Dynamic total body positron emission tomography (TB-PET) makes it feasible to measure the kinetics of the tracer in all organs of the body simultaneously which may lead to important applications in multi-organ disease and systems physiology. Since whole-body kinetics are highly heterogeneous with variable signal-to-noise ratios, parametric images should ideally comprise not only point estimates but also measures of posterior statistical uncertainty. However, standard Bayesian techniques, such as Markov chain Monte Carlo (MCMC), are computationally prohibitive at the total body scale. We introduce a generative consistency model (CM) that generates samples from the posterior distributions of the kinetic model parameters given measured time-activity curves and arterial input function. CM is able to collapse the hundreds of iterations required by standard diffusion models into just 3 denoising steps. The CM was evaluated using physiologically realistic simulations and an application to a subject's dynamic [18F]FDG TB-PET dataset analyzed with a standard single-input two-tissue compartment model. When trained on 500,000 physiologically realistic two-tissue compartment model simulations, the CM produces similar accuracy to MCMC (median absolute percent error $\lt {5}\%$ ; median K-L divergence $\lt {0}.{5}$ ) but is more than five orders of magnitude faster. CM produces more reliable $\mathit {{K}_{i}}$ images than the Patlak method by avoiding the assumption of irreversibility, while also offering valuable information on statistical uncertainty of parameter estimates and the underlying model. The proposed framework removes the computational barrier to routine, fully Bayesian parametric imaging in TB-PET and is readily extensible to other tracers and compartment models.

Recent work has shown improved lesion detectability and flexibility to reconstruction hyperparameters (e.g. scanner geometry or dose level) when PET images are reconstructed by leveraging pre-trained diffusion models. Such methods train a diffusion model (without sinogram data) on high-quality, but still noisy, PET images. In this work, we propose a simple method for generating subject-specific PET images from a dataset of multi-subject PET-MR scans, synthesizing "pseudo-PET" images by transforming between different patients' anatomy using image registration. The images we synthesize retain information from the subject's MR scan, leading to higher resolution and the retention of anatomical features compared to the original set of PET images. With simulated and real [^18F]FDG datasets, we show that pre-training a personalized diffusion model with subject-specific "pseudo-PET" images improves reconstruction accuracy with low-count data. In particular, the method shows promise in combining information from a guidance MR scan without overly imposing anatomical features, demonstrating an improved trade-off between reconstructing PET-unique image features versus features present in both PET and MR. We believe this approach for generating and utilizing synthetic data has further applications to medical imaging tasks, particularly because patient-specific PET images can be generated without resorting to generative deep learning or large training datasets.

Flow-based generative models provide strong unconditional priors for inverse problems, but guiding their dynamics for conditional generation remains challenging. Recent work casts training-free conditional generation in flow models as an optimal control problem; however, solving the resulting trajectory optimisation is computationally and memory intensive, requiring differentiation through the flow dynamics or adjoint solves. We propose MPC-Flow, a model predictive control framework that formulates inverse problem solving with flow-based generative models as a sequence of control sub-problems, enabling practical optimal control-based guidance at inference time. We provide theoretical guarantees linking MPC-Flow to the underlying optimal control objective and show how different algorithmic choices yield a spectrum of guidance algorithms, including regimes that avoid backpropagation through the generative model trajectory. We evaluate MPC-Flow on benchmark image restoration tasks, spanning linear and non-linear settings such as in-painting, deblurring, and super-resolution, and demonstrate strong performance and scalability to massive state-of-the-art architectures via training-free guidance of FLUX.2 (32B) in a quantised setting on consumer hardware.

Recovering true signals from noisy measurements is a central challenge in inverse problems spanning medical imaging, geophysics, and signal processing. Current solutions nearly always balance prior assumptions regarding the true signal (regularization) with agreement to noisy measured data (data fidelity). Conventional data fidelity loss functions, such as mean-squared error (MSE) or negative log-likelihood, seek pointwise agreement with noisy measurements, often leading to overfitting to noise. In this work, we instead evaluate data fidelity collectively by testing whether the observed measurements are statistically consistent with the noise distributions implied by the current estimate. We adopt this aggregated perspective and introduce $\textit{distributional consistency (DC) loss}$, a data-fidelity objective that replaces pointwise matching with distribution-level calibration. DC loss acts as a direct and practical plug-in replacement for standard data consistency terms: i) it is compatible with modern unsupervised regularizers that operate without paired measurement–ground-truth data, ii) it is optimized in the same way as traditional losses, and iii) it avoids overfitting to measurement noise even without the use of priors. Its scope naturally fits many practical inverse problems where the measurement-noise distribution is known and where the measured dataset consists of many independent noisy values. We demonstrate efficacy in two key example application areas: i) in image denoising with deep image prior, using DC instead of MSE loss removes the need for early stopping and achieves higher PSNR; ii) in medical image reconstruction from Poisson-noisy data, DC loss reduces artifacts in highly-iterated reconstructions and enhances the efficacy of hand-crafted regularization. These results position DC loss as a statistically grounded, performance-enhancing alternative to conventional fidelity losses for an important class of unsupervised noise-dominated inverse problems.

Multiplexed positron emission tomography (mPET) imaging allows simultaneous observation of physiological and pathological information from multiple tracers in a single PET scan. Although supervised deep learning has demonstrated superior performance in mPET image separation compared to purely model-based methods, acquiring large amounts of paired single-tracer data and multi-tracer data for training poses a practical challenge and needs extended scan durations for patients. In addition, the generalisation ability of the supervised learning framework is a concern, as the patient being scanned and their tracer kinetics may potentially fall outside the training distribution. In this work, we propose a self-supervised learning framework based on the deep image prior (DIP) for mPET image separation using just one dataset. In particular, we integrate the multi-tracer compartmental model into the DIP framework to estimate the parametric maps of each tracer from the measured dynamic dual-tracer activity images. Consequently, the separated dynamic single-tracer activity images can be recovered from the estimated tracer-specific parametric maps. In the proposed method, dynamic dual-tracer activity images are used as the training label, and the static dual-tracer image (reconstructed from the same patient data from the start to the end of acquisition) is used as the network input. The performance of the proposed method was evaluated on a simulated brain phantom for dynamic dual-tracer [18F]FDG+[11C]MET activity image separation and parametric map estimation. The results demonstrate that the proposed method outperforms the conventional voxel-wise multi-tracer compartmental modeling method (vMTCM) and the two-step method DIP-Dn+vMTCM (where dynamic dual-tracer activity images are first denoised using a U-net within the DIP framework, followed by vMTCM separation) in terms of lower bias and standard deviation in the separated single-tracer images and also for the estimated parametric maps for each tracer, at both voxel and ROI levels.

INTRODUCTION:In vitro data from primates provide conflicting evidence about the suitability of the cerebellum as a reference region for quantifying type 5 metabotropic glutamate receptor (mGluR5) binding parameters with positron emission tomography (PET). METHODS:We first measured mGluR5 density in postmortem human cerebellum using [3H]ABP688 autoradiography (n=5) and immunohistochemistry (n=6). Next, in vivo experiments were conducted in healthy volunteers (n=6) using a high-resolution PET scanner (HRRT) to compare [11C]ABP688 binding potential (BPND) values obtained with reference tissue methods and the two-tissue compartment model vs. metabolite-corrected arterial input function. RESULTS:The postmortem data showed that, relative to the hippocampus, the cerebellum had 35% less mGluR5 immunoreactivity and 94% fewer [3H]ABP688 binding sites. In vivo brain regional [11C]ABP688 BPND values using the cerebellum as a reference region were highly correlated with BPND values and distribution volumes derived by arterial input methods (R2 > 0.9). CONCLUSION:The scarce availability of cerebellar allosteric binding sites at autoradiography, compared to immunohistochemistry results, might reflect the presence of distinct mGluR5 isoforms or conformational state. Together with our PET data, these data support the proposition that [11C]ABP688 BPND using the cerebellum as a reference region provides accurate quantification of mGluR5 allosteric binding in vivo. Studies relying on this method could, therefore, be used in clinical populations, providing that stronger initial assumptions are met.

Positron emission tomography/computed tomography (PET/CT) imaging plays a pivotal role in oncology, aiding tumor metabolism assessment, disease staging, and therapy response evaluation. Traditionally, semi-quantitative metrics such as SUVmax have been extensively used, though these methods face limitations in reproducibility and predictive capability. Recent advancements in artificial intelligence (AI), particularly deep learning, have revolutionized PET imaging, significantly enhancing image quantification accuracy, and biomarker extraction capabilities, thereby enabling more precise clinical decision-making.

Diffusion models (DMs) have recently been introduced as a regularizing prior for PET image reconstruction, integrating DMs trained on high-quality PET images with unsupervised schemes that condition on measured data. While these approaches have potential generalization advantages due to their independence from the scanner geometry and the injected activity level, they forgo the opportunity to explicitly model the interaction between the DM prior and noisy measurement data, potentially limiting reconstruction accuracy. To address this, we propose a supervised DM-based algorithm for PET reconstruction. Our method enforces the non-negativity of PET's Poisson likelihood model and accommodates the wide intensity range of PET images. Through experiments on realistic brain PET phantoms, we demonstrate that our approach outperforms or matches state-of-the-art deep learning-based methods quantitatively across a range of dose levels. We further conduct ablation studies to demonstrate the benefits of the proposed components in our model, as well as its dependence on training data, parameter count, and number of diffusion steps. Additionally, we show that our approach enables more accurate posterior sampling than unsupervised DM-based methods, suggesting improved uncertainty estimation. Finally, we extend our methodology to a practical approach for fully 3D PET and present example results from real [^18F]FDG brain PET data.

Medical image reconstruction with pre-trained score-based generative models (SGMs) has advantages over other existing state-of-the-art deep-learned reconstruction methods, including improved resilience to different scanner setups and advanced image distribution modeling. SGM-based reconstruction has recently been applied to simulated positron emission tomography (PET) datasets, showing improved contrast recovery for out-of-distribution lesions relative to the state-of-the-art. However, existing methods for SGM-based reconstruction from PET data suffer from slow reconstruction, burdensome hyperparameter tuning and slice inconsistency effects (in 3D). In this work, we propose a practical methodology for fully 3D reconstruction that accelerates reconstruction and reduces the number of critical hyperparameters by matching the likelihood of an SGM's reverse diffusion process to a current iterate of the maximum-likelihood expectation maximization algorithm. Using the example of low-count reconstruction from simulated [^18F]DPA-714 datasets, we show our methodology can match or improve on the NRMSE and SSIM of existing state-of-the-art SGM-based PET reconstruction while reducing reconstruction time and the need for hyperparameter tuning. We evaluate our methodology against state-of-the-art supervised and conventional reconstruction algorithms. Finally, we demonstrate a first-ever implementation of SGM-based reconstruction for real 3D PET data, specifically [^18F]DPA-714 data, where we integrate perpendicular pre-trained SGMs to eliminate slice inconsistency issues.

Diffusion models have recently enabled state-of-the-art reconstruction of positron emission tomography (PET) images while requiring only image training data. However, domain shift remains a key concern for clinical adoption: priors trained on images from one anatomy, acquisition protocol or pathology may produce artefacts on out-of-distribution data. We propose integrating steerable conditional diffusion (SCD) with our previously-introduced likelihood-scheduled diffusion (PET-LiSch) framework to improve the alignment of the diffusion model's prior to the target subject. At reconstruction time, for each diffusion step, we use low-rank adaptation (LoRA) to align the diffusion model prior with the target domain on the fly. Experiments on realistic synthetic 2D brain phantoms demonstrate that our approach suppresses hallucinated artefacts under domain shift, i.e. when our diffusion model is trained on perturbed images and tested on normal anatomy, our approach suppresses the hallucinated structure, outperforming both OSEM and diffusion model baselines qualitatively and quantitatively. These results provide a proof-of-concept that steerable priors can mitigate domain shift in diffusion-based PET reconstruction and motivate future evaluation on real data.

This article reviews recent advancements in PET/computed tomography imaging, emphasizing the transformative impact of total-body and long-axial field-of-view scanners, which offer increased sensitivity, larger coverage, and faster, lower-dose imaging. It highlights the growing role of artificial intelligence (AI) in enhancing image reconstruction, resolution, and multi-tracer applications, enabling rapid processing and improved quantification. AI-driven techniques, such as super-resolution, positron range correction, and motion compensation, are improving lesion detectability and image quality. The review underscores the potential of these innovations to revolutionize clinical and research PET imaging, while also noting the challenges in validation and implementation for routine practice.

Reduced dose Positron Emission Tomography (PET) lowers the radiation dose to patients and reduces costs. Lower count data, however, degrades reconstructed image quality. Advanced reconstruction methods help mitigate image quality losses, but it is important to assess the resulting images from a clinical perspective. Two experienced clinicians assessed four PET reconstruction algorithms for [18F]FDG brain data, compared to a clinical standard reference (Maximum-Likelihood Expectation-Maximization (MLEM)), based on seven clinical image quality metrics: global quality rating, pattern recognition, diagnostic confidence (all on a scale of 0-4), sharpness, caudate-putamen separation, noise, and contrast (on a scale between 0-2). The reconstruction methods assessed were a guided and unguided version of self-supervised maximum a posteriori EM (MAPEM) (where the guidance case used the patient's MR image to control the smoothness penalty). For 3 of the 11 patient datasets reconstructed, post-smoothed versions of the MAPEM reconstruction were also considered, where the smoothing was with the point-spread-function used in the resolution modelling. Statistically significant improvements were observed in sharpness, caudate-putamen separation, and contrast for self-supervised MR-guided MAPEM compared to MLEM. For example, MLEM scored between 1-1.1 out of 2 for sharpness, caudate-putamen separation and contrast, whereas self-supervised MR-guided MAPEM scored between 1.5-1.75. In addition to the clinical evaluation, pre-trained Convolutional Neural Networks (CNNs) were used to assess the image quality of a further 62 images. The CNNs demonstrated similar trends to the clinician, showing their potential as automated standalone observers. Both the clinical and CNN assessments suggest when using only 5% of the standard injected dose, self-supervised MR-guided MAPEM reconstruction matches the 100% MLEM case for overall performance. This makes the images far more clinically useful than standard MLEM.

This review focuses on positron emission tomography (PET) imaging algorithms and traces the evolution of PET image reconstruction methods. First, we provide an overview of conventional PET image reconstruction methods from filtered backprojection through to recent iterative PET image reconstruction algorithms, and then review deep learning methods for PET data up to the latest innovations within three main categories. The first category involves post-processing methods for PET image denoising. The second category comprises direct image reconstruction methods that learn mappings from sinograms to the reconstructed images in an end-to-end manner. The third category comprises iterative reconstruction methods that combine conventional iterative image reconstruction with neural-network enhancement. We discuss future perspectives on PET imaging and deep learning technology.

Introduction:In multiplexed positron emission tomography (mPET) imaging, physiological and pathological information from different radiotracers can be observed simultaneously in a single dynamic PET scan. The separation of mPET signals within a single PET scan is challenging due to the fact that the PET scanner measures the sum of the PET signals of all the tracers. The conventional multi-tracer compartment modeling (MTCM) method requires staggered injections and assumes that the arterial input functions (AIFs) of each tracer are known. Methods:In this work, we propose a deep learning-based method to separate triple-tracer PET images without explicitly knowing the AIFs. A dynamic triple-tracer noisy MLEM reconstruction was used as the network input, and dynamic single-tracer noisy MLEM reconstructions were used as training labels. Results:A simulation study was performed to evaluate the performance of the proposed framework on triple-tracer ([ F 18 ]FDG+ Rb 82 +[ Tc 99m ]sestamibi) PET myocardial imaging. The results show that the proposed methodology substantially reduced the noise level compared to the results obtained from single-tracer imaging. Additionally, it achieved lower bias and standard deviation in the separated single-tracer images compared to the MTCM-based method at both the voxel and region of interest (ROI) levels. Discussion:As compared to MTCM separation, the proposed method uses spatiotemporal information for separation, which improves the separation performance at both the voxel and ROI levels. The simulation study also demonstrates the feasibility and potential of the proposed DL-based method for the application to pre-clinical and clinical studies.

Large high-quality medical image datasets are difficult to acquire but necessary for many deep learning applications. For positron emission tomography (PET), reconstructed image quality is limited by inherent Poisson noise. We propose a novel method for synthesising diverse and realistic pseudo-PET images with improved signal-to-noise ratio. We also show how our pseudo-PET images may be exploited as a generative prior for single-subject PET image reconstruction. Firstly, we perform deep-learned deformable registration of multi-subject magnetic resonance (MR) images paired to multi-subject PET images. We then use the anatomically-learned deformation fields to transform multiple PET images to the same reference space, before averaging random subsets of the transformed multi-subject data to form a large number of varying pseudo-PET images. We observe that using MR information for registration imbues the resulting pseudo-PET images with improved anatomical detail compared to the originals. We consider applications to PET image reconstruction, by generating pseudo-PET images in the same space as the intended single-subject reconstruction and using them as training data for a diffusion model-based reconstruction method. We show visual improvement and reduced background noise in our 2D reconstructions as compared to OSEM, MAP-EM and an existing state-of-the-art diffusion model-based approach. Our method shows the potential for utilising highly subject-specific prior information within a generative reconstruction framework. Future work may compare the benefits of our approach to explicitly MR-guided reconstruction methodologies.

Multiplexed positron emission tomography (mPET) imaging can simultaneously observe multiple targets of interest using different tracers in a single scan. Separation of mPET signals within a single PET scan is challenging due to the fact that each tracer gives rise to indistinguishable 511 keV photon pairs, and thus no unique energy information for differentiating the source of each photon pair. The majority of separation methods in mPET imaging primarily focus on dynamic mPET images for separation due to the assistance provided by the differing tracer dynamics. Short-duration static imaging is more routinely used in diagnosis and treatment monitoring due to its convenience and relative simplicity compared to dynamic imaging. Separating static mPET images, however, is more challenging than dynamic ones as the separation process relies solely on spatial information. Nonetheless, PET list-mode acquisition during a regular “static PET” protocol allows for flexibility in dynamic time framing prior to reconstruction. This motivates us to consider separating single-tracer images from multiplexed data arising from a standard “static” data acquisition interval by using dynamic framing of the data. Given a target static window for single tracer scan information, in this work, we investigate the best mPET acquisition start time Δa for a fixed delay time Δf before injecting 2nd tracer, for best prediction of single tracer separation in target window. We propose an adapted version of a kinetic model-informed deep network (KM-net) which allows investigation of the impact of Δa. The results showed that for Δt = 15 mins, using the entire mPET dynamic data (Δa = 0 mins) for separation achieves better performance compared to Δa = 15 min (simultaneous dual-tracer information only) and Δa = 25 mins (target window information only). Future work will focus on investigating the impact of Δt and the separation performance at the ROI level.

Filtered backprojection (FBP) is a widely known direct one-step PET reconstruction method that has been surpassed by alternative iterative methods with superior physics and noise modelling. However, iterative image reconstruction for fully 3D sinogram data can be computationally demanding. With the recent arrival of long axial field of view PET scanners, direct (non- iterative) deep learning (DL) based approaches have gained appeal due to their speed advantage when dealing with large datasets. Most data-driven DL based reconstruction methods to date have primarily used supervised learning for optimisation; if these methods were to be used on patients who are outliers of the training set, erroneous reconstructions could occur. In contrast, with this work we propose a model that uses self-supervised DL to model the filtering process within FBP to execute 3D reconstructions, while using a Poisson noise model and a more general forward model than just the Radon transform. Preliminary experiments of bias-variance trade-off show comparable results with our method against OSEM when reconstructing noisy data. The methodology will need expanding to utilise fully 3D data, explore generalisation of the learned filters, investigate the degree of self-supervised fine tuning, and explore other maximum a posteriori objective functions. These optimisations could result in overall speed benefits for training and final image reconstruction. Then, the next steps would be to use real-patient data to compare the reconstruction quality and speed of our method to that of vendor supplied reconstruction methods and state-of-the-art data-driven methods.

Score-based generative models (SGMs) have recently shown promising results for image reconstruction on simulated positron emission tomography (PET) datasets. In this work we have developed and implemented practical methodology for 3D image reconstruction with SGMs, and perform (to our knowledge) the first SGM-based reconstruction of real fully 3D PET data. We train an SGM on full-count reference brain images, and extend methodology to allow SGM-based reconstructions at very low counts (1% of original, to simulate low-dose or short-duration scanning). We then perform reconstructions for multiple independent realisations of 1% count data, allowing us to analyse the bias and variance characteristics of the method. We sample from the learned posterior distribution of the generative algorithm to calculate uncertainty images for our reconstructions. We evaluate the method's performance on real full- and low-count PET data and compare with conventional OSEM and MAP-EM baselines, showing that our SGM-based low-count reconstructions match full-dose reconstructions more closely and in a bias-variance trade-off comparison, our SGM-reconstructed images have lower variance than existing baselines. Future work will compare to supervised deep-learned methods, with other avenues for investigation including how data conditioning affects the SGM's posterior distribution and the algorithm's performance with different tracers.

Advanced iterative image reconstruction methods, for example using the kernel method and the deep image prior, have improved the quality of positron emission tomography (PET) images. To realise the benefits of such approaches, raw PET data are needed in order to perform an image reconstruction. However, raw data may not always be available, and even when it is, there are complex scanner-specific data corrections (e.g. scatter, attenuation and normalisation) as well as the need for a fully 3D forward and back projector. In this work we take the benefits of both the kernel method and the deep image prior (DIP) and introduce them to our methodology of synthesised image reconstruction, a framework specifically designed to allow image-reconstruction improvements to be applied to images already reconstructed by scanner-specific software with all data corrections already accounted for. This approach has already shown success for spatial resolution recovery, delivering improvements compared to conventional post-reconstruction image-space based methods. Specifically, synthesised image reconstruction creates a new reconstruction problem from a standard reconstructed image. This present work takes the synthesised reconstruction framework further by introducing DIP with the kernel method, and corresponding image quality improvements are obtained. This finds application in a number of settings where there is no access to the original raw PET data, or no access to the projector and scanner geometry information, hence making state of the art methods more accessible to a wider range of applications.

Echocardiography (echo) is the first imaging modality used when assessing cardiac function. The measurement of functional biomarkers from echo relies upon the segmentation of cardiac structures and deep learning models have been proposed to automate the segmentation process. However, in order to translate these tools to widespread clinical use it is important that the segmentation models are robust to a wide variety of images (e.g. acquired from different scanners, by operators with different levels of expertise etc.). To achieve this level of robustness it is necessary that the models are trained with multiple diverse datasets. A significant challenge faced when training with multiple diverse datasets is the variation in label presence, i.e. the combined data are often partially-labelled. Adaptations of the cross entropy loss function have been proposed to deal with partially labelled data. In this paper we show that training naively with such a loss function and multiple diverse datasets can lead to a form of shortcut learning, where the model associates label presence with domain characteristics, leading to a drop in performance. To address this problem, we propose a novel label dropout scheme to break the link between domain characteristics and the presence or absence of labels. We demonstrate that label dropout improves echo segmentation Dice score by 62% and 25% on two cardiac structures when training using multiple diverse partially labelled datasets.