This paper proposes a new approach for PET reconstruction using learned regularization operators guided by MRI. It extends the Plug-and-Play framework we previously proposed for standalone PET reconstruction. In contrast to existing AI-based reconstruction methods, our method can be proved to converge to a unique fixed point, thus bridging the gap between practical performance and theoretical guarantees. It relies on a preconditioned ADMM algorithm and leverages a learned, firmly nonexpansive neural network, defined with respect to a metric derived from the Fisher Information Matrix that reflects the statistical uncertainty of the Poisson model. The network is trained to satisfy the fixed-point equation associated with the reconstruction problem. In particular, we plugged various MRI-conditioned operators into our algorithm, from multibranch and multichannel U-Nets to a learned proximity operator as a deep equilibrium model. We investigated the quantitative performance of the method trained on a dataset of clinical [18F]-FDG PET and MR images acquired on a hybrid PET-MR system for three dose-reduction factors, comparing it with anatomical guidance using the Bowsher and Deep Image Prior methods. Our results illustrate that our multibranch U-Net without skip connections at higher decomposition levels achieved better bias-standard deviation trade-offs than the other U-Nets and the considered baselines. When synthetic lesions were simulated in the PET image alone, the deep equilibrium model outperformed the multibranch U-Net, making it a prime candidate for robust low-count MR-guided PET reconstruction.

Organic anion-transporting polypeptides (OATP) transporter function, which mediates many drugs' liver uptake, was investigated as a molecular determinant of pharmacokinetic variability. Whole-body PET imaging using 11C-glyburide, a metabolically stable OATP probe, was performed in 16 healthy humans. Ten subjects underwent another 11C-glyburide PET acquisition after OATP inhibition using rifampicin. Subjects were sorted according to age and sex: males<30y (24.0 ± 3.2 y, n = 7), males>50y (57.5 ± 5.6 y, n = 4), and females>50y (60.6 ± 2.4 y, n = 5). The blood-to-liver transfer rate (k uptake) was estimated to describe OATP function. Rifampicin decreased k uptake (-73 ± 13%, P < 0.001) and liver exposure (-50 ± 10%, P < 0.001) while increasing exposure in blood (+24 ± 24%, P < 0.01), myocardium, spleen, and brain (P < 0.05). No evidence of extra-hepatic rifampicin-inhibitable transport of 11C-glyburide was found. Baseline liver exposure was 42.6 ± 18.4% higher (P < 0.05) in females>50y compared with males>50 y, consistent with higher k uptake values (P < 0.05), with negligible impact on blood exposure (P < 0.05). In males, neither liver exposure, blood exposure, nor k uptake were affected by aging (P < 0.05). k uptake was positively and negatively correlated with liver (P < 0.01, R 2 = 0.78) and blood (P < 0.01, R 2 = 0.40) exposures respectively. The impact of OATP function (k uptake) on liver exposure was 4-fold more pronounced than on blood exposure. OATP function may thus drive important sex-related differences in liver exposure, which were not discernible through conventional blood-based pharmacokinetics.

The reliability of a new academic software, PET KinetiX, designed for fast parametric 4D-PET imaging computation, is assessed under simulated conditions. 4D-PET data were simulated using the XCAT digital phantom and realistic time-activity curves (ground truth). Four hundred analytical simulations were reconstructed using CASToR, an open-source software for tomographic reconstruction, replicating the clinical characteristics of two available PET systems with short and long axial fields of view (SAFOV and LAFOV). A total of 2,800 Patlak and 2TCM kinetic parametric maps of 18F-FDG were generated using PET KinetiX. The mean biases and standard deviations of the kinetic parametric maps were computed for each tissue label and compared to the biases of unprocessed SUV data. Additionally, the mean absolute ratio of kinetic-to-SUV contrast-to-noise ratio (CNR) was estimated for each tissue structure, along with the corresponding standard deviations. The Ki and vb parametric maps produced by PET KinetiX faithfully reproduced the predefined multi-tissue structures of the XCAT digital phantom for both Patlak and 2TCM models. Image definition was influenced by the 4D-PET input data: a higher number of iterations resulted in sharper rendering and higher standard deviations in PET signal characteristics. Biases relative to the ground truth varied across tissue structures and hardware configurations, similarly to unprocessed SUV data. In most tissue structures, Patlak kinetic-to-SUV CNR ratios exceeded 1 for both SAFOV and LAFOV configurations. The highest kinetic-to-SUV CNR ratio was observed in 2TCM k₃ maps within tumor regions. PET KinetiX currently generates Ki and vb parametric maps that are qualitatively comparable to unprocessed SUV data, with improved CNR in most cases. The 2TCM k₃ parametric maps for tumor structures exhibited the highest CNR enhancement, warranting further evaluation across different anatomical regions and radiotracer applications.

Objective. Deep learning has shown great promise for improving medical image reconstruction, including positron emission tomography (PET). However, concerns remain about the stability and robustness of these methods, especially when trained on limited data. This work aims to explore the use of the Plug-and-Play (PnP) framework in PET reconstruction to address these concerns. Approach. We propose a convergent PnP algorithm for low-count PET reconstruction based on the Douglas-Rachford splitting method. We consider several denoisers trained to satisfy fixed-point conditions, with convergence properties ensured either during training or by design, including a spectrally normalized network and a deep equilibrium model. We evaluate the bias-standard deviation tradeoff across clinically relevant regions and an unseen pathological case in a synthetic experiment and a real study. Comparisons are made with model-based iterative reconstruction, post-reconstruction denoising, a deep end-to-end unfolded network and PnP with a Gaussian denoiser. Main results. Our method achieves lower bias than post-reconstruction processing and reduced standard deviation at matched bias compared to model-based iterative reconstruction. While spectral normalization underperforms in generalization, the deep equilibrium model remains competitive with convolutional networks for PnP reconstruction and generalizes better to the unseen pathology. Compared to the end-to-end unfolded network, it also generalizes more consistently. Significance. This study demonstrates the potential of the PnP framework to improve image quality and quantification accuracy in PET reconstruction. It also highlights the importance of how convergence conditions are imposed on the denoising network to ensure robust and generalizable performance.

This letter extends the capabilities of Plug-and-Play ADMM, a popular algorithm for solving inverse problems while leveraging deep learning priors. Convergence results on PnP ADMM often rely on the Douglas-Rachford (DR) splitting method and require a firmly nonexpansive constraint on the plugged network. Common convolutional architectures do not inherently verify this constraint, and many works are now trying to circumvent it. Building on recent advancements in the DR method for handling weakly monotone operators, we propose a modification of PnP ADMM for low-count Positron Emission Tomography reconstruction, allowing for networks trained on reconstruction-specific tasks with a more general averageness constraint. Our numerical experiments on simulated brain data demonstrate that this flexibility simplifies training and improves reconstruction quality.

We propose in this work a framework for synergistic positron emission tomography (PET)/computed tomography (CT) reconstruction using a joint generative model as a penalty. We use a synergistic penalty function that promotes PET/CT pairs that are likely to occur together. The synergistic penalty function is based on a generative model, namely β-variational autoencoder (β-VAE). The model generates a PET/CT image pair from the same latent variable which contains the information that is shared between the two modalities. This sharing of inter-modal information can help reduce noise during reconstruction. Our result shows that our method was able to utilize the information between two modalities. The proposed method was able to outperform individually reconstructed images of PET (i.e., by maximum likelihood expectation maximization (MLEM)) and CT (i.e., by weighted least squares (WLS)) in terms of peak signal-to-noise ratio (PSNR). Future work will focus on optimizing the parameters of the β-VAE network and further exploration of other generative network models.

Les performances d'une nouvelle solution logicielle d'imagerie paramétrique TEP post-reconstruction, dénommée PET KinetiX, sont validées sur fantôme numérique. Des données TEP-4D thoraciques au 18F-FDG ont été simulées par approche analytique, à partir de courbes temps/activité 18F-FDG réalistes de 60 minutes dont les paramètres k1, k2 et k3 sont prédéfinis. Ces données ont été simulées sans bruit ou avec un niveau de bruit réaliste, puis reconstruites de manière similaire aux données cliniques pour obtenir des images tomographiques dynamiques. Ces images TEP-4D ont été traitées avec PET KinetiX (approche IDIF) permettant de générer des cartes paramétriques de KiPatlak et V (modèle de Patlak), ainsi que de k1, k2, k3 et Ki2TCM (modèle irréversible à 2 compartiments). Pour chaque constante d'échange, le biais des valeurs estimées via PET KinetiX par rapport à la vérité terrain (valeur simulée prédéfinie) a été calculé par organe : Biais ( %) = (ConstantePET KinetiX − Constantesimu)/Constante simu × 100. Les données quantitatives sont exprimées en médiane [IQR]. Pour les images reconstruites sans bruit, le biais estimé de PET KinetiX était inférieur à 0,5 % pour les constantes V, KiPatlak, k1, k2, k3, Ki2TCM. Pour les images reconstruites bruitées, les biais estimés de PET KinetiX varient entre 1,4 % et 23 % en fonction des organes caractérisant l'impact de la propagation du bruit dans les images reconstruites et les cartes paramétriques. PET KinetiX génère des données paramétriques fidèles par rapport aux données simulées de référence, validant ses performances en conditions simulées contrôlées bruitées et non bruitées. L'analyse des différents biais permet de préciser la robustesse des calculs.

Dual modality Positron Emission Tomography (PET)/Magnetic Resonance Imaging (MRI) systems provide seamless hardware-based image coregistration, making MRI-guided PET reconstruction a natural approach. In this work, we investigate the adaptability of the plug-and-play (PnP) paradigm for MRI-guided PET reconstruction. Inspired by proximal optimization algorithms and fixed point theory, the PnP approach proposes to replace the proximity operator of the regularization with a more general denoiser. Precisely, we integrate a deep denoiser - a DRUnet - into the Alternating Direction Method of Multipliers (ADMM) algorithm such that convergence of the iterates to a controlled set of fixed points is ensured. Results on simulated [18F]-FDG PET scans demonstrate that multibranch architectures are more compatible with the PnP framework than multichannel architectures and that the PnP fixed-point solutions have high likelihood and a lower mean squared error than the reconstruction obtained with a classical MRI-guided Bowsher regularization and without MRI guidance.

This article presents a physics-informed deep learning method for the quantitative estimation of the spatial coordinates of gamma interactions within a monolithic scintillator, with a focus on Positron Emission Tomography (PET) imaging. A Density Neural Network approach is designed to estimate the 2-dimensional gamma photon interaction coordinates in a fast lead tungstate (PbWO4) monolithic scintillator detector. We introduce a custom loss function to estimate the inherent uncertainties associated with the reconstruction process and to incorporate the physical constraints of the detector. This unique combination allows for more robust and reliable position estimations and the obtained results demonstrate the effectiveness of the proposed approach and highlights the significant benefits of the uncertainties estimation. We discuss its potential impact on improving PET imaging quality and show how the results can be used to improve the exploitation of the model, to bring benefits to the application and how to evaluate the validity of the given prediction and the associated uncertainties. Importantly, our proposed methodology extends beyond this specific use case, as it can be generalized to other applications beyond PET imaging.

The analytical projector (system matrix) used in most PET reconstructions does not incorporate Compton scattering and other important physical effects that affect the process generating the PET data, which can lead to biases. In our work, we define the projector from the generative model of a Monte-Carlo simulator, which already encompasses many of these effects. Based on the simulator's implicit distribution, we propose to learn a continuous analytic surrogate for the projector by using a neural density estimator. This avoids the discretization bottleneck associated with direct Monte-Carlo estimation of the PET system matrix, which leads to very high simulation cost. We compare our method with reconstructions using the classical projector, in which corrective terms are factored into a geometrically derived system matrix. Our experiments were carried out in the 2D setting, which enables smaller-scale testing.

In this work, we propose a synergistic PET/MR reconstruction method based on the ADMM algorithm and a pre-trained bimodal Variational Auto Encoder (VAE) as a constraint. Because of the multiple modalities, balancing the VAE's loss becomes a challenge. To solve this, we adapt an adaptive loss balancing method and apply it to the training of the VAE. We evaluate our approach on 2D slices from 44 different patients and show that the presented approach performs particularly well on low dose/highly undersampled data.

This work explores plug-and-play algorithms for PET reconstruction, combining deep learning with model-based variational methods. We aim to integrate classical convolutional architectures into algorithms such as ADMM and Forward-Backward (FB) while ensuring convergence and maintaining fixed-point control. We focus on the scenario where only high- and low-count reconstructed PET images are available for training our networks. Experimental results demonstrate that the proposed methods consistently reach fixed points with high likelihood and low mean squared error, thus showcasing the potential of convergent plug-and-play techniques for PET reconstruction.

Objective. In this study, we explore positron emission tomography (PET)/magnetic resonance imaging (MRI) joint reconstruction within a deep learning framework, introducing a novel synergistic method. Approach. We propose a new approach based on a variational autoencoder (VAE) constraint combined with the alternating direction method of multipliers (ADMM) optimization technique. We explore three VAE architectures, joint VAE, product of experts-VAE and multimodal JS divergence (MMJSD), to determine the optimal latent representation for the two modalities. We then trained and evaluated the architectures on a brain PET/MRI dataset. Main results. We showed that our approach takes advantage of each modality sharing information to each other, which results in improved peak signal-to-noise ratio and structural similarity as compared with traditional reconstruction, particularly for short acquisition times. We find that the one particular architecture, MMJSD, is the most effective for our methodology. Significance. The proposed method outperforms conventional approaches especially in noisy and undersampled conditions by making use of the two modalities together to compensate for the missing information.

To decipher the relevance of visual and semi-quantitative 6-fluoro-(18F)-L-DOPA (18F-DOPA) interpretation methods for the diagnostic of idiopathic Parkinson disease (IPD) in hybrid positron emission tomography (PET) and magnetic resonance imaging. A total of 110 consecutive patients (48 IPD and 62 controls) with 11 months of median clinical follow-up (reference standard) were included. A composite visual assessment from five independent nuclear imaging readers, together with striatal standard uptake value (SUV) to occipital SUV ratio, striatal gradients and putamen asymmetry-based semi-quantitative PET metrics automatically extracted used to train machine learning models to classify IPD versus controls. Using a ratio of 70/30 for training and testing sets, respectively, five classification models—k-NN, LogRegression, support vector machine, random forest and gradient boosting—were trained by using 100 times repeated nested cross-validation procedures. From the best model on average, the contribution of PET parameters was deciphered using the Shapley additive explanations method (SHAP). Cross-validated receiver operating characteristic curves (cv-ROC) of the most contributive PET parameters were finally estimated and compared. The best machine learning model (k-NN) provided final cv-ROC of 0.81. According to SHAP analyses, visual PET metric was the most important contributor to the model overall performance, followed by the minimum between left and right striatal to occipital SUV ratio. The 10-time cv-ROC curves of visual, min SUVr or both showed quite similar performance (mean area under the ROC of 0.81, 0.81 and 0.79, respectively, for visual, min SUVr or both). Visual expert analysis remains the most relevant parameter to predict IPD diagnosis at 11 months of median clinical follow-up in 18F-FDOPA. The min SUV ratio appears interesting in the perspective of simple semi-automated diagnostic workflows.

PET imaging is witnessing the development of new generations of detectors with less than 100ps CTR (Coincidence Time Resolution). Such a high CTR promises enhanced image quality. Another way to improve image quality is to use a total body (TB) geometry, increasing device sensitivity. Our work aims to quantify the expected improvements of TB geometry and high CTR detectors on clinical imaging and 4D pharmacokinetic studies. To do so, our first step is to model one of the gold-standard commercial devices, the GE SIGNA PET/MR, using the GATE Monte Carlo software. The simulation is validated against experimental data for sensitivity, Noise Equivalent Count Rate (NECR), spatial resolution, CTR and image analysis according to NEMA protocols. Results show good agreement for spatial resolution (3,1 vs 3,2 mm), sensitivity (23,6 vs 24,1 cps/kBq), NECR (peak at 221 vs 226,1 kcps respectively at 15,0 and 18,0 kBq/mL) and contrast recovery coefficients. For the performance illustration, 18 F FDG brain exams are simulated with a 390 ps and a 100 ps CTR. For the same purpose, 18 F FDG total body exams are also compared: an image reconstructed with three bed steps of the SIGNA with 390 ps CTR to one with a TB geometry, i.e. three times larger axial FOV with a 100 ps CTR. Images show expected contrast enhancement and background noise reduction in simulated clinical images. Future work is planned to be focused on the simulation of 4D exams and the quantification of these improvements in image quality.

In this work, we investigate hybrid PET reconstruction algorithms based on coupling a model-based variational reconstruction and the application of a separately learnt Deep Neural Network operator (DNN) in an ADMM Plug and Play framework. Following recent results in optimization, fixed point convergence of the scheme can be achieved by enforcing an additional constraint on network parameters during learning. We propose such an ADMM algorithm and show in a realistic [18F]-FDG synthetic brain exam that the proposed scheme indeed lead experimentally to convergence to a meaningful fixed point. When the proposed constraint is not enforced during learning of the DNN, the proposed ADMM algorithm was observed experimentally not to converge.

Positron emission tomography (PET) is a quantitative imaging modality widely used in oncology, neurology, and pharmacology. The data acquired by a PET scanner correspond to projections of the concentration activity, assumed to follow a Poisson distribution. The reconstruction of images from tomographic projections corrupted by Poisson noise is a challenging ill-posed large-scale inverse problem. Several available solvers use the majorization-minimization (MM) principle, though relying on various construction strategies with a lack of unifying framework. This work fills the gap by introducing the concept of Bregman majorization. This leads to a unified view of MM-based methods for image reconstruction in the presence of Poisson noise. From this general approach, we exhibit three algorithmic solutions and compare their computational efficiency on a problem of dynamic PET image reconstruction, either using GPU or CPU processing.

La maladie d'Alzheimer (MA) est caractérisée par l'accumulation anormale dans le cerveau des protéines tau et amyloïde et est souvent révélée par des troubles de la mémoire. Cependant, ceux-ci peuvent aussi se rencontrer dans d'autres maladies et conduire à des diagnostics par excès. L'objectif de l'étude est de définir l'apport de l'imagerie moléculaire par TEP pour le diagnostic étiologique chez des patients amnésiques bien caractérisés. Trente-six patients consultant pour un syndrome amnésique progressif évocateur de maladie d'Alzheimer ainsi que trente sujets sains ont été inclus dans l'étude. Tous les sujets ont bénéficié d'un bilan neuropsychologique et de neuro-imagerie : IRM à 3 T (atrophie) et deux examens TEP : [11 C]-PIB (332 ± 61 MBq ; dépôts amyloïdes) et [18F]-Flortaucipir (376 ± 21 MBq ; protéine tau) réalisés sur un tomographe à haute résolution (HRRT ; Siemens). Les sujets ont bénéficié d'un suivi clinique et IRM à 2 ans ainsi que d'une seconde TEP Tau (n = 20). La signature moléculaire de la MA était définie par une rétention amyloïde corticale positive (PIB index > 1,45) et une TEP tau positive dans les régions temporales médianes (z-score > 1,96). Les patients ne remplissant pas ces critères étant considérés comme présentant une pathologie non-MA. Selon ces critères, 21/36 patients ont été classés comme MA (PIB index : 2,9 ± 0,6 ; Tau 1,8 ± 0,7) et 15 comme non-MA (PIB index : 1,3 ± 0,2 ; Tau 1,2 ± 0,1). Les déficits neuropsychologiques et l'atrophie des hippocampes étaient similaires dans les deux groupes. Parmi les patients non-MA : 3 avaient une fixation PIB élevée mais pas de fixation Tau et 5 avaient une fixation Tau circonscrite au cortex entorhinal ou à l'amygdale mais étaient PIB négatifs. Le suivi longitudinal a montré une évolution plus importante du déclin cognitif et de l'atrophie temporale médiane dans le groupe MA vs non-MA. De même, à 2 ans, la fixation du traceur tau a augmenté chez les patients MA. (n = 12), mais est restée stable chez les non-MA. (n = 8). Le couplage de l'imagerie TEP amyloïde et tau a permis d'affiner le diagnostic étiologique chez des patients présentant des troubles mnésiques évocateurs de MA, pour lesquels cette maladie a néanmoins été éliminée chez environ 40 % d'entre eux. Chez les patients non-MA, l'imagerie TEP-tau a parfois permis de détecter une possible tauopathie limitée aux lobes temporaux médians, qui pourrait correspondre à une tauopathie primaire liée à l'âge.