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

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.

Image reconstruction using UNET-transformer network for fast and low-dose PET scans

INTRODUCTION

Low-dose and fast PET imaging (low-count PET) play a significant role in enhancing patient safety, healthcare efficiency, and patient comfort during medical imaging procedures. To achieve high-quality images with low-count PET scans, effective reconstruction models are crucial for denoising and enhancing image quality. The main goal of this paper is to develop an effective and accurate deep learning-based method for reconstructing low-count PET images, which is a challenging problem due to the limited amount of available data and the high level of noise in the acquired images. The proposed method aims to improve the quality of reconstructed PET images while preserving important features, such as edges and small details, by combining the strengths of UNET and Transformer networks.

MATERIAL AND METHODS

The proposed TrUNET-MAPEM model integrates a residual UNET-transformer regularizer into the unrolled maximum a posteriori expectation maximization (MAPEM) algorithm for PET image reconstruction. A loss function based on a combination of structural similarity index (SSIM) and mean squared error (MSE) is utilized to evaluate the accuracy of the reconstructed images. The simulated dataset was generated using the Brainweb phantom, while the real patient dataset was acquired using a Siemens Biograph mMR PET scanner. We also implemented state-of-the-art methods for comparison purposes: OSEM, MAPOSEM, and supervised learning using 3D-UNET network. The reconstructed images are compared to ground truth images using metrics such as peak signal-to-noise ratio (PSNR), structural similarity index (SSIM), and relative root mean square error (rRMSE) to quantitatively evaluate the accuracy of the reconstructed images.

RESULTS

Our proposed TrUNET-MAPEM approach was evaluated using both simulated and real patient data. For the patient data, our model achieved an average PSNR of 33.72 dB, an average SSIM of 0.955, and an average rRMSE of 0.39. These results outperformed other methods which had average PSNRs of 36.89 dB, 34.12 dB, and 33.52 db, average SSIMs of 0.944, 0.947, and 0.951, and average rRMSEs of 0.59, 0.49, and 0.42. For the simulated data, our model achieved an average PSNR of 31.23 dB, an average SSIM of 0.95, and an average rRMSE of 0.55. These results also outperformed other state-of-the-art methods, such as OSEM, MAPOSEM, and 3DUNET-MAPEM. The model demonstrates the potential for clinical use by successfully reconstructing smooth images while preserving edges. The comparison with other methods demonstrates the superiority of our approach, as it outperforms all other methods for all three metrics.

CONCLUSION

The proposed TrUNET-MAPEM model presents a significant advancement in the field of low-count PET image reconstruction. The results demonstrate the potential for clinical use, as the model can produce images with reduced noise levels and better edge preservation compared to other reconstruction and post-processing algorithms. The proposed approach may have important clinical applications in the early detection and diagnosis of various diseases.

Fast and memory-efficient reconstruction of sparse Poisson data in listmode with non-smooth priors with application to time-of-flight PET

Objective. Complete time of flight (TOF) sinograms of state-of-the-art TOF PET scanners have a large memory footprint. Currently, they contain ∼4 · 109 data bins which amount to ∼17 GB in 32 bit floating point precision. Moreover, their size will continue to increase with advances in the achievable detector TOF resolution and increases in the axial field of view. Using iterative algorithms to reconstruct such enormous TOF sinograms becomes increasingly challenging due to the memory requirements and the computation time needed to evaluate the forward model for every data bin. This is especially true for more advanced optimization algorithms such as the stochastic primal-dual hybrid gradient (SPDHG) algorithm which allows for the use of non-smooth priors for regularization using subsets with guaranteed convergence. SPDHG requires the storage of additional sinograms in memory, which severely limits its application to data sets from state-of-the-art TOF PET systems using conventional computing hardware. Approach. Motivated by the generally sparse nature of the TOF sinograms, we propose and analyze a new listmode (LM) extension of the SPDHG algorithm for image reconstruction of sparse data following a Poisson distribution. The new algorithm is evaluated based on realistic 2D and 3D simulationsn, and a real data set acquired on a state-of-the-art TOF PET/CT system. The performance of the newly proposed LM SPDHG algorithm is compared against the conventional sinogram SPDHG and the listmode EM-TV algorithm. Main results. We show that the speed of convergence of the proposed LM-SPDHG is equivalent the original SPDHG operating on binned data (TOF sinograms). However, we find that for a TOF PET system with 400 ps TOF resolution and 25 cm axial FOV, the proposed LM-SPDHG reduces the required memory from approximately 56 to 0.7 GB for a short dynamic frame with 107 prompt coincidences and to 12.4 GB for a long static acquisition with 5·108 prompt coincidences. Significance. In contrast to SPDHG, the reduced memory requirements of LM-SPDHG enables a pure GPU implementation on state-of-the-art GPUs—avoiding memory transfers between host and GPU—which will substantially accelerate reconstruction times. This in turn will allow the application of LM-SPDHG in routine clinical practice where short reconstruction times are crucial.

Future Directions in Molecular Imaging of Neurodegenerative Disorders

The improvement of existing techniques and the development of new molecular imaging methods are an exciting and rapidly developing field in clinical care and research of neurodegenerative disorders. In the clinic, molecular imaging has the potential to improve early and differential diagnosis and to stratify and monitor therapy in these disorders. Meanwhile, in research, these techniques improve our understanding of the underlying pathophysiology and pathobiochemistry of these disorders and allow for drug testing. This article is an overview on our perspective on future developments in neurodegeneration tracers and the associated imaging technologies. For example, we predict that the current portfolio of β-amyloid and tau aggregate tracers will be improved and supplemented by tracers allowing imaging of other protein aggregation pathologies, such as α-synuclein and transactive response DNA binding protein 43 kDa. Future developments will likely also be observed in imaging neurotransmitter systems. This refers to both offering imaging to a broader population in cases involving the dopaminergic, cholinergic, and serotonergic systems and making possible the imaging of systems not yet explored, such as the glutamate and opioid systems. Tracers will be complemented by improved tracers of neuroinflammation and synaptic density. Technologywise, the use of hybrid PET/MRI, dedicated brain PET, and total-body PET scanners, as well as advanced image acquisition and processing protocols, will open doors toward broader and more efficient clinical use and novel research applications. Molecular imaging has the potential of becoming a standard and essential clinical and research tool to diagnose and study neurodegenerative disorders and to guide treatments. On that road, we will need to redefine the role of molecular imaging in relation to that of emerging blood-based biomarkers. Taken together, the unique features of molecular imaging-that is, the potential to provide direct noninvasive information on the presence, extent, localization, and quantity of molecular pathologic processes in the living body-together with the predicted novel tracer and imaging technology developments, provide optimism about a bright future for this approach to improved care and research on neurodegenerative disorders.

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.

Anatomically aided PET image reconstruction using deep neural networks

PURPOSE

The developments of PET/CT and PET/MR scanners provide opportunities for improving PET image quality by using anatomical information. In this paper, we propose a novel co-learning three-dimensional (3D) convolutional neural network (CNN) to extract modality-specific features from PET/CT image pairs and integrate complementary features into an iterative reconstruction framework to improve PET image reconstruction.

METHODS

We used a pretrained deep neural network to represent PET images. The network was trained using low-count PET and CT image pairs as inputs and high-count PET images as labels. This network was then incorporated into a constrained maximum likelihood framework to regularize PET image reconstruction. Two different network structures were investigated for the integration of anatomical information from CT images. One was a multichannel CNN, which treated PET and CT volumes as separate channels of the input. The other one was multibranch CNN, which implemented separate encoders for PET and CT images to extract latent features and fed the combined latent features into a decoder. Using computer-based Monte Carlo simulations and two real patient datasets, the proposed method has been compared with existing methods, including the maximum likelihood expectation maximization (MLEM) reconstruction, a kernel-based reconstruction and a CNN-based deep penalty method with and without anatomical guidance.

RESULTS

Reconstructed images showed that the proposed constrained ML reconstruction approach produced higher quality images than the competing methods. The tumors in the lung region have higher contrast in the proposed constrained ML reconstruction than in the CNN-based deep penalty reconstruction. The image quality was further improved by incorporating the anatomical information. Moreover, the liver standard deviation was lower in the proposed approach than all the competing methods at a matched lesion contrast.

CONCLUSIONS

The supervised co-learning strategy can improve the performance of constrained maximum likelihood reconstruction. Compared with existing techniques, the proposed method produced a better lesion contrast versus background standard deviation trade-off curve, which can potentially improve lesion detection.

Motion estimation and correction for simultaneous PET/MR using SIRF and CIL

SIRF is a powerful PET/MR image reconstruction research tool for processing data and developing new algorithms. In this research, new developments to SIRF are presented, with focus on motion estimation and correction. SIRF's recent inclusion of the adjoint of the resampling operator allows gradient propagation through resampling, enabling the MCIR technique. Another enhancement enabled registering and resampling of complex images, suitable for MRI. Furthermore, SIRF's integration with the optimization library CIL enables the use of novel algorithms. Finally, SPM is now supported, in addition to NiftyReg, for registration. Results of MR and PET MCIR reconstructions are presented, using FISTA and PDHG, respectively. These demonstrate the advantages of incorporating motion correction and variational and structural priors. This article is part of the theme issue 'Synergistic tomographic image reconstruction: part 2'.

Synergistic multi-spectral CT reconstruction with directional total variation

This work considers synergistic multi-spectral CT reconstruction where information from all available energy channels is combined to improve the reconstruction of each individual channel. We propose to fuse these available data (represented by a single sinogram) to obtain a polyenergetic image which keeps structural information shared by the energy channels with increased signal-to-noise ratio. This new image is used as prior information during a channel-by-channel minimization process through the directional total variation. We analyse the use of directional total variation within variational regularization and iterative regularization. Our numerical results on simulated and experimental data show improvements in terms of image quality and in computational speed. This article is part of the theme issue 'Synergistic tomographic image reconstruction: part 2'.

Towards lower-dose PET using physics-based uncertainty-aware multimodal learning with robustness to out-of-distribution data

Radiation exposure in positron emission tomography (PET) imaging limits its usage in the studies of radiation-sensitive populations, e.g., pregnant women, children, and adults that require longitudinal imaging. Reducing the PET radiotracer dose or acquisition time reduces photon counts, which can deteriorate image quality. Recent deep-neural-network (DNN) based methods for image-to-image translation enable the mapping of low-quality PET images (acquired using substantially reduced dose), coupled with the associated magnetic resonance imaging (MRI) images, to high-quality PET images. However, such DNN methods focus on applications involving test data that match the statistical characteristics of the training data very closely and give little attention to evaluating the performance of these DNNs on new out-of-distribution (OOD) acquisitions. We propose a novel DNN formulation that models the (i) underlying sinogram-based physics of the PET imaging system and (ii) the uncertainty in the DNN output through the per-voxel heteroscedasticity of the residuals between the predicted and the high-quality reference images. Our sinogram-based uncertainty-aware DNN framework, namely, suDNN, estimates a standard-dose PET image using multimodal input in the form of (i) a low-dose/low-count PET image and (ii) the corresponding multi-contrast MRI images, leading to improved robustness of suDNN to OOD acquisitions. Results on in vivo simultaneous PET-MRI, and various forms of OOD data in PET-MRI, show the benefits of suDNN over the current state of the art, quantitatively and qualitatively.

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.

Noise2Noise Improved by Trainable Wavelet Coefficients for PET Denoising

The significant statistical noise and limited spatial resolution of positron emission tomography (PET) data in sinogram space results in the degradation of the quality and accuracy of reconstructed images. Although high-dose radiotracers and long acquisition times improve the PET image quality, the patients’ radiation exposure increases and the patient is more likely to move during the PET scan. Recently, various data-driven techniques based on supervised deep neural network learning have made remarkable progress in reducing noise in images. However, these conventional techniques require clean target images that are of limited availability for PET denoising. Therefore, in this study, we utilized the Noise2Noise framework, which requires only noisy image pairs for network training, to reduce the noise in the PET images. A trainable wavelet transform was proposed to improve the performance of the network. The proposed network was fed wavelet-decomposed images consisting of low- and high-pass components. The inverse wavelet transforms of the network output produced denoised images. The proposed Noise2Noise filter with wavelet transforms outperforms the original Noise2Noise method in the suppression of artefacts and preservation of abnormal uptakes. The quantitative analysis of the simulated PET uptake confirms the improved performance of the proposed method compared with the original Noise2Noise technique. In the clinical data, 10 s images filtered with Noise2Noise are virtually equivalent to 300 s images filtered with a 6 mm Gaussian filter. The incorporation of wavelet transforms in Noise2Noise network training results in the improvement of the image contrast. In conclusion, the performance of Noise2Noise filtering for PET images was improved by incorporating the trainable wavelet transform in the self-supervised deep learning framework.

MR-guided motion-corrected PET image reconstruction for cardiac PET-MR

Simultaneous PET-MR imaging has shown potential for the comprehensive assessment of myocardial health from a single examination. Furthermore, MR-derived respiratory motion information has been shown to improve PET image quality by incorporating this information into the PET image reconstruction. Separately, MR-based anatomically guided PET image reconstruction has been shown to perform effective denoising, but this has been so far demonstrated mainly in brain imaging. To date the combined benefits of motion compensation and anatomical guidance have not been demonstrated for myocardial PET-MR imaging. This work addresses this by proposing a single cardiac PET-MR image reconstruction framework which fully utilises MR-derived information to allow both motion compensation and anatomical guidance within the reconstruction. Methods: Fifteen patients underwent a 18F-FDG cardiac PET-MR scan with a previously introduced acquisition framework. The MR data processing and image reconstruction pipeline produces respiratory motion fields and a high-resolution respiratory motion-corrected MR image with good tissue contrast. This MR-derived information was then included in a respiratory motion-corrected, cardiac-gated, anatomically guided image reconstruction of the simultaneously acquired PET data. Reconstructions were evaluated by measuring myocardial contrast and noise and compared to images from several comparative intermediate methods using the components of the proposed framework separately. Results: Including respiratory motion correction, cardiac gating, and anatomical guidance significantly increased contrast. In particular, myocardium-to-blood pool contrast increased by 143% on average (p<0.0001) compared to conventional uncorrected, non-guided PET images. Furthermore, anatomical guidance significantly reduced image noise compared to non-guided image reconstruction by 16.1% (p<0.0001). Conclusion: The proposed framework for MR-derived motion compensation and anatomical guidance of cardiac PET data was shown to significantly improve image quality compared to alternative reconstruction methods. Each component of the reconstruction pipeline was shown to have a positive impact on the final image quality. These improvements have the potential to improve clinical interpretability and diagnosis based on cardiac PET-MR images.

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.

AW-SDRLSE: Adaptive Weighting and Scalable Distance Regularized Level Set Evolution for Lymphoma Segmentation on PET Images

Accurate lymphoma segmentation on Positron Emission Tomography (PET) images is of great importance for medical diagnoses, such as for distinguishing benign and malignant. To this end, this paper proposes an adaptive weighting and scalable distance regularized level set evolution (AW-SDRLSE) method for delineating lymphoma boundaries on 2D PET slices. There are three important characteristics with respect to AW-SDRLSE: 1) A scalable distance regularization term is proposed and a parameter q can control the contour's convergence rate and precision in theory. 2) A novel dynamic annular mask is proposed to calculate mean intensities of local interior and exterior regions and further define the region energy term. 3) As the level set method is sensitive to parameters, we thus propose an adaptive weighting strategy for the length and area energy terms using local region intensity and boundary direction information. AW-SDRLSE is evaluated on 90 cases of real PET data with a mean Dice coefficient of 0.8796. Comparative results demonstrate the accuracy and robustness of AW-SDRLSE as well as its performance advantages as compared with related level set methods. In addition, experimental results indicate that AW-SDRLSE can be a fine segmentation method for improving the lymphoma segmentation results obtained by deep learning (DL) methods significantly.

Incorporation of anatomical MRI knowledge for enhanced mapping of brain metabolism using functional PET

Functional positron emission tomography (fPET) imaging using continuous infusion of [18F]-fluorodeoxyglucose (FDG) is a novel neuroimaging technique to track dynamic glucose utilization in the brain. In comparison to conventional static or dynamic bolus PET, fPET maintains a sustained supply of glucose in the blood plasma which improves sensitivity to measure dynamic glucose changes in the brain, and enables mapping of dynamic brain activity in task-based and resting-state fPET studies. However, there is a trade-off between temporal resolution and spatial noise due to the low concentration of FDG and the limited sensitivity of multi-ring PET scanners. Images from fPET studies suffer from partial volume errors and residual scatter noise that may cause the cerebral metabolic functional maps to be biased. Gaussian smoothing filters used to denoise the fPET images are suboptimal, as they introduce additional partial volume errors. In this work, a post-processing framework based on a magnetic resonance (MR) Bowsher-like prior was used to improve the spatial and temporal signal to noise characteristics of the fPET images. The performance of the MR guided method was compared with conventional denosing methods using both simulated and in vivo task fPET datasets. The results demonstrate that the MR-guided fPET framework denoises the fPET images and improves the partial volume correction, consequently enhancing the sensitivity to identify brain activation, and improving the anatomical accuracy for mapping changes of brain metabolism in response to a visual stimulation task. The framework extends the use of functional PET to investigate the dynamics of brain metabolic responses for faster presentation of brain activation tasks, and for applications in low dose PET imaging.

Di-chromatic interpolation of magnetic resonance metabolic images

OBJECTIVE

Magnetic resonance imaging with hyperpolarized contrast agents can provide unprecedented in vivo measurements of metabolism, but yields images that are lower resolution than that achieved with proton anatomical imaging. In order to spatially localize the metabolic activity, the metabolic image must be interpolated to the size of the proton image. The most common methods for choosing the unknown values rely exclusively on values of the original uninterpolated image.

METHODS

In this work, we present an alternative method that uses the higher-resolution proton image to provide additional spatial structure. The interpolated image is the result of a convex optimization algorithm which is solved with the fast iterative shrinkage threshold algorithm (FISTA).

RESULTS

Results are shown with images of hyperpolarized pyruvate, lactate, and bicarbonate using data of the heart and brain from healthy human volunteers, a healthy porcine heart, and a human with prostate cancer.

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.

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.

Faster PET reconstruction with non-smooth priors by randomization and preconditioning

Uncompressed clinical data from modern positron emission tomography (PET) scanners are very large, exceeding 350 million data points (projection bins). The last decades have seen tremendous advancements in mathematical imaging tools many of which lead to non-smooth (i.e. non-differentiable) optimization problems which are much harder to solve than smooth optimization problems. Most of these tools have not been translated to clinical PET data, as the state-of-the-art algorithms for non-smooth problems do not scale well to large data. In this work, inspired by big data machine learning applications, we use advanced randomized optimization algorithms to solve the PET reconstruction problem for a very large class of non-smooth priors which includes for example total variation, total generalized variation, directional total variation and various different physical constraints. The proposed algorithm randomly uses subsets of the data and only updates the variables associated with these. While this idea often leads to divergent algorithms, we show that the proposed algorithm does indeed converge for any proper subset selection. Numerically, we show on real PET data (FDG and florbetapir) from a Siemens Biograph mMR that about ten projections and backprojections are sufficient to solve the MAP optimisation problem related to many popular non-smooth priors; thus showing that the proposed algorithm is fast enough to bring these models into routine clinical practice.

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.

Magnetic Resonance Fingerprinting: Implications and Opportunities for PET/MR

Magnetic Resonance Imaging (MRI) can be used to assess anatomical structure, and its sensitivity to a variety of tissue properties enables superb contrast between tissues as well as the ability to characterize these tissues. However, despite vast potential for quantitative and functional evaluation, MRI is typically used qualitatively, in which the underlying tissue properties are not measured, and thus the brightness of each pixel is not quantitatively meaningful. Positron Emission Tomography (PET) is an inherently quantitative imaging modality that interrogates functional activity within a tissue, probed by a molecule of interest coupled with an appropriate tracer. These modalities can complement one another to provide clinical information regarding both structure and function, but there are still technical and practical hurdles in the way of the integrated use of both modalities. Recent advances in MRI have moved the field in an increasingly quantitative direction, which is complementary to PET, and could also potentially help solve some of the challenges in PET/MR. Magnetic Resonance Fingerprinting (MRF) is a recently described MRI-based technique which can efficiently and simultaneously quantitatively map several tissue properties in a single exam. Here, the basic principles behind the quantitative approach of MRF are laid out, and the potential implications for combined PET/MR are discussed.

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.

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.