The differentiable shift-variant filtered backprojection (SV-FBP) framework enables data-driven estimation of redundancy weights for cone-beam CT reconstruction under general source trajectories, removing the need for analytically derived weighting schemes. In this work, we present a systematic study of the robustness and adaptability of differentiable SV-FBP under challenging acquisition settings. We show that the framework remains stable across highly irregular and discontinuous trajectories, indicating that reconstruction performance is largely insensitive to trajectory ordering or continuity. Instead, the spatial distribution of sampling points plays a more dominant role. Under sparse-view conditions, differentiable SV-FBP achieves competitive reconstruction quality while providing an order-of-magnitude reduction in computation time compared to iterative reconstruction methods at moderate sampling densities. However, we identify a clear transition regime under severe undersampling, where the absence of iterative data consistency leads to performance degradation. Furthermore, we demonstrate that the framework remains applicable to non-planar multi-isocenter geometries, such as Lissajous-saddle trajectories, without requiring architectural modifications. These findings provide new insights into the behavior and limitations of the differentiable SV-FBP model and highlight it as a flexible and efficient solution for non-standard and robotic CBCT acquisition scenarios.
This paper proposes a Gaussian-Based Shift-Variant filtered backprojection (FBP) neural network, which is designed for the efficient reconstruction of non-circular trajectory cone beam computed tomography. The traditional differentiable shift-variant FBP model consists of a filtering component and a backprojection process. The filtering component includes operations such as weightings, differentiations, a 2D Radon transform, and a 2D backprojection. The proposed methods build on this framework by introducing a trainable 2D Gaussian model to represent the trajectory-related part in the filtering process, achieving a substantial reduction in the number of trainable parameters. Experimental results demonstrate that the proposed model reduces the parameter count by 99%, while only sacrificing a slight amount of reconstruction quality. Furthermore, the training time for each trajectory is reduced to one-fourth of the original, significantly accelerating convergence. These enhancements demonstrate a considerable augmentation in the model's practicality and effectiveness, making it a valuable asset for real-world applications.
This paper presents a novel Direct Integration Theorem (DIT), derived as a non-trivial corollary of the classical Central Slice Theorem (CST). The DIT provides a mathematically consistent transition from the continuous to the discrete domain - a fundamental challenge in computed tomography - thereby eliminating the need for frequency-domain interpolation without resorting to conventional ramp-filtering. The proposed approach circumvents two principal limitations inherent in traditional methods: (i) the zero-frequency singularity and spectral distortions introduced by the mandatory ramp-filtering step, and (ii) discretization inaccuracies associated with frequency-domain interpolation. Based on the DIT, we develop a rigorous framework for consistent discrete solutions of the inverse Radon problem. Mathematical modeling demonstrates that this approach achieves quasi-exact reconstruction, with errors constrained solely by sampling parameters and grid geometry. Furthermore, while Filtered Back Projection (FBP) inherently distorts the variance of the reconstructed image, the DIT-based algorithm preserves it. Comparative simulations confirm that the proposed method eliminates common artifacts, such as intensity cupping, and consistently outperforms FBP in terms of PSNR, SSIM, and reprojection fidelity, faithfully restoring the original image's statistical characteristics.
Sparse-view CT reduces radiation dose and scanning time by acquiring fewer projection views, but angular undersampling makes reconstruction severely ill-posed, causing streak artifacts, structural blurring, and loss of fine details. Existing supervised methods are often tied to specific sampling settings, whereas generative methods may introduce anatomically inconsistent hallucination-like structures under severe undersampling. We propose Lucid, a sparsity-adaptive, consistency-guided reconstruction framework based on a Flow Matching generative prior for sparse-view CT. Lucid is trained only on high-quality CT images to learn a continuous transport between a Gaussian distribution and the high-quality CT image distribution, independent of view sampling. During inference, the sampling sparsity level is explicitly incorporated to adapt the generative trajectory of a single pretrained model. Specifically, Lucid constructs a degradation-matched initial state by sparsity-weighted fusion of the sparse-view FBP image and Gaussian noise, performs sparsity-modulated Flow Matching updates, and applies projection-domain data-consistency correction after each prior update. Experiments under multiple sparse-view settings show that Lucid achieves stable reconstruction performance across different sampling densities, improves image quality and structural fidelity, and reduces the risk of hallucination-like structures in generative sparse-view CT reconstruction.