Dual-Domain Equivariant Generative Adversarial Network for Multimodal CT-PET Synthesis

We present a Dual-Domain Equivariant Generative Adversarial Network (DDE-GAN) for multimodal CT-PET image synthesis. Traditional GAN-based approaches often operate solely in the spatial domain and ignore geometric consistency, resulting in limited structural fidelity. DDE-GAN addresses these challenges by jointly learning from both spatial and frequency (Fourier) domains, capturing complementary anatomical and spectral information. Furthermore, rotational equivariance embedded in the physics of the CT and PET measurements are integrated into the loss of both the generator and discriminator to ensure consistent responses under rotations, improving anatomical accuracy. A hierarchical dual-domain training strategy enforces intra- and inter-domain consistency through multi-stage loss functions. Evaluated on the HECKTOR 2022 CT-PET dataset, DDE-GAN achieves superior synthesis quality over baseline models for CT-PET image synthesis. The results demonstrate that combining dual-domain learning with geometric equivariance substantially enhances multimodal image synthesis accuracy and robustness, enabling practical applications in PET completion and data augmentation.

EPC-3D-Diff: Equivariant Physics Consistent Conditional 3D Latent Diffusion for CBCT to CT Synthesis

Cone-beam CT (CBCT) is routinely acquired during radiotherapy for patient setup, but its quantitative reliability is degraded by scatter, noise, and reconstruction artifacts, limiting Hounsfield Unit (HU) accuracy. We propose EPC-3D-Diff, a novel conditional 3D latent diffusion framework for volumetric CBCT to CT synthesis that introduces a projection domain equivariance loss derived from acquisition physics. Unlike common image domain equivariance, we exploit the fact that an in plane rotation of the volume corresponds to an angular shift in its projections. During training, we enforce this relationship by forward projecting rotated synthesized CT volumes and matching them to appropriately angle shifted projections of the paired target CT, yielding a physics consistent equivariance constraint integrated into the diffusion objective. To capture full 3D context efficiently, conditional diffusion is performed in a compact latent space learnt by a lightweight 3D autoencoder, preserving axial depth while downsampling in plane resolution for stable training. We validate on a paired head CBCT/CT phantom dataset, including repeat scans, and paired clinical data using patient wise splits, and perform single and mixed domain training, ablations, and comparisons with diffusion and CycleGAN. EPC-3D-Diff generalizes well and achieved substantial improvements, +7.4 dB (phantom) and +1.8 dB (clinical data) in PSNR compared to state of the art methods, alongside improved SSIM and HU accuracy, within tissue boundaries. Overall, EPC-3D-Diff improves robustness and physics consistency, supporting HU aware synthesis for downstream radiotherapy workflows.

FOD-Diff: 3D Multi-Channel Patch Diffusion Model for Fiber Orientation Distribution

Diffusion MRI (dMRI) is a critical non-invasive technique to estimate fiber orientation distribution (FOD) for characterizing white matter integrity. Estimating FOD from single-shell low angular resolution dMRI (LAR-FOD) is limited by accuracy, whereas estimating FOD from multi-shell high angular resolution dMRI (HAR-FOD) requires a long scanning time, which limits its applicability. Diffusion models have shown promise in estimating HAR-FOD based on LAR-FOD. However, using diffusion models to efficiently generate HAR-FOD is challenging due to the large number of spherical harmonic (SH) coefficients in FOD. Here, we propose a 3D multi-channel patch diffusion model to predict HAR-FOD from LAR-FOD. We design the FOD-patch adapter by introducing the prior brain anatomy for more efficient patch-based learning. Furthermore, we introduce a voxel-level conditional coordinating module to enhance the global understanding of the model. We design the SH attention module to effectively learn the complex correlations of the SH coefficients. Our experimental results show that our method achieves the best performance in HAR-FOD prediction and outperforms other state-of-the-art methods.

EqDiff-CT: Equivariant Conditional Diffusion model for CT Image Synthesis from CBCT

Cone-beam computed tomography (CBCT) is widely used for image-guided radiotherapy (IGRT). It provides real time visualization at low cost and dose. However, photon scattering and beam hindrance cause artifacts in CBCT. These include inaccurate Hounsfield Units (HU), reducing reliability for dose calculation, and adaptive planning. By contrast, computed tomography (CT) offers better image quality and accurate HU calibration but is usually acquired offline and fails to capture intra-treatment anatomical changes. Thus, accurate CBCT-to-CT synthesis is needed to close the imaging-quality gap in adaptive radiotherapy workflows. To cater to this, we propose a novel diffusion-based conditional generative model, coined EqDiff-CT, to synthesize high-quality CT images from CBCT. EqDiff-CT employs a denoising diffusion probabilistic model (DDPM) to iteratively inject noise and learn latent representations that enable reconstruction of anatomically consistent CT images. A group-equivariant conditional U-Net backbone, implemented with e2cnn steerable layers, enforces rotational equivariance (cyclic C4 symmetry), helping preserve fine structural details while minimizing noise and artifacts. The system was trained and validated on the SynthRAD2025 dataset, comprising CBCT-CT scans across multiple head-and-neck anatomical sites, and we compared it with advanced methods such as CycleGAN and DDPM. EqDiff-CT provided substantial gains in structural fidelity, HU accuracy and quantitative metrics. Visual findings further confirm the improved recovery, sharper soft tissue boundaries, and realistic bone reconstructions. The findings suggest that the diffusion model has offered a robust and generalizable framework for CBCT improvements. The proposed solution helps in improving the image quality as well as the clinical confidence in the CBCT-guided treatment planning and dose calculations.

Direct Dual-Energy CT Material Decomposition using Model-based Denoising Diffusion Model

Dual-energy X-ray Computed Tomography (DECT) constitutes an advanced technology which enables automatic decomposition of materials in clinical images without manual segmentation using the dependency of the X-ray linear attenuation with energy. However, most methods perform material decomposition in the image domain as a post-processing step after reconstruction but this procedure does not account for the beam-hardening effect and it results in sub-optimal results. In this work, we propose a deep learning procedure called Dual-Energy Decomposition Model-based Diffusion (DEcomp-MoD) for quantitative material decomposition which directly converts the DECT projection data into material images. The algorithm is based on incorporating the knowledge of the spectral DECT model into the deep learning training loss and combining a score-based denoising diffusion learned prior in the material image domain. Importantly the inference optimization loss takes as inputs directly the sinogram and converts to material images through a model-based conditional diffusion model which guarantees consistency of the results. We evaluate the performance with both quantitative and qualitative estimation of the proposed DEcomp-MoD method on synthetic DECT sinograms from the low-dose AAPM dataset. Finally, we show that DEcomp-MoD outperform state-of-the-art unsupervised score-based model and supervised deep learning networks, with the potential to be deployed for clinical diagnosis.

Multimodal 3D Brain Tumor Segmentation with Adversarial Training and Conditional Random Field

Accurate brain tumor segmentation remains a challenging task due to structural complexity and great individual differences of gliomas. Leveraging the pre-eminent detail resilience of CRF and spatial feature extraction capacity of V-net, we propose a multimodal 3D Volume Generative Adversarial Network (3D-vGAN) for precise segmentation. The model utilizes Pseudo-3D for V-net improvement, adds conditional random field after generator and use original image as supplemental guidance. Results, using the BraTS-2018 dataset, show that 3D-vGAN outperforms classical segmentation models, including U-net, Gan, FCN and 3D V-net, reaching specificity over 99.8%.

Phy-Diff: Physics-guided Hourglass Diffusion Model for Diffusion MRI Synthesis

Diffusion MRI (dMRI) is an important neuroimaging technique with high acquisition costs. Deep learning approaches have been used to enhance dMRI and predict diffusion biomarkers through undersampled dMRI. To generate more comprehensive raw dMRI, generative adversarial network based methods are proposed to include b-values and b-vectors as conditions, but they are limited by unstable training and less desirable diversity. The emerging diffusion model (DM) promises to improve generative performance. However, it remains challenging to include essential information in conditioning DM for more relevant generation, i.e., the physical principles of dMRI and white matter tract structures. In this study, we propose a physics-guided diffusion model to generate high-quality dMRI. Our model introduces the physical principles of dMRI in the noise evolution in the diffusion process and introduce a query-based conditional mapping within the difussion model. In addition, to enhance the anatomical fine detials of the generation, we introduce the XTRACT atlas as prior of white matter tracts by adopting an adapter technique. Our experiment results show that our method outperforms other state-of-the-art methods and has the potential to advance dMRI enhancement.

End-to-End Model-based Deep Learning for Dual-Energy Computed Tomography Material Decomposition

Dual energy X-ray Computed Tomography (DECT) enables to automatically decompose materials in clinical images without the manual segmentation using the dependency of the X-ray linear attenuation with energy. In this work we propose a deep learning procedure called End-to-End Material Decomposition (E2E-DEcomp) for quantitative material decomposition which directly convert the CT projection data into material images. The algorithm is based on incorporating the knowledge of the spectral model DECT system into the deep learning training loss and combining a data-learned prior in the material image domain. Furthermore, the training does not require any energy-based images in the dataset but rather only sinogram and material images. We show the effectiveness of the proposed direct E2E-DEcomp method on the AAPM spectral CT dataset (Sidky and Pan, 2023) compared with state of the art supervised deep learning networks.

Rotational Augmented Noise2Inverse for Low-dose Computed Tomography Reconstruction

In this work, we present a novel self-supervised method for Low Dose Computed Tomography (LDCT) reconstruction. Reducing the radiation dose to patients during a CT scan is a crucial challenge since the quality of the reconstruction highly degrades because of low photons or limited measurements. Supervised deep learning methods have shown the ability to remove noise in images but require accurate ground truth which can be obtained only by performing additional high-radiation CT scans. Therefore, we propose a novel self-supervised framework for LDCT, in which ground truth is not required for training the convolutional neural network (CNN). Based on the Noise2Inverse (N2I) method, we enforce in the training loss the equivariant property of rotation transformation, which is induced by the CT imaging system, to improve the quality of the CT image in a lower dose. Numerical and experimental results show that the reconstruction accuracy of N2I with sparse views is degrading while the proposed rotational augmented Noise2Inverse (RAN2I) method keeps better image quality over a different range of sampling angles. Finally, the quantitative results demonstrate that RAN2I achieves higher image quality compared to N2I, and experimental results of RAN2I on real projection data show comparable performance to supervised learning.

Systematic Review on Learning-based Spectral CT

Spectral computed tomography (CT) has recently emerged as an advanced version of medical CT and significantly improves conventional (single-energy) CT. Spectral CT has two main forms: dual-energy computed tomography (DECT) and photon-counting computed tomography (PCCT), which offer image improvement, material decomposition, and feature quantification relative to conventional CT. However, the inherent challenges of spectral CT, evidenced by data and image artifacts, remain a bottleneck for clinical applications. To address these problems, machine learning techniques have been widely applied to spectral CT. In this review, we present the state-of-the-art data-driven techniques for spectral CT.