Kris Thielemans

Evangelos Papoutsellis, Margaret A. G. Duff, Jakob S. Jørgensen et al.

The Core Imaging Library (CIL) is an open-source versatile Python framework for solving inverse problems with special emphasis on imaging applications such as computed tomography (CT), using a plug-in architecture for data and operators, interfacing to toolboxes such as ASTRA, TIGRE and SIRF. A key component of CIL is its optimisation module enabling users to flexibly combine mathematical operators and functionals to form smooth and non-smooth optimisation problems and solve these with a range of first-order algorithms. The present work introduces an expansion of CIL with a new modular framework for stochastic optimisation, allowing researchers to easily use a variety of existing stochastic optimisation algorithms as well form new ones by combining modular building blocks. Users can flexibly configure algorithmic components, adapt to diverse problem structures, and experiment with various sampling and step size strategies. Rather than individual black-box implementations of each fixed algorithm with significant redundancies, our design is modular providing building blocks that can be flexibly combined to realise a wealth of algorithm instances. The framework is particularly well-suited for large-scale applications, where stochastic methods offer notable computational advantages over deterministic approaches. To demonstrate its versatility and practical utility, we present experiments on real-world datasets from imaging inverse problems, such as X-Ray CT and Positron Emission Tomography (PET) reconstruction. In summary, the presented software expansion aims to support the research community with a robust, extensible optimisation suite for developing, testing, and benchmarking stochastic methods for inverse problems.

Imraj RD Singh, Alexander Denker, Riccardo Barbano et al.

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.

Casper da Costa-Luis, Matthias J. Ehrhardt, Christoph Kolbitsch et al.

Introduction: We describe the foundation of PETRIC, an image reconstruction challenge to minimise the computational runtime of related algorithms for Positron Emission Tomography (PET). Purpose: Although several similar challenges are well-established in the field of medical imaging, there have been no prior challenges for PET image reconstruction. Methods: Participants are provided with open-source software for implementation of their reconstruction algorithm(s). We define the objective function and reconstruct "gold standard" reference images, and provide metrics for quantifying algorithmic performance. We also received and curated phantom datasets (acquired with different scanners, radionuclides, and phantom types), which we further split into training and evaluation datasets. The automated computational framework of the challenge is released as open-source software. Results: Four teams with nine algorithms in total participated in the challenge. Their contributions made use of various tools from optimisation theory including preconditioning, stochastic gradients, and artificial intelligence. While most of the submitted approaches appear very similar in nature, their specific implementation lead to a range of algorithmic performance. Conclusion: As the first challenge for PET image reconstruction, PETRIC's solid foundations allow researchers to reuse its framework for evaluating new and existing image reconstruction methods on new or existing datasets. Variant versions of the challenge have and will continue to be launched in the future.

Yuliang Huang, Imraj Singh, Thomas Joyce et al.

3D Cone-Beam CT (CBCT) is widely used in radiotherapy but suffers from motion artifacts due to breathing. A common clinical approach mitigates this by sorting projections into respiratory phases and reconstructing images per phase, but this does not account for breathing variability. Dynamic CBCT instead reconstructs images at each projection, capturing continuous motion without phase sorting. Recent advancements in 4D Gaussian Splatting (4DGS) offer powerful tools for modeling dynamic scenes, yet their application to dynamic CBCT remains underexplored. Existing 4DGS methods, such as HexPlane, use implicit motion representations, which are computationally expensive. While explicit low-rank motion models have been proposed, they lack spatial regularization, leading to inconsistencies in Gaussian motion. To address these limitations, we introduce a free-form deformation (FFD)-based spatial basis function and a deformation-informed framework that enforces consistency by coupling the temporal evolution of Gaussian's mean position, scale, and rotation under a unified deformation field. We evaluate our approach on six CBCT datasets, demonstrating superior image quality with a 6x speedup over HexPlane. These results highlight the potential of deformation-informed 4DGS for efficient, motion-compensated CBCT reconstruction. The code is available at https://github.com/Yuliang-Huang/DIGS.

Yuliang Huang, Bjoern Eiben, Kris Thielemans et al.

4D Computed Tomography (4DCT) is widely used for many clinical applications such as radiotherapy treatment planning, PET and ventilation imaging. However, common 4DCT methods reconstruct multiple breath cycles into a single, arbitrary breath cycle which can lead to various artefacts, impacting the downstream clinical applications. Surrogate driven motion models can estimate continuous variable motion across multiple cycles based on CT segments `unsorted' from 4DCT, but it requires respiration surrogate signals with strong correlation to the internal motion, which are not always available. The method proposed in this study eliminates such dependency by adapting the hyper-gradient method to the optimization of surrogate signals as hyper-parameters, while achieving better or comparable performance, as demonstrated on digital phantom simulations and real patient data. Our method produces a high-quality motion-compensated image together with estimates of the motion, including breath-to-breath variability, throughout the image acquisition. Our method has the potential to improve downstream clinical applications, and also enables retrospective analysis of open access 4DCT dataset where no respiration signals are stored. Code is avaibale at https://github.com/Yuliang-Huang/4DCT-irregular-motion.

Evangelos Papoutsellis, Casper da Costa-Luis, Daniel Deidda et al.

We introduce a stochastic framework into the open--source Core Imaging Library (CIL) which enables easy development of stochastic algorithms. Five such algorithms from the literature are developed, Stochastic Gradient Descent, Stochastic Average Gradient (-Amélioré), (Loopless) Stochastic Variance Reduced Gradient. We showcase the functionality of the framework with a comparative study against a deterministic algorithm on a simulated 2D PET dataset, with the use of the open-source Synergistic Image Reconstruction Framework. We observe that stochastic optimisation methods can converge in fewer passes of the data than a standard deterministic algorithm.

Arkadiusz Sitek, Sangtae Ahn, Evren Asma et al.

Artificial intelligence (AI) has significant potential to positively impact and advance medical imaging, including positron emission tomography (PET) imaging applications. AI has the ability to enhance and optimize all aspects of the PET imaging chain from patient scheduling, patient setup, protocoling, data acquisition, detector signal processing, reconstruction, image processing and interpretation. AI poses industry-specific challenges which will need to be addressed and overcome to maximize the future potentials of AI in PET. This paper provides an overview of these industry-specific challenges for the development, standardization, commercialization, and clinical adoption of AI, and explores the potential enhancements to PET imaging brought on by AI in the near future. In particular, the combination of on-demand image reconstruction, AI, and custom designed data processing workflows may open new possibilities for innovation which would positively impact the industry and ultimately patients.

Kerstin Kläser, Thomas Varsavsky, Pawel Markiewicz et al.

The ability to synthesise Computed Tomography images - commonly known as pseudo CT, or pCT - from MRI input data is commonly assessed using an intensity-wise similarity, such as an L2-norm between the ground truth CT and the pCT. However, given that the ultimate purpose is often to use the pCT as an attenuation map ($μ$-map) in Positron Emission Tomography Magnetic Resonance Imaging (PET/MRI), minimising the error between pCT and CT is not necessarily optimal. The main objective should be to predict a pCT that, when used as $μ$-map, reconstructs a pseudo PET (pPET) which is as close as possible to the gold standard PET. To this end, we propose a novel multi-hypothesis deep learning framework that generates pCTs by minimising a combination of the pixel-wise error between pCT and CT and a proposed metric-loss that itself is represented by a convolutional neural network (CNN) and aims to minimise subsequent PET residuals. The model is trained on a database of 400 paired MR/CT/PET image slices. Quantitative results show that the network generates pCTs that seem less accurate when evaluating the Mean Absolute Error on the pCT (69.68HU) compared to a baseline CNN (66.25HU), but lead to significant improvement in the PET reconstruction - 115a.u. compared to baseline 140a.u.

Kerstin Kläser, Pawel Markiewicz, Marta Ranzini et al.

Attenuation correction is an essential requirement of positron emission tomography (PET) image reconstruction to allow for accurate quantification. However, attenuation correction is particularly challenging for PET-MRI as neither PET nor magnetic resonance imaging (MRI) can directly image tissue attenuation properties. MRI-based computed tomography (CT) synthesis has been proposed as an alternative to physics based and segmentation-based approaches that assign a population-based tissue density value in order to generate an attenuation map. We propose a novel deep fully convolutional neural network that generates synthetic CTs in a recursive manner by gradually reducing the residuals of the previous network, increasing the overall accuracy and generalisability, while keeping the number of trainable parameters within reasonable limits. The model is trained on a database of 20 pre-acquired MRI/CT pairs and a four-fold random bootstrapped validation with a 80:20 split is performed. Quantitative results show that the proposed framework outperforms a state-of-the-art atlas-based approach decreasing the Mean Absolute Error (MAE) from 131HU to 68HU for the synthetic CTs and reducing the PET reconstruction error from 14.3% to 7.2%.