method is that we embed the neural network in the iterative reconstruction framework for image representation, rather than using it as a post-processing tool. We formulate the objective function as a constrained optimization problem and solve it using the alternating direction method of multipliers algorithm. Both simulation data and hybrid real data are used to evaluate the proposed method. Quantification results show that our proposed iterative neural network method can outperform the neural network denoising and conventional penalized maximum likelihood methods.

Hybrid PET/MR Kernelised Expectation Maximisation Reconstruction for Improved Image-Derived Estimation of the Input Function from the Aorta of Rabbits

Positron emission tomography (PET) provides simple noninvasive imaging biomarkers for multiple human diseases which can be used to produce quantitative information from single static images or to monitor dynamic processes. Such kinetic studies often require the tracer input function (IF) to be measured but, in contrast to direct blood sampling, the image-derived input function (IDIF) provides a noninvasive alternative technique to estimate the IF. Accurate estimation can, in general, be challenging due to the partial volume effect (PVE), which is particularly important in preclinical work on small animals. The recently proposed hybrid kernelised ordered subsets expectation maximisation (HKEM) method has been shown to improve accuracy and contrast across a range of different datasets and count levels and can be used on PET/MR or PET/CT data. In this work, we apply the method with the purpose of providing accurate estimates of the aorta IDIF for rabbit PET studies. In addition, we proposed a method for the extraction of the aorta region of interest (ROI) using the MR and the HKEM image, to minimise the PVE within the rabbit aortic region-a method which can be directly transferred to the clinical setting. A realistic simulation study was performed with ten independent noise realisations while two, real data, rabbit datasets, acquired with the Biograph Siemens mMR PET/MR scanner, were also considered. For reference and comparison, the data were reconstructed using OSEM, OSEM with Gaussian postfilter and KEM, as well as HKEM. The results across the simulated datasets and different time frames show reduced PVE and accurate IDIF values for the proposed method, with 5% average bias (0.8% minimum and 16% maximum bias). Consistent results were obtained with the real datasets. The results of this study demonstrate that HKEM can be used to accurately estimate the IDIF in preclinical PET/MR studies, such as rabbit mMR data, as well as in clinical human studies. The proposed algorithm is made available as part of an open software library, and it can be used equally successfully on human or animal data acquired from a variety of PET/MR or PET/CT scanners.

Positron emission tomography image reconstruction using feature extraction

PURPOSE

To reduce the cost of positron emission tomography (PET) scanning systems, image reconstruction algorithms for low-sampled data have been extensively studied. However, the current method based on total variation (TV) minimization regularization nested in the maximum likelihood-expectation maximization (MLEM) algorithm cannot distinguish true structures from noise resulting losing some fine features in the images. Thus, this work aims to recover fine features lost in the MLEM-TV algorithm from low-sampled data.

METHOD

A feature refinement (FR) approach previously developed for statistical interior computed tomography (CT) reconstruction is applied to PET imaging to recover fine features in this study. The proposed method starts with a constant initial image and the FR step is performed after each MLEM-TV iteration to extract the desired structural information lost during TV minimization. A feature descriptor is specifically designed to distinguish structure from noise and artifacts. A modified steepest descent method is adopted to minimize the objective function. After evaluating the impacts of different patch sizes on the outcome of the presented method, an optimal patch size of 7×7 is selected in this study to balance structure-detection ability and computational efficiency.

RESULTS

Applying MLEM-TV-FR algorithm to the simulated brain PET imaging using an emission activity phantom, a standard Shepp-Logan phantom, and mouse results in the increased peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) as comparing to using the conventional MLEM-TV algorithm, as well as the substantial reduction of the used sampling numbers, which improves the computational efficiency.

CONCLUSIONS

The presented algorithm can achieve image quality superior to that of the MLEM and MLEM-TV approaches in terms of the preservation of fine structure and the suppression of undesired artifacts and noise, indicating its useful potential for low-sampled data in PET imaging.

Effect of PET-MR Inconsistency in the Kernel Image Reconstruction Method

Anatomically-driven image reconstruction algorithms have become very popular in positron emission tomography (PET) where they have demonstrated improved image resolution and quantification. This work, consider the effect of spatial inconsistency between MR and PET images in hot and cold regions of the PET image. We investigate these effects on the kernel method from machine learning, in particular, the hybrid kernelized expectation maximization (HKEM). These were applied to Jaszczak phantom and patient data acquired with the Biograph Siemens mMR. The results show that even a small shift can cause a significant change in activity concentration. In general, the PET-MR inconsistencies can induce the partial volume effect, more specifically the 'spill-in' of the affected cold regions and the 'spill-out' from the hot regions. The maximum change was about 100% for the cold region and 10% for the hot lesion using KEM, against the 37% and 8% obtained with HKEM. The findings of this work suggest that including PET information in the kernel enhances the flexibility of the reconstruction in case of spatial inconsistency. Nevertheless, accurate registration and choice of the appropriate MR image for the creation of the kernel is essential to avoid artifacts, blurring, and bias.

Multi-Tracer Guided PET Image Reconstruction

Multi-tracer positron emission tomography (PET) has the potential to enhance PET imaging by providing complementary information from different physiological processes. However, one or more of the images may present high levels of noise. Guided image reconstruction methods transfer information from a guide image into the PET image reconstruction to encourage edge-preserving noise reduction. In this work we aim to reduce noise in poorer quality PET datasets via guidance from higher quality ones by using a weighted quadratic penalty approach. In particular, we applied this methodology to [18F]fluorodeoxyglucose (FDG) and [11C]methionine imaging of gliomas. 3D simulation studies showed that guiding the reconstruction of methionine datasets using pre-existing FDG images reduced reconstruction errors across the whole-brain (-8%) and within a tumour (-36%) compared to maximum likelihood expectation-maximisation (MLEM). Furthermore, guided reconstruction outperformed a comparable non-local means filter, indicating that regularising during reconstruction is preferable to post-reconstruction approaches. Hyperparameters selected from the 3D simulation study were applied to real data, where it was observed that the proposed FDG-guided methionine reconstruction allows for better edge preservation and noise reduction than standard MLEM. Overall, the results in this work demonstrate that transferring information between datasets in multi-tracer PET studies improves image quality and quantification performance.

Spatially-Compact MR-Guided Kernel EM for PET Image Reconstruction

Positron emission tomography (PET) is a highly sensitive functional and molecular imaging modality which can measure picomolar concentrations of an injected radionuclide. However, the physical sensitivity of PET is limited, and reducing the injected dose leads to low count data and noisy reconstructed images. A highly effective way of reducing noise is to reparameterise the reconstruction in terms of MR-derived spatial basis functions. Spatial basis functions derived using the kernel method have demonstrated excellent noise reduction properties and maintain shared PET-MR detailed structures. However, as previously shown in the literature, the MR-guided kernel method may lead to excessive smoothing of structures that are only present in the PET data. This work makes two main contributions in order to address this problem: first, we exploit the potential of the MR-guided kernel method to form more spatially-compact basis functions which are able to preserve PET-unique structures, and secondly, we consider reconstruction at the native MR resolution. The former contribution notably improves the recovery of structures which are unique to the PET data. These adaptations of the kernel method were compared to the conventional implementation of the MR-guided kernel method and also to MLEM, in terms of ability to recover PET unique structures for both simulated and real data. The spatially-compact kernel method showed clear visual and quantitative improvements in the reconstruction of the PET unique structures, relative to the conventional kernel method for all sizes of PET unique structures investigated, whilst maintaining to a large extent the impressive noise mitigating and detail preserving properties of the conventional MR-guided kernel method. We therefore conclude that a spatially-compact parameterisation of the MR-guided kernel method, should be the preferred implementation strategy in order to obviate unnecessary losses in PET-unique details.

Advances in PET Methodology

Recent advances in disease understanding, instrumentation technology, and computationally demanding image analysis approaches are opening new frontiers in the investigation of movement disorders and brain disease in general. A key aspect is the recognition of the need to determine molecular correlates to early functional and metabolic connectivity alterations, which are increasingly recognized as useful signatures of specific clinical disease phenotypes. Such multi-modal approaches are highly likely to provide new information on pathogenic mechanisms and to help the identification of novel therapeutic targets. This chapter describes recent methodological developments in PET starting with a very brief overview of radiotracers relevant to movement disorders while emphasizing the development of instrumentation, algorithms and imaging analysis methods relevant to multi-modal investigation of movement disorders.

Dynamic PET of human liver inflammation: impact of kinetic modeling with optimization-derived dual-blood input function

The hallmark of nonalcoholic steatohepatitis is hepatocellular inflammation and injury in the setting of hepatic steatosis. Recent work has indicated that dynamic 18F-FDG PET with kinetic modeling has the potential to assess hepatic inflammation noninvasively, while static FDG-PET is less promising. Because the liver has dual blood supplies, kinetic modeling of dynamic liver PET data is challenging in human studies. This paper aims to identify the optimal dual-input kinetic modeling approach for dynamic FDG-PET of human liver inflammation. Fourteen patients with nonalcoholic fatty liver disease were included. Each patient underwent 1 h dynamic FDG-PET/CT scan and had liver biopsy within six weeks. Three models were tested for kinetic analysis: the traditional two-tissue compartmental model with an image-derived single-blood input function (SBIF), a model with population-based dual-blood input function (DBIF), and a new model with optimization-derived DBIF through a joint estimation framework. The three models were compared using Akaike information criterion (AIC), F test and histopathologic inflammation score. Results showed that the optimization-derived DBIF model improved liver time activity curve fitting and achieved lower AIC values and higher F values than the SBIF and population-based DBIF models in all patients. The optimization-derived model significantly increased FDG K1 estimates by 101% and 27% as compared with traditional SBIF and population-based DBIF. K1 by the optimization-derived model was significantly associated with histopathologic grades of liver inflammation while the other two models did not provide a statistical significance. In conclusion, modeling of DBIF is critical for dynamic liver FDG-PET kinetic analysis in human studies. The optimization-derived DBIF model is more appropriate than SBIF and population-based DBIF for dynamic FDG-PET of liver inflammation.

An Efficient Approach to Perform MR-assisted PET Data Optimization in Simultaneous PET/MR Neuroimaging Studies

A main advantage of PET is that it provides quantitative measures of the radiotracer concentration, but its accuracy is confounded by several factors, including attenuation, subject motion, and limited spatial resolution. Using the information from one simultaneously acquired morphological MR sequence with embedded navigators, we propose an efficient method called MR-assisted PET data optimization (MaPET) to perform attenuation correction (AC), motion correction, and anatomy-aided reconstruction. Methods: For attenuation correction, voxel-wise linear attenuation coefficient maps were generated using an SPM8-based approach method on the MR volume. The embedded navigators were used to derive head motion estimates for event-based PET motion correction. The anatomy provided by the MR volume was incorporated into the PET image reconstruction using a kernel-based method. Region-based analyses were carried out to assess the quality of images generated through various stages of PET data optimization. Results: The optimized PET images reconstructed with MaPET was superior in image quality compared to images reconstructed using only attenuation correction, with high SNR and low coefficient of variation (5.08 and 0.229 in a composite cortical region compared to 3.12 and 0.570). The optimized images were also shown using the Cohen's d metric to achieve a greater effect size in distinguishing cortical regions with hypometabolism from regions of preserved metabolism in each individual for different diagnosis groups. Conclusion: We have shown the spatiotemporally correlated data acquired using a single MR sequence can be used for PET attenuation, motion and partial volume effects corrections and the MaPET method may enable more accurate assessment of pathological changes in dementia and other brain disorders.

Artificial Neural Network Enhanced Bayesian PET Image Reconstruction

In positron emission tomography (PET) image reconstruction, the Bayesian framework with various regularization terms has been implemented to constrain the radio tracer distribution. Varying the regularizing weight of a maximum a posteriori (MAP) algorithm specifies a lower bound of the tradeoff between variance and spatial resolution measured from the reconstructed images. The purpose of this paper is to build a patch-based image enhancement scheme to reduce the size of the unachievable region below the bound and thus to quantitatively improve the Bayesian PET imaging. We cast the proposed enhancement as a regression problem which models a highly nonlinear and spatial-varying mapping between the reconstructed image patches and an enhanced image patch. An artificial neural network model named multilayer perceptron (MLP) with backpropagation was used to solve this regression problem through learning from examples. Using the BrainWeb phantoms, we simulated brain PET data at different count levels of different subjects with and without lesions. The MLP was trained using the image patches reconstructed with a MAP algorithm of different regularization parameters for one normal subject at a certain count level. To evaluate the performance of the trained MLP, reconstructed images from other simulations and two patient brain PET imaging data sets were processed. In every testing cases, we demonstrate that the MLP enhancement technique improves the noise and bias tradeoff compared with the MAP reconstruction using different regularizing weights thus decreasing the size of the unachievable region defined by the MAP algorithm in the variance/resolution plane.

MR-Guided Kernel EM Reconstruction for Reduced Dose PET Imaging

PET image reconstruction is highly susceptible to the impact of Poisson noise, and if shorter acquisition times or reduced injected doses are used, the noisy PET data become even more limiting. The recent development of kernel expectation maximisation (KEM) is a simple way to reduce noise in PET images, and we show in this work that impressive dose reduction can be achieved when the kernel method is used with MR-derived kernels. The kernel method is shown to surpass maximum likelihood expectation maximisation (MLEM) for the reconstruction of low-count datasets (corresponding to those obtained at reduced injected doses) producing visibly clearer reconstructions for unsmoothed and smoothed images, at all count levels. The kernel EM reconstruction of 10% of the data had comparable whole brain voxel-level error measures to the MLEM reconstruction of 100% of the data (for simulated data, at 100 iterations). For regional metrics, the kernel method at reduced dose levels attained a reduced coefficient of variation and more accurate mean values compared to MLEM. However, the advances provided by the kernel method are at the expense of possible over-smoothing of features unique to the PET data. Further assessment on clinical data is required to determine the level of dose reduction that can be routinely achieved using the kernel method, whilst maintaining the diagnostic utility of the scan.

Direct Patlak Reconstruction From Dynamic PET Data Using the Kernel Method With MRI Information Based on Structural Similarity

Positron emission tomography (PET) is a functional imaging modality widely used in oncology, cardiology, and neuroscience. It is highly sensitive, but suffers from relatively poor spatial resolution, as compared with anatomical imaging modalities, such as magnetic resonance imaging (MRI). With the recent development of combined PET/MR systems, we can improve the PET image quality by incorporating MR information into image reconstruction. Previously, kernel learning has been successfully embedded into static and dynamic PET image reconstruction using either PET temporal or MRI information. Here, we combine both PET temporal and MRI information adaptively to improve the quality of direct Patlak reconstruction. We examined different approaches to combine the PET and MRI information in kernel learning to address the issue of potential mismatches between MRI and PET signals. Computer simulations and hybrid real-patient data acquired on a simultaneous PET/MR scanner were used to evaluate the proposed methods. Results show that the method that combines PET temporal information and MRI spatial information adaptively based on the structure similarity index has the best performance in terms of noise reduction and resolution improvement.

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.

Development and Evaluation of mini-EXPLORER: A Long Axial Field-of-View PET Scanner for Nonhuman Primate Imaging

We describe a long axial field-of-view (FOV) PET scanner for high-sensitivity and total-body imaging of nonhuman primates and present the physical performance and first phantom and animal imaging results. Methods: The mini-EXPLORER PET scanner was built using the components of a clinical scanner reconfigured with a detector ring diameter of 43.5 cm and an axial length of 45.7 cm. National Electrical Manufacturers Association (NEMA) NU-2 and NU-4 phantoms were used to measure sensitivity and count rate performance. Reconstructed spatial resolution was investigated by imaging a radially stepped point source and a Derenzo phantom. The effect of the wide acceptance angle was investigated by comparing performance with maximum acceptance angles of 14°-46°. Lastly, an initial assessment of the in vivo performance of the mini-EXPLORER was undertaken with a dynamic ¹⁸F-FDG nonhuman primate (rhesus monkey) imaging study. Results: The NU-2 total sensitivity was 5.0%, and the peak noise-equivalent count rate measured with the NU-4 monkey scatter phantom was 1,741 kcps, both obtained using the maximum acceptance angle (46°). The NU-4 scatter fraction was 16.5%, less than 1% higher than with a 14° acceptance angle. The reconstructed spatial resolution was approximately 3.0 mm at the center of the FOV, with a minor loss in axial spatial resolution (0.5 mm) when the acceptance angle increased from 14° to 46°. The rhesus monkey ¹⁸F-FDG study demonstrated the benefit of the high sensitivity of the mini-EXPLORER, including fast imaging (1-s early frames), excellent image quality (30-s and 5-min frames), and late-time-point imaging (18 h after injection), all obtained at a single bed position that captured the major organs of the rhesus monkey. Conclusion: This study demonstrated the physical performance and imaging capabilities of a long axial FOV PET scanner designed for high-sensitivity imaging of nonhuman primates. Further, the results of this study suggest that a wide acceptance angle can be used with a long axial FOV scanner to maximize sensitivity while introducing only minor trade-offs such as a small increase in scatter fraction and slightly degraded axial spatial resolution.

Simultaneous maximum a posteriori longitudinal PET image reconstruction

Positron emission tomography (PET) is frequently used to monitor functional changes that occur over extended time scales, for example in longitudinal oncology PET protocols that include routine clinical follow-up scans to assess the efficacy of a course of treatment. In these contexts PET datasets are currently reconstructed into images using single-dataset reconstruction methods. Inspired by recently proposed joint PET-MR reconstruction methods, we propose to reconstruct longitudinal datasets simultaneously by using a joint penalty term in order to exploit the high degree of similarity between longitudinal images. We achieved this by penalising voxel-wise differences between pairs of longitudinal PET images in a one-step-late maximum a posteriori (MAP) fashion, resulting in the MAP simultaneous longitudinal reconstruction (SLR) method. The proposed method reduced reconstruction errors and visually improved images relative to standard maximum likelihood expectation-maximisation (ML-EM) in simulated 2D longitudinal brain tumour scans. In reconstructions of split real 3D data with inserted simulated tumours, noise across images reconstructed with MAP-SLR was reduced to levels equivalent to doubling the number of detected counts when using ML-EM. Furthermore, quantification of tumour activities was largely preserved over a variety of longitudinal tumour changes, including changes in size and activity, with larger changes inducing larger biases relative to standard ML-EM reconstructions. Similar improvements were observed for a range of counts levels, demonstrating the robustness of the method when used with a single penalty strength. The results suggest that longitudinal regularisation is a simple but effective method of improving reconstructed PET images without using resolution degrading priors.

Anatomical image-guided fluorescence molecular tomography reconstruction using kernel method

Fluorescence molecular tomography (FMT) is an important in vivo imaging modality to visualize physiological and pathological processes in small animals. However, FMT reconstruction is ill-posed and ill-conditioned due to strong optical scattering in deep tissues, which results in poor spatial resolution. It is well known that FMT image quality can be improved substantially by applying the structural guidance in the FMT reconstruction. An approach to introducing anatomical information into the FMT reconstruction is presented using the kernel method. In contrast to conventional methods that incorporate anatomical information with a Laplacian-type regularization matrix, the proposed method introduces the anatomical guidance into the projection model of FMT. The primary advantage of the proposed method is that it does not require segmentation of targets in the anatomical images. Numerical simulations and phantom experiments have been performed to demonstrate the proposed approach’s feasibility. Numerical simulation results indicate that the proposed kernel method can separate two FMT targets with an edge-to-edge distance of 1 mm and is robust to false-positive guidance and inhomogeneity in the anatomical image. For the phantom experiments with two FMT targets, the kernel method has reconstructed both targets successfully, which further validates the proposed kernel method.

Dynamic PET simulator via tomographic emission projection for kinetic modeling and parametric image studies

PURPOSE

To develop and evaluate a fast and simple tool called dpetstep (Dynamic PET Simulator of Tracers via Emission Projection), for dynamic PET simulations as an alternative to Monte Carlo (MC), useful for educational purposes and evaluation of the effects of the clinical environment, postprocessing choices, etc., on dynamic and parametric images.

METHODS

The tool was developed in matlab using both new and previously reported modules of petstep (PET Simulator of Tracers via Emission Projection). Time activity curves are generated for each voxel of the input parametric image, whereby effects of imaging system blurring, counting noise, scatters, randoms, and attenuation are simulated for each frame. Each frame is then reconstructed into images according to the user specified method, settings, and corrections. Reconstructed images were compared to MC data, and simple Gaussian noised time activity curves (GAUSS).

RESULTS

dpetstep was 8000 times faster than MC. Dynamic images from dpetstep had a root mean square error that was within 4% on average of that of MC images, whereas the GAUSS images were within 11%. The average bias in dpetstep and MC images was the same, while GAUSS differed by 3% points. Noise profiles in dpetstep images conformed well to MC images, confirmed visually by scatter plot histograms, and statistically by tumor region of interest histogram comparisons that showed no significant differences (p < 0.01). Compared to GAUSS, dpetstep images and noise properties agreed better with MC.

CONCLUSIONS

The authors have developed a fast and easy one-stop solution for simulations of dynamic PET and parametric images, and demonstrated that it generates both images and subsequent parametric images with very similar noise properties to those of MC images, in a fraction of the time. They believe dpetstep to be very useful for generating fast, simple, and realistic results, however since it uses simple scatter and random models it may not be suitable for studies investigating these phenomena. dpetstep can be downloaded free of cost from https://github.com/CRossSchmidtlein/dPETSTEP.

History and future technical innovation in positron emission tomography

Instrumentation for positron emission tomography (PET) imaging has experienced tremendous improvements in performance over the past 60 years since it was first conceived as a medical imaging modality. Spatial resolution has improved by a factor of 10 and sensitivity by a factor of 40 from the early designs in the 1970s to the high-performance scanners of today. Multimodality configurations have emerged that combine PET with computed tomography (CT) and, more recently, with MR. Whole-body scans for clinical purposes can now be acquired in under 10 min on a state-of-the-art PET/CT. This paper will review the history of these technical developments over 40 years and summarize the important clinical research and healthcare applications that have been made possible by these technical advances. Some perspectives for the future of this technology will also be presented that promise to bring about new applications of this imaging modality in clinical research and healthcare.

Direct Parametric Reconstruction With Joint Motion Estimation/Correction for Dynamic Brain PET Data

Direct reconstruction of parametric images from raw photon counts has been shown to improve the quantitative analysis of dynamic positron emission tomography (PET) data. However it suffers from subject motion which is inevitable during the typical acquisition time of 1-2 hours. In this work we propose a framework to jointly estimate subject head motion and reconstruct the motion-corrected parametric images directly from raw PET data, so that the effects of distorted tissue-to-voxel mapping due to subject motion can be reduced in reconstructing the parametric images with motion-compensated attenuation correction and spatially aligned temporal PET data. The proposed approach is formulated within the maximum likelihood framework, and efficient solutions are derived for estimating subject motion and kinetic parameters from raw PET photon count data. Results from evaluations on simulated [¹¹C]raclopride data using the Zubal brain phantom and real clinical [¹⁸F]florbetapir data of a patient with Alzheimer's disease show that the proposed joint direct parametric reconstruction motion correction approach can improve the accuracy of quantifying dynamic PET data with large subject motion.

Anatomically-aided PET reconstruction using the kernel method

This paper extends the kernel method that was proposed previously for dynamic PET reconstruction, to incorporate anatomical side information into the PET reconstruction model. In contrast to existing methods that incorporate anatomical information using a penalized likelihood framework, the proposed method incorporates this information in the simpler maximum likelihood (ML) formulation and is amenable to ordered subsets. The new method also does not require any segmentation of the anatomical image to obtain edge information. We compare the kernel method with the Bowsher method for anatomically-aided PET image reconstruction through a simulated data set. Computer simulations demonstrate that the kernel method offers advantages over the Bowsher method in region of interest quantification. Additionally the kernel method is applied to a 3D patient data set. The kernel method results in reduced noise at a matched contrast level compared with the conventional ML expectation maximization algorithm.

MR-guided dynamic PET reconstruction with the kernel method and spectral temporal basis functions

Recent advances in dynamic positron emission tomography (PET) reconstruction have demonstrated that it is possible to achieve markedly improved end-point kinetic parameter maps by incorporating a temporal model of the radiotracer directly into the reconstruction algorithm. In this work we have developed a highly constrained, fully dynamic PET reconstruction algorithm incorporating both spectral analysis temporal basis functions and spatial basis functions derived from the kernel method applied to a co-registered T1-weighted magnetic resonance (MR) image. The dynamic PET image is modelled as a linear combination of spatial and temporal basis functions, and a maximum likelihood estimate for the coefficients can be found using the expectation-maximization (EM) algorithm. Following reconstruction, kinetic fitting using any temporal model of interest can be applied. Based on a BrainWeb T1-weighted MR phantom, we performed a realistic dynamic [(18)F]FDG simulation study with two noise levels, and investigated the quantitative performance of the proposed reconstruction algorithm, comparing it with reconstructions incorporating either spectral analysis temporal basis functions alone or kernel spatial basis functions alone, as well as with conventional frame-independent reconstruction. Compared to the other reconstruction algorithms, the proposed algorithm achieved superior performance, offering a decrease in spatially averaged pixel-level root-mean-square-error on post-reconstruction kinetic parametric maps in the grey/white matter, as well as in the tumours when they were present on the co-registered MR image. When the tumours were not visible in the MR image, reconstruction with the proposed algorithm performed similarly to reconstruction with spectral temporal basis functions and was superior to both conventional frame-independent reconstruction and frame-independent reconstruction with kernel spatial basis functions. Furthermore, we demonstrate that a joint spectral/kernel model can also be used for effective post-reconstruction denoising, through the use of an EM-like image-space algorithm. Finally, we applied the proposed algorithm to reconstruction of real high-resolution dynamic [(11)C]SCH23390 data, showing promising results.

Detail-Preserving PET Reconstruction with Sparse Image Representation and Anatomical Priors

Positron emission tomography (PET) reconstruction is an ill-posed inverse problem which typically involves fitting a high-dimensional forward model of the imaging process to noisy, and sometimes undersampled photon emission data. To improve the image quality, prior information derived from anatomical images of the same subject has been previously used in the penalised maximum likelihood (PML) method to regularise the model complexity and selectively smooth the image on a voxel basis in PET reconstruction. In this work, we propose a novel perspective of incorporating the prior information by exploring the sparse property of natural images. Instead of a regular voxel grid, the sparse image representation jointly determined by the prior image and the PET data is used in reconstruction to leverage between the image details and smoothness, and this prior is integrated into the PET forward model and has a closed-form expectation maximisation (EM) solution. Simulations show that the proposed approach achieves improved bias versus variance trade-off and higher contrast recovery than the current state-of-the-art methods, and preserves the image details better. Application to clinical PET data shows promising results.