Evaluation of three MRI-based anatomical priors for quantitative PET brain imaging

An Intelligent Model of Segmentation and Classification Using Enhanced Optimization-Based Attentive Mask RCNN and Recurrent MobileNet With LSTM for Multiple Sclerosis Types With Clinical Brain MRI

In healthcare sector, magnetic resonance imaging (MRI) images are taken for multiple sclerosis (MS) assessment, classification, and management. However, interpreting an MRI scan requires an exceptional amount of skill because abnormalities on scans are frequently inconsistent with clinical symptoms, making it difficult to convert the findings into effective treatment strategies. Furthermore, MRI is an expensive process, and its frequent utilization to monitor an illness increases healthcare costs. To overcome these drawbacks, this research employs advanced technological approaches to develop a deep learning system for classifying types of MS through clinical brain MRI scans. The major innovation of this model is to influence the convolution network with attention concept and recurrent-based deep learning for classifying the disorder; this also proposes an optimization algorithm for tuning the parameter to enhance the performance. Initially, the total images as 3427 are collected from database, in which the collected samples are categorized for training and testing phase. Here, the segmentation is carried out by adaptive and attentive-based mask regional convolution neural network (AA-MRCNN). In this phase, the MRCNN's parameters are finely tuned with an enhanced pine cone optimization algorithm (EPCOA) to guarantee outstanding efficiency. Further, the segmented image is given to recurrent MobileNet with long short term memory (RM-LSTM) for getting the classification outcomes. Through experimental analysis, this deep learning model is acquired 95.4% for accuracy, 95.3% for sensitivity, and 95.4% for specificity. Hence, these results prove that it has high potential for appropriately classifying the sclerosis disorder.

PET Mapping of Receptor Occupancy Using Joint Direct Parametric Reconstruction

Receptor occupancy (RO) studies using PET neuroimaging play a critical role in the development of drugs targeting the central nervous system (CNS). The conventional approach to estimate drug receptor occupancy consists in estimation of binding potential changes between two PET scans (baseline and post-drug injection). This estimation is typically performed separately for each scan by first reconstructing dynamic PET scan data before fitting a kinetic model to time activity curves. This approach fails to properly model the noise in PET measurements, resulting in poor RO estimates, especially in low receptor density regions.

OBJECTIVE

In this work, we evaluate a novel joint direct parametric reconstruction framework to directly estimate distributions of RO and other kinetic parameters in the brain from a pair of baseline and post-drug injection dynamic PET scans.

METHODS

The proposed method combines the use of regularization on RO maps with alternating optimization to enable estimation of occupancy even in low binding regions.

RESULTS

Simulation results demonstrate the quantitative improvement of this method over conventional approaches in terms of accuracy and precision of occupancy. The proposed method is also evaluated in preclinical in-vivo experiments using 11C-MK-6884 and a muscarinic acetylcholine receptor 4 positive allosteric modulator drug, showing improved estimation of receptor occupancy as compared to traditional estimators.

CONCLUSION

The proposed joint direct estimation framework improves RO estimation compared to conventional methods, especially in intermediate to low-binding regions.

SIGNIFICANCE

This work could potentially facilitate the evaluation of new drug candidates targeting the CNS.

PET image reconstruction using weighted nuclear norm maximization and deep learning prior

The ill-posed Positron emission tomography (PET) reconstruction problem usually results in limited resolution and significant noise. Recently, deep neural networks have been incorporated into PET iterative reconstruction framework to improve the image quality. In this paper, we propose a new neural network-based iterative reconstruction method by using weighted nuclear norm (WNN) maximization, which aims to recover the image details in the reconstruction process. The novelty of our method is the application of WNN maximization rather than WNN minimization in PET image reconstruction. Meanwhile, a neural network is used to control the noise originated from WNN maximization. Our method is evaluated on simulated and clinical datasets. The simulation results show that the proposed approach outperforms state-of-the-art neural network-based iterative methods by achieving the best contrast/noise tradeoff with a remarkable contrast improvement on the lesion contrast recovery. The study on clinical datasets also demonstrates that our method can recover lesions of different sizes while suppressing noise in various low-dose PET image reconstruction tasks. Our code is available athttps://github.com/Kuangxd/PETReconstruction.

Deep learning applications for quantitative and qualitative PET in PET/MR: technical and clinical unmet needs

We aim to provide an overview of technical and clinical unmet needs in deep learning (DL) applications for quantitative and qualitative PET in PET/MR, with a focus on attenuation correction, image enhancement, motion correction, kinetic modeling, and simulated data generation. (1) DL-based attenuation correction (DLAC) remains an area of limited exploration for pediatric whole-body PET/MR and lung-specific DLAC due to data shortages and technical limitations. (2) DL-based image enhancement approximating MR-guided regularized reconstruction with a high-resolution MR prior has shown promise in enhancing PET image quality. However, its clinical value has not been thoroughly evaluated across various radiotracers, and applications outside the head may pose challenges due to motion artifacts. (3) Robust training for DL-based motion correction requires pairs of motion-corrupted and motion-corrected PET/MR data. However, these pairs are rare. (4) DL-based approaches can address the limitations of dynamic PET, such as long scan durations that may cause patient discomfort and motion, providing new research opportunities. (5) Monte-Carlo simulations using anthropomorphic digital phantoms can provide extensive datasets to address the shortage of clinical data. This summary of technical/clinical challenges and potential solutions may provide research opportunities for the research community towards the clinical translation of DL solutions.

Anatomically Guided PET Image Reconstruction Using Conditional Weakly-Supervised Multi-Task Learning Integrating Self-Attention

To address the lack of high-quality training labels in positron emission tomography (PET) imaging, weakly-supervised reconstruction methods that generate network-based mappings between prior images and noisy targets have been developed. However, the learned model has an intrinsic variance proportional to the average variance of the target image. To suppress noise and improve the accuracy and generalizability of the learned model, we propose a conditional weakly-supervised multi-task learning (MTL) strategy, in which an auxiliary task is introduced serving as an anatomical regularizer for the PET reconstruction main task. In the proposed MTL approach, we devise a novel multi-channel self-attention (MCSA) module that helps learn an optimal combination of shared and task-specific features by capturing both local and global channel-spatial dependencies. The proposed reconstruction method was evaluated on NEMA phantom PET datasets acquired at different positions in a PET/CT scanner and 26 clinical whole-body PET datasets. The phantom results demonstrate that our method outperforms state-of-the-art learning-free and weakly-supervised approaches obtaining the best noise/contrast tradeoff with a significant noise reduction of approximately 50.0% relative to the maximum likelihood (ML) reconstruction. The patient study results demonstrate that our method achieves the largest noise reductions of 67.3% and 35.5% in the liver and lung, respectively, as well as consistently small biases in 8 tumors with various volumes and intensities. In addition, network visualization reveals that adding the auxiliary task introduces more anatomical information into PET reconstruction than adding only the anatomical loss, and the developed MCSA can abstract features and retain PET image details.

Resolution enhancement, noise suppression, and joint T2* decay estimation in dual-echo sodium-23 MR imaging using anatomically guided reconstruction

PURPOSE

Sodium MRI is challenging because of the low tissue concentration of the 23 Na nucleus and its extremely fast biexponential transverse relaxation rate. In this article, we present an iterative reconstruction framework using dual-echo 23 Na data and exploiting anatomical prior information (AGR) from high-resolution, low-noise, 1 H MR images. This framework enables the estimation and modeling of the spatially varying signal decay due to transverse relaxation during readout (AGRdm), which leads to images of better resolution and reduced noise resulting in improved quantification of the reconstructed 23 Na images.

METHODS

The proposed framework was evaluated using reconstructions of 30 noise realizations of realistic simulations of dual echo twisted projection imaging (TPI) 23 Na data. Moreover, three dual echo 23 Na TPI brain datasets of healthy controls acquired on a 3T Siemens Prisma system were reconstructed using conventional reconstruction, AGR and AGRdm.

RESULTS

Our simulations show that compared to conventional reconstructions, AGR and AGRdm show improved bias-noise characteristics in several regions of the brain. Moreover, AGR and AGRdm images show more anatomical detail and less noise in the reconstructions of the experimental data sets. Compared to AGR and the conventional reconstruction, AGRdm shows higher contrast in the sodium concentration ratio between gray and white matter and between gray matter and the brain stem.

CONCLUSION

AGR and AGRdm generate 23 Na images with high resolution, high levels of anatomical detail, and low levels of noise, potentially enabling high-quality 23 Na MR imaging at 3T.

Neural KEM: A Kernel Method With Deep Coefficient Prior for PET Image Reconstruction

Image reconstruction of low-count positron emission tomography (PET) data is challenging. Kernel methods address the challenge by incorporating image prior information in the forward model of iterative PET image reconstruction. The kernelized expectation-maximization (KEM) algorithm has been developed and demonstrated to be effective and easy to implement. A common approach for a further improvement of the kernel method would be adding an explicit regularization, which however leads to a complex optimization problem. In this paper, we propose an implicit regularization for the kernel method by using a deep coefficient prior, which represents the kernel coefficient image in the PET forward model using a convolutional neural-network. To solve the maximum-likelihood neural network-based reconstruction problem, we apply the principle of optimization transfer to derive a neural KEM algorithm. Each iteration of the algorithm consists of two separate steps: a KEM step for image update from the projection data and a deep-learning step in the image domain for updating the kernel coefficient image using the neural network. This optimization algorithm is guaranteed to monotonically increase the data likelihood. The results from computer simulations and real patient data have demonstrated that the neural KEM can outperform existing KEM and deep image prior methods.

Feasibility of dose reduction for [18F]FDG-PET/MR imaging of patients with non-lesional epilepsy

The aim of the study was to evaluate the effect of reduced injected [18F]FDG activity levels on the quantitative and diagnostic accuracy of PET images of patients with non-lesional epilepsy (NLE).Nine healthy volunteers and nine patients with NLE underwent 60-min dynamic list-mode (LM) scans on a fully-integrated PET/MRI system. Injected FDG activity levels were reduced virtually by randomly removing counts from the last 10-min of the LM data, so as to simulate the following activity levels: 50 %, 35 %, 20 %, and 10 % of the original activity. Four image reconstructions were evaluated: standard OSEM, OSEM with resolution recovery (PSF), the A-MAP, and the Asymmetrical Bowsher (AsymBowsher) algorithms. For the A-MAP algorithms, two weights were selected (low and high). Image contrast and noise levels were evaluated for all subjects while the lesion-to-background ratio (L/B) was only evaluated for patients. Patient images were scored by a Nuclear Medicine physician on a 5-point scale to assess clinical impression associated with the various reconstruction algorithms.The image contrast and L/B ratio characterizing all four reconstruction algorithms were similar, except for reconstructions based on only 10 % of total counts. Based on clinical impression, images with diagnostic quality can be achieved with as low as 35 % of the standard injected activity. The selection of algorithms utilizing an anatomical prior did not provide a significant advantage for clinical readings, despite a small improvement in L/B (< 5 %) using the A-MAP and AsymBowsher reconstruction algorithms.In patients with NLE who are undergoing [18F]FDG-PET/MR imaging, the injected [18F]FDG activity can be reduced to 35 % of the original dose levels without compromising.

Enhancing the spatial resolution of hyperpolarized carbon-13 MRI of human brain metabolism using structure guidance

PURPOSE

Dynamic nuclear polarization is an emerging imaging method that allows noninvasive investigation of tissue metabolism. However, the relatively low metabolic spatial resolution that can be achieved limits some applications, and improving this resolution could have important implications for the technique.

METHODS

We propose to enhance the 3D resolution of carbon-13 magnetic resonance imaging (13 C-MRI) using the structural information provided by hydrogen-1 MRI (1 H-MRI). The proposed approach relies on variational regularization in 3D with a directional total variation regularizer, resulting in a convex optimization problem which is robust with respect to the parameters and can efficiently be solved by many standard optimization algorithms. Validation was carried out using an in silico phantom, an in vitro phantom and in vivo data from four human volunteers.

RESULTS

The clinical data used in this study were upsampled by a factor of 4 in-plane and by a factor of 15 out-of-plane, thereby revealing occult information. A key finding is that 3D super-resolution shows superior performance compared to several 2D super-resolution approaches: for example, for the in silico data, the mean-squared-error was reduced by around 40% and for all data produced increased anatomical definition of the metabolic imaging.

CONCLUSION

The proposed approach generates images with enhanced anatomical resolution while largely preserving the quantitative measurements of metabolism. Although the work requires clinical validation against tissue measures of metabolism, it offers great potential in the field of 13 C-MRI and could significantly improve image quality in the future.

PET/MR Technology: Advancement and Challenges

When this article was written, it coincided with the 11th anniversary of the installation of our PET/MR device in Munich. In fact, this was the first fully integrated device to be in clinical use. During this time, we have observed many interesting behaviors, to put it kindly. However, it is more critical that in this process, our understanding of the system also improved - including the advantages and limitations from a technical, logistical, and medical perspective. The last decade of PET/MRI research has certainly been characterized by most sites looking for a "key application." There were many ideas in this context and before and after the devices became available, some of which were based on the earlier work with integrating data from single devices. These involved validating classical PET methods with MRI (eg, perfusion or oncology diagnostics). More important, however, were the scenarios where intermodal synergies could be expected. In this review, we look back on this decade-long journey, at the challenges overcome and those still to come.

Adaptive rectification based adversarial network with spectrum constraint for high-quality PET image synthesis

Positron emission tomography (PET) is a typical nuclear imaging technique, which can provide crucial functional information for early brain disease diagnosis. Generally, clinically acceptable PET images are obtained by injecting a standard-dose radioactive tracer into human body, while on the other hand the cumulative radiation exposure inevitably raises concerns about potential health risks. However, reducing the tracer dose will increase the noise and artifacts of the reconstructed PET image. For the purpose of acquiring high-quality PET images while reducing radiation exposure, in this paper, we innovatively present an adaptive rectification based generative adversarial network with spectrum constraint, named AR-GAN, which uses low-dose PET (LPET) image to synthesize standard-dose PET (SPET) image of high-quality. Specifically, considering the existing differences between the synthesized SPET image by traditional GAN and the real SPET image, an adaptive rectification network (AR-Net) is devised to estimate the residual between the preliminarily predicted image and the real SPET image, based on the hypothesis that a more realistic rectified image can be obtained by incorporating both the residual and the preliminarily predicted PET image. Moreover, to address the issue of high-frequency distortions in the output image, we employ a spectral regularization term in the training optimization objective to constrain the consistency of the synthesized image and the real image in the frequency domain, which further preserves the high-frequency detailed information and improves synthesis performance. Validations on both the phantom dataset and the clinical dataset show that the proposed AR-GAN can estimate SPET images from LPET images effectively and outperform other state-of-the-art image synthesis approaches.

Dynamic PET image reconstruction incorporating a median nonlocal means kernel method

In dynamic positron emission tomography (PET) imaging, the reconstructed image of a single frame often exhibits high noise due to limited counting statistics of projection data. This study proposed a median nonlocal means (MNLM)-based kernel method for dynamic PET image reconstruction. The kernel matrix is derived from median nonlocal means of pre-reconstructed composite images. Then the PET image intensities in all voxels were modeled as a kernel matrix multiplied by coefficients and incorporated into the forward model of PET projection data. Then, the coefficients of each feature were estimated by the maximum likelihood method. Using simulated low-count dynamic data of Zubal head phantom, the quantitative performance of the proposed MNLM kernel method was investigated and compared with the maximum-likelihood method, conventional kernel method with and without median filter, and nonlocal means (NLM) kernel method. Simulation results showed that the MNLM kernel method achieved visual and quantitative accuracy improvements (in terms of the ensemble mean squared error, bias versus variance, and contrast versus noise performances). Especially for frame 2 with the lowest count level of a single frame, the MNLM kernel method achieves lower ensemble mean squared error (10.43%) than the NLM kernel method (13.68%), conventional kernel method with and without median filter (11.88% and 23.50%), and MLEM algorithm (24.77%). The study on real low-dose ¹⁸F-FDG rat data also showed that the MNLM kernel method outperformed other methods in visual and quantitative accuracy improvements (in terms of regional noise versus intensity mean performance).

Anatomical-guided attention enhances unsupervised PET image denoising performance

Although supervised convolutional neural networks (CNNs) often outperform conventional alternatives for denoising positron emission tomography (PET) images, they require many low- and high-quality reference PET image pairs. Herein, we propose an unsupervised 3D PET image denoising method based on an anatomical information-guided attention mechanism. The proposed magnetic resonance-guided deep decoder (MR-GDD) utilizes the spatial details and semantic features of MR-guidance image more effectively by introducing encoder-decoder and deep decoder subnetworks. Moreover, the specific shapes and patterns of the guidance image do not affect the denoised PET image, because the guidance image is input to the network through an attention gate. In a Monte Carlo simulation of [¹⁸F]fluoro-2-deoxy-D-glucose (FDG), the proposed method achieved the highest peak signal-to-noise ratio and structural similarity (27.92 ± 0.44 dB/0.886 ± 0.007), as compared with Gaussian filtering (26.68 ± 0.10 dB/0.807 ± 0.004), image guided filtering (27.40 ± 0.11 dB/0.849 ± 0.003), deep image prior (DIP) (24.22 ± 0.43 dB/0.737 ± 0.017), and MR-DIP (27.65 ± 0.42 dB/0.879 ± 0.007). Furthermore, we experimentally visualized the behavior of the optimization process, which is often unknown in unsupervised CNN-based restoration problems. For preclinical (using [¹⁸F]FDG and [¹¹C]raclopride) and clinical (using [¹⁸F]florbetapir) studies, the proposed method demonstrates state-of-the-art denoising performance while retaining spatial resolution and quantitative accuracy, despite using a common network architecture for various noisy PET images with 1/10th of the full counts. These results suggest that the proposed MR-GDD can reduce PET scan times and PET tracer doses considerably without impacting patients.

Generation of attenuation correction factors from time-of-flight PET emission data using high-resolution residual U-net

Attenuation correction of annihilation photons is essential in PET image reconstruction for providing accurate quantitative activity maps. In the absence of an aligned CT device to obtain attenuation information, we propose the high-resolution residual U-net (HRU-Net) to extract attenuation correction factors (ACF) directly from time-of-flight (TOF) PET emission data. HRU-Net is built upon the U-Net encoding-decoding architecture and it utilizes four blocks of modified residual connections in each stage. In each residual block, concatenation is performed to incorporate input and output feature vectors. In addition, flexible and efficient elements of convolutional neural network (CNN) such as dilated convolutions, pre-activation order of a batch normalization (BN) layer, a rectified linear unit (ReLU) layer and a convolution layer, and residual connections are utilized to extract high resolution features. To illustrate the effectiveness of the proposed method, HRU-Net estimated ACF, attenuation maps and activity maps are compared with maximum likelihood ACF (MLACF) algorithm, U-Net, and HC-Net. An ablation study is conducted using non-TOF and TOF sinograms as inputs of networks. The experimental results show that HRU-Net with TOF projections as inputs leads to normalized root mean square error (NRMSE) of 4.84% ± 1.58%, outperforming MLACF, U-Net and HC-Net with NRMSE of 47.82% ± 13.62%, 6.92% ± 1.94%, and 7.99% ± 2.49%, respectively.

Voxel-based partial volume correction of PET images via subtle MRI guided non-local means regularization

PURPOSE

Positron emission tomography (PET) images tend to be significantly degraded by the partial volume effect (PVE) resulting from the limited spatial resolution of the reconstructed images. Our purpose is to propose a partial volume correction (PVC) method to tackle this issue.

METHODS

In the present work, we explore a voxel-based PVC method under the least squares framework (LS) employing anatomical non-local means (NLMA) regularization. The well-known non-local means (NLM) filter utilizes the high degree of information redundancy that typically exists in images, and is typically used to directly reduce image noise by replacing each voxel intensity with a weighted average of its non-local neighbors. Here we explore NLM as a regularization term within iterative-deconvolution model to perform PVC. Further, an anatomical-guided version of NLM was proposed that incorporates MRI information into NLM to improve resolution and suppress image noise. The proposed approach makes subtle usage of the accompanying MRI information to define a more appropriate search space within the prior model. To optimize the regularized LS objective function, we used the Gauss-Seidel (GS) algorithm with the one-step-late (OSL) technique.

RESULTS

After the import of NLMA, the visual and quality results are all improved. With a visual check, we notice that NLMA reduce the noise compared to other PVC methods. This is also validated in bias-noise curve compared to non-MRI-guided PVC framework. We can see NLMA gives better bias-noise trade-off compared to other PVC methods.

CONCLUSIONS

Our efforts were evaluated in the base of amyloid brain PET imaging using the BrainWeb phantom and in vivo human data. We also compared our method with other PVC methods. Overall, we demonstrated the value of introducing subtle MRI-guidance in the regularization process, the proposed NLMA method resulting in promising visual as well as quantitative performance improvements.

Deconvolution-based partial volume correction of PET images with parallel level set regularization

The partial volume effect (PVE), caused by the limited spatial resolution of positron emission tomography (PET), degrades images both qualitatively and quantitatively. Anatomical information provided by magnetic resonance (MR) images has the potential to play an important role in partial volume correction (PVC) methods. Post-reconstruction MR-guided PVC methods typically use segmented MR tissue maps, and further, assume that PET activity distribution is uniform in each region, imposing considerable constraints through anatomical guidance. In this work, we present a post-reconstruction PVC method based on deconvolution with parallel level set (PLS) regularization. We frame the problem as an iterative deconvolution task with PLS regularization that incorporates anatomical information without requiring MR segmentation or assuming uniformity of PET distributions within regions. An efficient algorithm for non-smooth optimization of the objective function (invoking split Bregman framework) is developed so that the proposed method can be feasibly applied to 3D images and produces sharper images compared to PLS method with smooth optimization. The proposed method was evaluated together with several other PVC methods using both realistic simulation experiments based on the BrainWeb phantom as well asin vivohuman data. Our proposed method showed enhanced quantitative performance when realistic MR guidance was provided. Further, the proposed method is able to reduce image noise while preserving structure details onin vivohuman data, and shows the potential to better differentiate amyloid positive and amyloid negative scans. Overall, our results demonstrate promise to provide superior performance in clinical imaging scenarios.

Anatomy-guided PET reconstruction usingl1bowsher prior

Advances in simultaneous positron emission tomography/magnetic resonance imaging (PET/MRI) technology have led to an active investigation of the anatomy-guided regularized PET image reconstruction algorithm based on MR images. Among the various priors proposed for anatomy-guided regularized PET image reconstruction, Bowsher's method based on second-order smoothing priors sometimes suffers from over-smoothing of detailed structures. Therefore, in this study, we propose a Bowsher prior based on thel1-norm and an iteratively reweighting scheme to overcome the limitation of the original Bowsher method. In addition, we have derived a closed solution for iterative image reconstruction based on this non-smooth prior. A comparison study between the originall2and proposedl1Bowsher priors was conducted using computer simulation and real human data. In the simulation and real data application, small lesions with abnormal PET uptake were better detected by the proposedl1Bowsher prior methods than the original Bowsher prior. The originall2Bowsher leads to a decreased PET intensity in small lesions when there is no clear separation between the lesions and surrounding tissue in the anatomical prior. However, the proposedl1Bowsher prior methods showed better contrast between the tumors and surrounding tissues owing to the intrinsic edge-preserving property of the prior which is attributed to the sparseness induced byl1-norm, especially in the iterative reweighting scheme. Besides, the proposed methods demonstrated lower bias and less hyper-parameter dependency on PET intensity estimation in the regions with matched anatomical boundaries in PET and MRI. Therefore, these methods will be useful for improving the PET image quality based on the anatomical side information.

Quantitative bone SPECT/CT reconstruction utilizing anatomical information

Background

Bone SPECT/CT has been shown to offer superior sensitivity and specificity compared to conventional whole-body planar scanning. Furthermore, bone SPECT/CT allows quantitative imaging, which is challenging with planar methods. In order to gain better quantitative accuracy, Bayesian reconstruction algorithms, including both image derived and anatomically guided priors, have been utilized in reconstruction in PET/CT scanning, but they have not been widely used in SPECT/CT studies. Therefore, the aim of this work was to evaluate the performance of CT-guided reconstruction in quantitative bone SPECT.

Methods

Three Bayesian reconstruction methods were evaluated against the conventional ordered subsets expectation maximization (OSEM) reconstruction method. One of the studied Bayesian methods was the relative difference prior (RDP), which has recently gained popularity in PET reconstruction. The other two methods, anatomically guided smoothing prior (AMAP-S) and anatomically guided relative difference prior (AMAP-R), utilized anatomical information from the CT scan. The reconstruction methods were evaluated in terms of quantitative accuracy with artificial lesions inserted in clinical patient studies and with 20 real clinical patients. Maximum and mean standardized uptake values (SUVs) of the lesions were defined.

Results

The analyses showed that all studied Bayesian methods performed better than OSEM and the anatomical priors also outperformed RDP. The average relative error in mean SUV for the artificial lesion study for OSEM, RDP, AMAP-S, and AMAP-R was − 53%, − 35%, − 15%, and − 10%, when the CT study had matching lesions. In the patient study, the RDP method gave 16 ± 9% higher maximum SUV values than OSEM, while AMAP-S and AMAP-R offered increases of 36 ± 8% and 36 ± 9%, respectively. Mean SUV increased for RDP, AMAP-S, and AMAP-R by 18 ± 9%, 26 ± 5%, and 33 ± 5% when compared to OSEM.

Conclusions

The Bayesian methods with anatomical prior, especially the relative difference prior-based method (AMAP-R), outperformed OSEM and reconstruction without anatomical prior in terms of quantitative accuracy.

Approximating anatomically-guided PET reconstruction in image space using a convolutional neural network

In the last two decades, it has been shown that anatomically-guided PET reconstruction can lead to improved bias-noise characteristics in brain PET imaging. However, despite promising results in simulations and first studies, anatomically-guided PET reconstructions are not yet available for use in routine clinical because of several reasons. In light of this, we investigate whether the improvements of anatomically-guided PET reconstruction methods can be achieved entirely in the image domain with a convolutional neural network (CNN). An entirely image-based CNN post-reconstruction approach has the advantage that no access to PET raw data is needed and, moreover, that the prediction times of trained CNNs are extremely fast on state of the art GPUs which will substantially facilitate the evaluation, fine-tuning and application of anatomically-guided PET reconstruction in real-world clinical settings. In this work, we demonstrate that anatomically-guided PET reconstruction using the asymmetric Bowsher prior can be well-approximated by a purely shift-invariant convolutional neural network in image space allowing the generation of anatomically-guided PET images in almost real-time. We show that by applying dedicated data augmentation techniques in the training phase, in which 16 [18F]FDG and 10 [18F]PE2I data sets were used, lead to a CNN that is robust against the used PET tracer, the noise level of the input PET images and the input MRI contrast. A detailed analysis of our CNN in 36 [18F]FDG, 18 [18F]PE2I, and 7 [18F]FET test data sets demonstrates that the image quality of our trained CNN is very close to the one of the target reconstructions in terms of regional mean recovery and regional structural similarity.

Technical Note: Ultra high-resolution radiotracer-specific digital pet brain phantoms based on the BigBrain atlas

PURPOSE

To introduce a method that allows the generation of ultra high-resolution (submillimeter) heterogeneous digital PET brain phantoms and to provide a new publicly available [18 F ]FDG phantom as an example.

METHOD

The radiotracer distribution of the phantom is estimated by minimizing the Kullback-Leibler distance between the parameterized unknown phantom distribution and a radiotracer-specific template used as a reference. The phantom is modelled using the histological and tissue classified volumes of the BigBrain atlas to provide both high resolution and heterogeneity. The Hammersmith brain atlas is also included to allow the estimation of different activity values in different anatomical regions of the brain. Using this method, a realistic [18 F ]FDG phantom was produced, where a single real [18 F ]FDG scan was used as the reference to match. An MRI T1-weighted image, obtained from the BigBrain atlas, and a pseudo-CT are included to complete the dataset. A full PET-MRI dataset was simulated and reconstructed with MR-guided methods for the new [18 F ]FDG phantom.

RESULTS

An ultra high-resolution (400 μm voxel size) and heterogeneous phantom for [18 F ]FDG was obtained. The radiotracer activity follows the patterns observed in the scan used as a reference. The simulated PET-MRI dataset provided a realistic simulation that was able to be reconstructed with MR-guided methods. By visual inspection, the reconstructed images showed similar patterns to the real data and the improvements in contrast and noise with respect to the standard MLEM reconstruction were more modest compared to simulations done with a simpler phantom, which was created from the same MRI image used to assist the reconstruction.

CONCLUSIONS

A method to create high-resolution heterogeneous digital brain phantoms for different PET radiotracers has been presented and successfully employed to create a new publicly available [18 F ]FDG phantom. The generated phantom is of high resolution, is heterogeneous, and simulates the uptake of the radiotracer in the different regions of the brain.

Bootstrap-Optimised Regularised Image Reconstruction for Emission Tomography

In emission tomography, iterative image reconstruction from noisy measured data usually results in noisy images, and so regularisation is often used to compensate for noise. However, in practice, an appropriate, automatic and precise specification of the strength of regularisation for image reconstruction from a given noisy measured dataset remains unresolved. Existing approaches are either empirical approximations with no guarantee of generalisation, or else are computationally intensive cross-validation methods requiring full reconstructions for a limited set of preselected regularisation strengths. In contrast, we propose a novel methodology embedded within iterative image reconstruction, using one or more bootstrapped replicates of the measured data for precise optimisation of the regularisation. The approach uses a conventional unregularised iterative update of a current image estimate from the noisy measured data, and then also uses the bootstrap replicate to obtain a bootstrap update of the current image estimate. The method then seeks the regularisation hyperparameters which, when applied to the bootstrap update of the image, lead to a best fit of the regularised bootstrap update to the conventional measured data update. This corresponds to estimating the degree of regularisation needed in order to map the noisy update to a model of the mean of an ensemble of noisy updates. For a given regularised objective function (e.g. penalised likelihood), no hyperparameter selection or tuning is required. The method is demonstrated for positron emission tomography (PET) data at different noise levels, and delivers near-optimal reconstructions (in terms of reconstruction error) without any knowledge of the ground truth, nor any form of training data.

Analysis of partial volume correction on quantification and regional heterogeneity in cardiac PET

BACKGROUND

The partial volume correction (PVC) of cardiac PET datasets using anatomical side information during reconstruction is appealing but not straightforward. Other techniques, which do not make use of additional anatomical information, could be equally effective in improving the reconstructed myocardial activity.

METHODS

Resolution modeling in combination with different noise suppressing priors was evaluated as a means to perform PVC. Anatomical priors based on a high-resolution CT are compared to non-anatomical, edge-preserving priors (relative difference and total variation prior). The study is conducted on ex vivo datasets from ovine hearts. A simulation study additionally clarifies the relationship between prior effectiveness and myocardial wall thickness.

RESULTS

Simple resolution modeling during data reconstruction resulted in over- and underestimation of activity, which hampers the absolute left ventricular quantification when compared to the ground truth. Both the edge-preserving and the anatomy-based PVC techniques improve the absolute quantification, with comparable results (Student t-test, P = .17). The relative tracer distribution was preserved with any reconstruction technique (repeated ANOVA, P = .98).

CONCLUSIONS

The use of edge-preserving priors emerged as optimal choice for quantification of tracer uptake in the left ventricular wall of the available datasets. Anatomical priors visually outperformed edge-preserving priors when the thinnest structures were of interest.

Partial volume and motion correction in cardiac PET: First results from an in vs ex vivo comparison using animal datasets

BACKGROUND

In a previous study on ex vivo, static cardiac datasets, we investigated the benefits of performing partial volume correction (PVC) in cardiac 18F-Fluorodeoxyglucose(FDG) PET datasets. In the present study, we extend the analysis to in vivo cardiac datasets, with the aim of defining which reconstruction technique maximizes quantitative accuracy and, ultimately, makes PET a better diagnostic tool for cardiac pathologies.

METHODS

In vivo sheep datasets were acquired and reconstructed with/without motion correction and using several reconstruction algorithms (with/without resolution modeling, with/without non-anatomical priors). Corresponding ex vivo scans of the excised sheep hearts were performed on a small-animal PET scanner (Siemens Focus 220, microPET) to provide high-resolution reference data unaffected by respiratory and cardiac motion. A comparison between the in vivo cardiac reconstructions and the corresponding ex vivo ground truth was performed.

RESULTS

The use of an edge-preserving prior (Total Variation (TV) prior in this work) in combination with motion correction reduces the bias in absolute quantification when compared to the standard clinical reconstructions (- 0.83 vs - 3.74 SUV units), when the end-systolic gate is considered. At end-diastole, motion correction improves absolute quantification but the PVC with priors does not improve the similarity to the ground truth more than a regular iterative reconstruction with motion correction and without priors. Relative quantification was not influenced much by the chosen reconstruction algorithm.

CONCLUSIONS

The relative ranking of the algorithms suggests superiority of the PVC reconstructions with dual gating in terms of overall absolute quantification and noise properties. A well-tuned edge-preserving prior, such as TV, enhances the noise properties of the resulting images of the heart. The end-systolic gate yields the most accurate quantification of cardiac datasets.

Intercomparison of MR-informed PET image reconstruction methods

PURPOSE

Numerous image reconstruction methodologies for positron emission tomography (PET) have been developed that incorporate magnetic resonance (MR) imaging structural information, producing reconstructed images with improved suppression of noise and reduced partial volume effects. However, the influence of MR structural information also increases the possibility of suppression or bias of structures present only in the PET data (PET-unique regions). To address this, further developments for MR-informed methods have been proposed, for example, through inclusion of the current reconstructed PET image, alongside the MR image, in the iterative reconstruction process. In this present work, a number of kernel and maximum a posteriori (MAP) methodologies are compared, with the aim of identifying methods that enable a favorable trade-off between the suppression of noise and the retention of unique features present in the PET data.

METHODS

The reconstruction methods investigated were: the MR-informed conventional and spatially compact kernel methods, referred to as KEM and KEM largest value sparsification (LVS) respectively; the MR-informed Bowsher and Gaussian MR-guided MAP methods; and the PET-MR-informed hybrid kernel and anato-functional MAP methods. The trade-off between improving the reconstruction of the whole brain region and the PET-unique regions was investigated for all methods in comparison with postsmoothed maximum likelihood expectation maximization (MLEM), evaluated in terms of structural similarity index (SSIM), normalized root mean square error (NRMSE), bias, and standard deviation. Both simulated BrainWeb (10 noise realizations) and real [18 F] fluorodeoxyglucose (FDG) three-dimensional datasets were used. The real [18 F]FDG dataset was augmented with simulated tumors to allow comparison of the reconstruction methodologies for the case of known regions of PET-MR discrepancy and evaluated at full counts (100%) and at a reduced (10%) count level.

RESULTS

For the high-count simulated and real data studies, the anato-functional MAP method performed better than the other methods under investigation (MR-informed, PET-MR-informed and postsmoothed MLEM), in terms of achieving the best trade-off for the reconstruction of the whole brain and PET-unique regions, assessed in terms of the SSIM, NRMSE, and bias vs standard deviation. The inclusion of PET information in the anato-functional MAP method enables the reconstruction of PET-unique regions to attain similarly low levels of bias as unsmoothed MLEM, while moderately improving the whole brain image quality for low levels of regularization. However, for low count simulated datasets the anato-functional MAP method performs poorly, due to the inclusion of noisy PET information in the regularization term. For the low counts simulated dataset, KEM LVS and to a lesser extent, HKEM performed better than the other methods under investigation in terms of achieving the best trade-off for the reconstruction of the whole brain and PET-unique regions, assessed in terms of the SSIM, NRMSE, and bias vs standard deviation.

CONCLUSION

For the reconstruction of noisy data, multiple MR-informed methods produce favorable whole brain vs PET-unique region trade-off in terms of the image quality metrics of SSIM and NRMSE, comfortably outperforming the whole image denoising of postsmoothed MLEM.

MRI-Driven PET Image Optimization for Neurological Applications

Positron emission tomography (PET) and magnetic resonance imaging (MRI) are established imaging modalities for the study of neurological disorders, such as epilepsy, dementia, psychiatric disorders and so on. Since these two available modalities vary in imaging principle and physical performance, each technique has its own advantages and disadvantages over the other. To acquire the mutual complementary information and reinforce each other, there is a need for the fusion of PET and MRI. This combined dual-modality (either sequential or simultaneous) could generate preferable soft tissue contrast of brain tissue, flexible acquisition parameters, and minimized exposure to radiation. The most unique superiority of PET/MRI is mainly manifested in MRI-based improvement for the inherent limitations of PET, such as motion artifacts, partial volume effect (PVE) and invasive procedure in quantitative analysis. Head motion during scanning significantly deteriorates the effective resolution of PET image, especially for the dynamic scan with lengthy time. Hybrid PET/MRI device can offer motion correction (MC) for PET data through MRI information acquired simultaneously. Regarding the PVE associated with limited spatial resolution, the process and reconstruction of PET data can be further optimized by using acquired MRI either sequentially or simultaneously. The quantitative analysis of dynamic PET data mainly relies upon an invasive arterial blood sampling procedure to acquire arterial input function (AIF). An image-derived input function (IDIF) method without the need of arterial cannulization, can serve as a potential alternative estimation of AIF. Compared with using PET data only, combining anatomical or functional information from MRI for improving the accuracy in IDIF approach has been demonstrated. Yet, due to the interference and inherent disparity between the two modalities, these methods for optimizing PET image based on MRI still have many technical challenges. This review discussed upon the most recent progress, current challenges and future directions of MRI-driven PET data optimization for neurological applications, with either sequential or simultaneous acquisition approach.

PET Reconstruction of the Posterior Image Probability, Including Multimodal Images

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

PET Image Reconstruction Using Deep Image Prior

Recently, deep neural networks have been widely and successfully applied in computer vision tasks and have attracted growing interest in medical imaging. One barrier for the application of deep neural networks to medical imaging is the need for large amounts of prior training pairs, which is not always feasible in clinical practice. This is especially true for medical image reconstruction problems, where raw data are needed. Inspired by the deep image prior framework, in this paper, we proposed a personalized network training method where no prior training pairs are needed, but only the patient's own prior information. The network is updated during the iterative reconstruction process using the patient-specific prior information and measured data. We formulated the maximum-likelihood estimation as a constrained optimization problem and solved it using the alternating direction method of multipliers algorithm. Magnetic resonance imaging guided positron emission tomography reconstruction was employed as an example to demonstrate the effectiveness of the proposed framework. Quantification results based on simulation and real data show that the proposed reconstruction framework can outperform Gaussian post-smoothing and anatomically guided reconstructions using the kernel method or the neural-network penalty.

3D Auto-Context-Based Locality Adaptive Multi-Modality GANs for PET Synthesis

Positron emission tomography (PET) has been substantially used recently. To minimize the potential health risk caused by the tracer radiation inherent to PET scans, it is of great interest to synthesize the high-quality PET image from the low-dose one to reduce the radiation exposure. In this paper, we propose a 3D auto-context-based locality adaptive multi-modality generative adversarial networks model (LA-GANs) to synthesize the high-quality FDG PET image from the low-dose one with the accompanying MRI images that provide anatomical information. Our work has four contributions. First, different from the traditional methods that treat each image modality as an input channel and apply the same kernel to convolve the whole image, we argue that the contributions of different modalities could vary at different image locations, and therefore a unified kernel for a whole image is not optimal. To address this issue, we propose a locality adaptive strategy for multi-modality fusion. Second, we utilize 1 ×1 ×1 kernel to learn this locality adaptive fusion so that the number of additional parameters incurred by our method is kept minimum. Third, the proposed locality adaptive fusion mechanism is learned jointly with the PET image synthesis in a 3D conditional GANs model, which generates high-quality PET images by employing large-sized image patches and hierarchical features. Fourth, we apply the auto-context strategy to our scheme and propose an auto-context LA-GANs model to further refine the quality of synthesized images. Experimental results show that our method outperforms the traditional multi-modality fusion methods used in deep networks, as well as the state-of-the-art PET estimation approaches.

Enhancement of Partial Volume Correction in MR-Guided PET Image Reconstruction by Using MRI Voxel Sizes

Positron emission tomography (PET) suffers from poor spatial resolution which results in quantitative bias when evaluating the radiotracer uptake in small anatomical regions, such as the striatum in the brain which is of importance in this paper of neurodegenerative diseases. These partial volume effects need to be compensated for by employing partial volume correction (PVC) methods in order to achieve quantitatively accurate images. Two important PVC methods applied during the reconstruction are resolution modeling, which suffers from Gibbs artifacts, and penalized likelihood using anatomical priors. The introduction of clinical simultaneous PET-MR scanners has attracted new attention for the latter methods and brought new opportunities to use MRI information to assist PET image reconstruction in order to improve image quality. In this context, MR images are usually down-sampled to the PET resolution before being used in MR-guided PET reconstruction. However, the reconstruction of PET images using the MRI voxel size could achieve a better utilization of the high resolution anatomical information and improve the PVC obtained with these methods. In this paper, we evaluate the importance of the use of MRI voxel sizes when reconstructing PET images with MR-guided maximum a posteriori (MAP) methods, specifically the modified Bowsher method. We also propose a method to avoid the artifacts that arise when PET reconstructions are performed in a higher resolution matrix than the standard for a given scanner. The MR-guided MAP reconstructions were implemented with a modified Lange prior that included anatomical information with the Bowsher method. The methods were evaluated with and without resolution modeling for simulated and real brain data. We show that the use of the MRI voxel sizes when reconstructing PET images with MR-guided MAP enhances PVC by improving the contrast and reducing the bias in six different regions of the brain using regional metrics for a single simulated data set and ensemble metrics for ten noise realizations. Similar results were obtained for real data, where a good enhancement of the contrast was achieved. The combination of MR-guided MAP reconstruction with point-spread function modeling and MRI voxel sizes proved to be an attractive method to achieve considerable enhancement of PVC, while reducing and controlling the noise level and Gibbs artifacts.

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.

Multi-modal synergistic PET and MR reconstruction using mutually weighted quadratic priors

PURPOSE

To propose a framework for synergistic reconstruction of PET-MR and multi-contrast MR data to improve the image quality obtained from noisy PET data and from undersampled MR data.

THEORY AND METHODS

Weighted quadratic priors were devised to preserve common boundaries between PET-MR images while reducing noise, PET Gibbs ringing, and MR undersampling artifacts. These priors are iteratively reweighted using normalized multi-modal Gaussian similarity kernels. Synergistic PET-MR reconstructions were built on the PET maximum a posteriori expectation maximization algorithm and the MR regularized sensitivity encoding method. The proposed approach was compared to conventional methods, total variation, and prior-image weighted quadratic regularization methods. Comparisons were performed on a simulated [18 F]fluorodeoxyglucose-PET and T1 /T2 -weighted MR brain phantom, 2 in vivo T1 /T2 -weighted MR brain datasets, and an in vivo [18 F]fluorodeoxyglucose-PET and fluid-attenuated inversion recovery/T1 -weighted MR brain dataset.

RESULTS

Simulations showed that synergistic reconstructions achieve the lowest quantification errors for all image modalities compared to conventional, total variation, and weighted quadratic methods. Whereas total variation regularization preserved modality-unique features, this method failed to recover PET details and was not able to reduce MR artifacts compared to our proposed method. For in vivo MR data, our method maintained similar image quality for 3× and 14× accelerated data. Reconstruction of the PET-MR dataset also demonstrated improved performance of our method compared to the conventional independent methods in terms of reduced Gibbs and undersampling artifacts.

CONCLUSION

The proposed methodology offers a robust multi-modal synergistic image reconstruction framework that can be readily built on existing established algorithms.

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.

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.

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.

Coupled regularization with multiple data discrepancies

We consider a class of regularization methods for inverse problems where a coupled regularization is employed for the simultaneous reconstruction of data from multiple sources. Applications for such a setting can be found in multi-spectral or multimodality inverse problems, but also in inverse problems with dynamic data. We consider this setting in a rather general framework and derive stability and convergence results, including convergence rates. In particular, we show how parameter choice strategies adapted to the interplay of different data channels allow to improve upon convergence rates that would be obtained by treating all channels equally. Motivated by concrete applications, our results are obtained under rather general assumptions that allow to include the Kullback-Leibler divergence as data discrepancy term. To simplify their application to concrete settings, we further elaborate several practically relevant special cases in detail. To complement the analytical results, we also provide an algorithmic framework and source code that allows to solve a class of jointly regularized inverse problems with any number of data discrepancies. As concrete applications, we show numerical results for multi-contrast MR and joint MR-PET reconstruction.

PET/MRI: a frontier in era of complementary hybrid imaging

With primitive approaches, the diagnosis and therapy were operated at the cellular, molecular, or even at the genetic level. As the diagnostic techniques are more concentrated towards molecular level, multi modal imaging becomes specifically essential. Multi-modal imaging has extensive applications in clinical as well as in pre-clinical studies. Positron Emission Tomography (PET) has flourished in the field of nuclear medicine, which has motivated it to fuse with Computed Tomography (CT) and Magnetic Resonance Imaging (MRI) for PET/CT and PET/MRI respectively. However, the challenges in PET/CT are due to the inability of simultaneous acquisition and reduced soft tissue contrast, which has led to the development of PET/MRI. Also, MRI offers the better soft tissue contrast over CT. Hence, fusion of PET and MRI results in combining structural information with functional image from PET. Yet, it has many technical challenges due to the interference between the modalities. Also, it must be resolved with various approaches for addressing the shortcomings of each system and improvise on the image quantification system. This review elaborates on the various challenges in the present PET/MRI system and the future directions of the hybrid modality. Also, the different data acquisition and analysis techniques of PET/MRI system are discussed with enhanced details on the software tools.

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.

Penalized maximum likelihood simultaneous longitudinal PET image reconstruction with difference-image priors

PURPOSE

Many clinical contexts require the acquisition of multiple positron emission tomography (PET) scans of a single subject, for example, to observe and quantitate changes in functional behaviour in tumors after treatment in oncology. Typically, the datasets from each of these scans are reconstructed individually, without exploiting the similarities between them. We have recently shown that sharing information between longitudinal PET datasets by penalizing voxel-wise differences during image reconstruction can improve reconstructed images by reducing background noise and increasing the contrast-to-noise ratio of high-activity lesions. Here, we present two additional novel longitudinal difference-image priors and evaluate their performance using two-dimesional (2D) simulation studies and a three-dimensional (3D) real dataset case study.

METHODS

We have previously proposed a simultaneous difference-image-based penalized maximum likelihood (PML) longitudinal image reconstruction method that encourages sparse difference images (DS-PML), and in this work we propose two further novel prior terms. The priors are designed to encourage longitudinal images with corresponding differences which have (a) low entropy (DE-PML), and (b) high sparsity in their spatial gradients (DTV-PML). These two new priors and the originally proposed longitudinal prior were applied to 2D-simulated treatment response [¹⁸ F]fluorodeoxyglucose (FDG) brain tumor datasets and compared to standard maximum likelihood expectation-maximization (MLEM) reconstructions. These 2D simulation studies explored the effects of penalty strengths, tumor behaviour, and interscan coupling on reconstructed images. Finally, a real two-scan longitudinal data series acquired from a head and neck cancer patient was reconstructed with the proposed methods and the results compared to standard reconstruction methods.

RESULTS

Using any of the three priors with an appropriate penalty strength produced images with noise levels equivalent to those seen when using standard reconstructions with increased counts levels. In tumor regions, each method produces subtly different results in terms of preservation of tumor quantitation and reconstruction root mean-squared error (RMSE). In particular, in the two-scan simulations, the DE-PML method produced tumor means in close agreement with MLEM reconstructions, while the DTV-PML method produced the lowest errors due to noise reduction within the tumor. Across a range of tumor responses and different numbers of scans, similar results were observed, with DTV-PML producing the lowest errors of the three priors and DE-PML producing the lowest bias. Similar improvements were observed in the reconstructions of the real longitudinal datasets, although imperfect alignment of the two PET images resulted in additional changes in the difference image that affected the performance of the proposed methods.

CONCLUSION

Reconstruction of longitudinal datasets by penalizing difference images between pairs of scans from a data series allows for noise reduction in all reconstructed images. An appropriate choice of penalty term and penalty strength allows for this noise reduction to be achieved while maintaining reconstruction performance in regions of change, either in terms of quantitation of mean intensity via DE-PML, or in terms of tumor RMSE via DTV-PML. Overall, improving the image quality of longitudinal datasets via simultaneous reconstruction has the potential to improve upon currently used methods, allow dose reduction, or reduce scan time while maintaining image quality at current levels.

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.

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

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

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.

Evaluation of Parallel Level Sets and Bowsher's Method as Segmentation-Free Anatomical Priors for Time-of-Flight PET Reconstruction

In this article, we evaluate Parallel Level Sets (PLS) and Bowsher's method as segmentation-free anatomical priors for regularized brain positron emission tomography (PET) reconstruction. We derive the proximity operators for two PLS priors and use the EM-TV algorithm in combination with the first order primal-dual algorithm by Chambolle and Pock to solve the non-smooth optimization problem for PET reconstruction with PLS regularization. In addition, we compare the performance of two PLS versions against the symmetric and asymmetric Bowsher priors with quadratic and relative difference penalty function. For this aim, we first evaluate reconstructions of 30 noise realizations of simulated PET data derived from a real hybrid positron emission tomography/magnetic resonance imaging (PET/MR) acquisition in terms of regional bias and noise. Second, we evaluate reconstructions of a real brain PET/MR data set acquired on a GE Signa time-of-flight PET/MR in a similar way. The reconstructions of simulated and real 3D PET/MR data show that all priors were superior to post-smoothed maximum likelihood expectation maximization with ordered subsets (OSEM) in terms of bias-noise characteristics in different regions of interest where the PET uptake follows anatomical boundaries. Our implementation of the asymmetric Bowsher prior showed slightly superior performance compared with the two versions of PLS and the symmetric Bowsher prior. At very high regularization weights, all investigated anatomical priors suffer from the transfer of non-shared gradients.

Magnetic Resonance-Derived Improvements in PET Imaging

Simultaneous PET-MR imaging improves deficiencies in PET images. The primary areas in which magnetic resonance (MR) has been applied to guide PET results are in correction for patient motion and in improving the effects of PET resolution and partial volume averaging. MR-guided motion correction of PET has been applied to respiratory, cardiac, and gross body movements and shown to improve lesion detectability and contrast. Partial volume correction or resolution improvement of PET governed by MR imaging anatomic information improves visualization of structures and quantitative accuracy. Evaluation in clinical applications is needed to determine their true impacts.

MR-guided joint reconstruction of activity and attenuation in brain PET-MR

With the advent of time-of-flight (TOF) PET scanners, joint maximum-likelihood reconstruction of activity and attenuation (MLAA) maps has recently regained attention for the estimation of PET attenuation maps from emission data. However, the estimated attenuation and activity maps are scaled by unknown scaling factors. We recently demonstrated that in hybrid PET-MR, the scaling issue of this algorithm can be effectively addressed by imposing MR spatial constraints on the estimation of attenuation maps using a penalized MLAA (P-MLAA⁺) algorithm. With the advent of simultaneous PET-MR systems, MRI-guided PET image reconstruction has also gained attention for improving the quantitative accuracy of PET images, usually degraded by noise and partial volume effects. The aim of this study is therefore to increase the benefits of MRI information for improving the quantitative accuracy of PET images by exploiting MRI-based anatomical penalty functions to guide the reconstruction of both activity and attenuation maps during their joint estimation. We employed an anato-functional joint entropy penalty function for the reconstruction of activity and an anatomical quadratic penalty function for the reconstruction of attenuation. The resulting algorithm was referred to as P-MLAA⁺⁺ since it exploits both activity and attenuation penalty functions. The performance of the P-MLAA algorithms were compared with MLAA and the widely used activity reconstruction algorithms such as maximum likelihood expectation maximization (MLEM) and penalized MLEM (P-MLEM) both corrected for attenuation using a conventional MRI segmentation-based attenuation correction (MRAC) method. The studied methods were evaluated using simulations and clinical studies taking the PET image reconstructed using reference CT-based attenuation maps as a reference. The simulation results showed that the proposed method can notably improve the visual quality of the PET images by reducing noise while preserving structural boundaries and at the same time improving the quantitative accuracy of the PET images. Our clinical reconstruction results showed that the MLEM-MRAC, P-MLEM-MRAC, MLAA, P-MLAA⁺ and P-MLAA⁺⁺ algorithms result in, on average, quantification errors of -13.5 ± 3.1%, -13.4 ± 3.1%, -2.0 ± 6.5%, -3.0 ± 3.5% and -4.2 ± 3.6%, respectively, in different regions of the brain. In conclusion, whilst the P-MLAA⁺ algorithm showed the best overall quantification performance, the proposed P-MLAA⁺⁺ algorithm provided simultaneous partial volume and attenuation corrections with only a minor compromise of PET quantification.

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.

PET image reconstruction using multi-parametric anato-functional priors

In this study, we investigate the application of multi-parametric anato-functional (MR-PET) priors for the maximum a posteriori (MAP) reconstruction of brain PET data in order to address the limitations of the conventional anatomical priors in the presence of PET-MR mismatches. In addition to partial volume correction benefits, the suitability of these priors for reconstruction of low-count PET data is also introduced and demonstrated, comparing to standard maximum-likelihood (ML) reconstruction of high-count data. The conventional local Tikhonov and total variation (TV) priors and current state-of-the-art anatomical priors including the Kaipio, non-local Tikhonov prior with Bowsher and Gaussian similarity kernels are investigated and presented in a unified framework. The Gaussian kernels are calculated using both voxel- and patch-based feature vectors. To cope with PET and MR mismatches, the Bowsher and Gaussian priors are extended to multi-parametric priors. In addition, we propose a modified joint Burg entropy prior that by definition exploits all parametric information in the MAP reconstruction of PET data. The performance of the priors was extensively evaluated using 3D simulations and two clinical brain datasets of [18F]florbetaben and [18F]FDG radiotracers. For simulations, several anato-functional mismatches were intentionally introduced between the PET and MR images, and furthermore, for the FDG clinical dataset, two PET-unique active tumours were embedded in the PET data. Our simulation results showed that the joint Burg entropy prior far outperformed the conventional anatomical priors in terms of preserving PET unique lesions, while still reconstructing functional boundaries with corresponding MR boundaries. In addition, the multi-parametric extension of the Gaussian and Bowsher priors led to enhanced preservation of edge and PET unique features and also an improved bias-variance performance. In agreement with the simulation results, the clinical results also showed that the Gaussian prior with voxel-based feature vectors, the Bowsher and the joint Burg entropy priors were the best performing priors. However, for the FDG dataset with simulated tumours, the TV and proposed priors were capable of preserving the PET-unique tumours. Finally, an important outcome was the demonstration that the MAP reconstruction of a low-count FDG PET dataset using the proposed joint entropy prior can lead to comparable image quality to a conventional ML reconstruction with up to 5 times more counts. In conclusion, multi-parametric anato-functional priors provide a solution to address the pitfalls of the conventional priors and are therefore likely to increase the diagnostic confidence in MR-guided PET image reconstructions.