Dual-domain U-Nets with embedded back projection operators for motion-resolved 4D CBCT reconstruction

Four-dimensional cone beam CT (4D CBCT) is important for image-guided radiation therapy of thoracic cancers, but its use is limited by long scan times, causing high patient dose and motion/sparse-sampling artifacts. We propose a deep learning method for motion-resolved 4D CBCT reconstruction from conventional free-breathing scans, without a respiratory signal or explicit projection binning. Our CNN takes free-breathing 3D CBCT projections as input and predicts a static volume at maximum inhalation plus ten displacement vector fields (DVFs) spanning a breathing cycle. The network extends U-Net: the encoder acts on filtered projection stacks, the decoder acts in the volume domain, and skip connections are replaced with non-trainable back-projection functions at multiple resolutions to transfer features between domains. The model is trained on simulated CBCT scans and evaluated on 11 unseen simulated patients and 13 clinical free-breathing scans. Two additional models (60 s and 6 s scans) were evaluated by clinical experts on three and two scans, comparing single phases of our 4D reconstruction to reference 3D SART-TV images for tumor and esophagus visibility. Experts preferred our method for tumor visibility (59% vs. 36% no preference, 5% reference) and esophagus visibility (47% vs. 42%, 11%). On simulated data, image quality matched SART-TV (mean RMSE: -1.19 HU, PSNR: +0.09 dB, SSIM: -0.009) while enabling 4D reconstruction. On clinical scans, our method showed sharper dynamic structures (e.g., diaphragm) and fewer motion streak artifacts than traditional reconstruction. This non-patient-specific CNN predicts static volumes and full 4D respiratory motion models from a single free-breathing scan, without a respiratory surrogate or projection binning, reducing motion artifacts while adding motion-modeling capability.

Projected Energy Matching for Generative 3D Priors

Energy Matching has emerged as a powerful generative framework that combines flow model efficiency with the explicit likelihood of Energy-Based Models (EBMs) via a single, time-independent scalar potential. However, directly training this potential on high-dimensional 3D data remains computationally challenging. While distilling a pre-trained flow model circumvents some of the initial training costs, we demonstrate that velocity fields inevitably contain non-conservative rotational artifacts (curl). Forcing a strictly conservative scalar potential to match this unconstrained field creates a "structural conflict", which degrades generation quality and mode coverage. To solve this, we propose Projected Energy Matching, a scalable framework that resolves these structural and computational bottlenecks. We introduce Helmholtz Distillation, a structural relaxation that leverages a Hutchinson trace estimator to explicitly absorb rotational noise into an auxiliary residual network. We subsequently refine this landscape using Negative Caching, a memory-efficient strategy that reuses negative samples across micro-batches, rendering sampling tractable during contrastive training with gradient accumulation. We deploy our method as an unconditional prior for real-world medical CT inverse problems, specifically sparse-view reconstruction. Ultimately, our amortized pipeline reduces total compute to a small fraction of that required by standard energy matching, while achieving high-fidelity reconstructions and successfully resolving severe measurement artifacts.

Artifact Reduction in 3D and 4D Cone-beam Computed Tomography Images with Deep Learning -- A Review

Deep learning based approaches have been used to improve image quality in cone-beam computed tomography (CBCT), a medical imaging technique often used in applications such as image-guided radiation therapy, implant dentistry or orthopaedics. In particular, while deep learning methods have been applied to reduce various types of CBCT image artifacts arising from motion, metal objects, or low-dose acquisition, a comprehensive review summarizing the successes and shortcomings of these approaches, with a primary focus on the type of artifacts rather than the architecture of neural networks, is lacking in the literature. In this review, the data generation and simulation pipelines, and artifact reduction techniques are specifically investigated for each type of artifact. We provide an overview of deep learning techniques that have successfully been shown to reduce artifacts in 3D, as well as in time-resolved (4D) CBCT through the use of projection- and/or volume-domain optimizations, or by introducing neural networks directly within the CBCT reconstruction algorithms. Research gaps are identified to suggest avenues for future exploration. One of the key findings of this work is an observed trend towards the use of generative models including GANs and score-based or diffusion models, accompanied with the need for more diverse and open training datasets and simulations.