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.

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.

To obtain high-quality Positron emission tomography (PET) images while minimizing radiation exposure, numerous methods have been proposed to reconstruct standard-dose PET (SPET) images from the corresponding low-dose PET (LPET) images. However, these methods heavily rely on voxel-based representations, which fall short of adequately accounting for the precise structure and fine-grained context, leading to compromised reconstruction. In this paper, we propose a 3D point-based context clusters GAN, namely PCC-GAN, to reconstruct high-quality SPET images from LPET. Specifically, inspired by the geometric representation power of points, we resort to a point-based representation to enhance the explicit expression of the image structure, thus facilitating the reconstruction with finer details. Moreover, a context clustering strategy is applied to explore the contextual relationships among points, which mitigates the ambiguities of small structures in the reconstructed images. Experiments on both clinical and phantom datasets demonstrate that our PCC-GAN outperforms the state-of-the-art reconstruction methods qualitatively and quantitatively. Code is available at https://github.com/gluucose/PCCGAN.

Score-based generative models have demonstrated highly promising results for medical image reconstruction tasks in magnetic resonance imaging or computed tomography. However, their application to Positron Emission Tomography (PET) is still largely unexplored. PET image reconstruction involves a variety of challenges, including Poisson noise with high variance and a wide dynamic range. To address these challenges, we propose several PET-specific adaptations of score-based generative models. The proposed framework is developed for both 2D and 3D PET. In addition, we provide an extension to guided reconstruction using magnetic resonance images. We validate the approach through extensive 2D and 3D $\textit{in-silico}$ experiments with a model trained on patient-realistic data without lesions, and evaluate on data without lesions as well as out-of-distribution data with lesions. This demonstrates the proposed method's robustness and significant potential for improved PET reconstruction.

[Objective] This study aims to introduce a novel back projection-induced U-Net-shaped architecture, called ReconU-Net, for deep learning-based direct positron emission tomography (PET) image reconstruction. Additionally, our objective is to analyze the behavior of direct PET image reconstruction and gain deeper insights by comparing the proposed ReconU-Net architecture with other encoder-decoder architectures without skip connections. [Approach] The proposed ReconU-Net architecture uniquely integrates the physical model of the back projection operation into the skip connection. This distinctive feature facilitates the effective transfer of intrinsic spatial information from the input sinogram to the reconstructed image via an embedded physical model. The proposed ReconU-Net was trained using Monte Carlo simulation data from the Brainweb phantom and tested on both simulated and real Hoffman brain phantom data. [Main results] The proposed ReconU-Net method generated a reconstructed image with a more accurate structure compared to other deep learning-based direct reconstruction methods. Further analysis showed that the proposed ReconU-Net architecture has the ability to transfer features of multiple resolutions, especially non-abstract high-resolution information, through skip connections. Despite limited training on simulated data, the proposed ReconU-Net successfully reconstructed the real Hoffman brain phantom, unlike other deep learning-based direct reconstruction methods, which failed to produce a reconstructed image. [Significance] The proposed ReconU-Net can improve the fidelity of direct PET image reconstruction, even when dealing with small training datasets, by leveraging the synergistic relationship between data-driven modeling and the physics model of the imaging process.

Positron emission tomography (PET) is an important functional medical imaging technique often used in the evaluation of certain brain disorders, whose reconstruction problem is ill-posed. The vast majority of reconstruction methods in PET imaging, both iterative and deep learning, return a single estimate without quantifying the associated uncertainty. Due to ill-posedness and noise, a single solution can be misleading or inaccurate. Thus, providing a measure of uncertainty in PET image reconstruction can help medical practitioners in making critical decisions. This paper proposes a deep learning-based method for uncertainty quantification in PET image reconstruction via posterior sampling. The method is based on training a conditional generative adversarial network whose generator approximates sampling from the posterior in Bayesian inversion. The generator is conditioned on reconstruction from a low-dose PET scan obtained by a conventional reconstruction method and a high-quality magnetic resonance image and learned to estimate a corresponding standard-dose PET scan reconstruction. We show that the proposed model generates high-quality posterior samples and yields physically-meaningful uncertainty estimates.

Deep image prior (DIP) has been successfully applied to positron emission tomography (PET) image restoration, enabling represent implicit prior using only convolutional neural network architecture without training dataset, whereas the general supervised approach requires massive low- and high-quality PET image pairs. To answer the increased need for PET imaging with DIP, it is indispensable to improve the performance of the underlying DIP itself. Here, we propose a self-supervised pre-training model to improve the DIP-based PET image denoising performance. Our proposed pre-training model acquires transferable and generalizable visual representations from only unlabeled PET images by restoring various degraded PET images in a self-supervised approach. We evaluated the proposed method using clinical brain PET data with various radioactive tracers ($^{18}$F-florbetapir, $^{11}$C-Pittsburgh compound-B, $^{18}$F-fluoro-2-deoxy-D-glucose, and $^{15}$O-CO$_{2}$) acquired from different PET scanners. The proposed method using the self-supervised pre-training model achieved robust and state-of-the-art denoising performance while retaining spatial details and quantification accuracy compared to other unsupervised methods and pre-training model. These results highlight the potential that the proposed method is particularly effective against rare diseases and probes and helps reduce the scan time or the radiotracer dose without affecting the patients.

Deep image prior (DIP) has recently attracted attention owing to its unsupervised positron emission tomography (PET) image reconstruction, which does not require any prior training dataset. In this paper, we present the first attempt to implement an end-to-end DIP-based fully 3D PET image reconstruction method that incorporates a forward-projection model into a loss function. To implement a practical fully 3D PET image reconstruction, which could not be performed due to a graphics processing unit memory limitation, we modify the DIP optimization to block-iteration and sequentially learn an ordered sequence of block sinograms. Furthermore, the relative difference penalty (RDP) term was added to the loss function to enhance the quantitative PET image accuracy. We evaluated our proposed method using Monte Carlo simulation with [$^{18}$F]FDG PET data of a human brain and a preclinical study on monkey brain [$^{18}$F]FDG PET data. The proposed method was compared with the maximum-likelihood expectation maximization (EM), maximum-a-posterior EM with RDP, and hybrid DIP-based PET reconstruction methods. The simulation results showed that the proposed method improved the PET image quality by reducing statistical noise and preserved a contrast of brain structures and inserted tumor compared with other algorithms. In the preclinical experiment, finer structures and better contrast recovery were obtained by the proposed method. This indicated that the proposed method can produce high-quality images without a prior training dataset. Thus, the proposed method is a key enabling technology for the straightforward and practical implementation of end-to-end DIP-based fully 3D PET image reconstruction.

List-mode positron emission tomography (PET) image reconstruction is an important tool for PET scanners with many lines-of-response and additional information such as time-of-flight and depth-of-interaction. Deep learning is one possible solution to enhance the quality of PET image reconstruction. However, the application of deep learning techniques to list-mode PET image reconstruction has not been progressed because list data is a sequence of bit codes and unsuitable for processing by convolutional neural networks (CNN). In this study, we propose a novel list-mode PET image reconstruction method using an unsupervised CNN called deep image prior (DIP) which is the first trial to integrate list-mode PET image reconstruction and CNN. The proposed list-mode DIP reconstruction (LM-DIPRecon) method alternatively iterates the regularized list-mode dynamic row action maximum likelihood algorithm (LM-DRAMA) and magnetic resonance imaging conditioned DIP (MR-DIP) using an alternating direction method of multipliers. We evaluated LM-DIPRecon using both simulation and clinical data, and it achieved sharper images and better tradeoff curves between contrast and noise than the LM-DRAMA, MR-DIP and sinogram-based DIPRecon methods. These results indicated that the LM-DIPRecon is useful for quantitative PET imaging with limited events while keeping accurate raw data information. In addition, as list data has finer temporal information than dynamic sinograms, list-mode deep image prior reconstruction is expected to be useful for 4D PET imaging and motion correction.

Convolutional neural networks (CNNs) have recently achieved remarkable performance in positron emission tomography (PET) image reconstruction. In particular, CNN-based direct PET image reconstruction, which directly generates the reconstructed image from the sinogram, has potential applicability to PET image enhancements because it does not require image reconstruction algorithms, which often produce some artifacts. However, these deep learning-based, direct PET image reconstruction algorithms have the disadvantage that they require a large number of high-quality training datasets. In this study, we propose an unsupervised direct PET image reconstruction method that incorporates a deep image prior framework. Our proposed method incorporates a forward projection model with a loss function to achieve unsupervised direct PET image reconstruction from sinograms. To compare our proposed direct reconstruction method with the filtered back projection (FBP) and maximum likelihood expectation maximization (ML-EM) algorithms, we evaluated using Monte Carlo simulation data of brain [$^{18}$F]FDG PET scans. The results demonstrate that our proposed direct reconstruction quantitatively and qualitatively outperforms the FBP and ML-EM algorithms with respect to peak signal-to-noise ratio and structural similarity index.