Gradient-Based Trajectory Optimisation over Continuous Poses for Sparse-View Cone-Beam CT

X-ray computed tomography (CT) reconstructs volumetric representations of objects from projection images obtained by transmitting X-rays through a target. Recent splat-based tomography, which represents a volume as a continuous distribution of 3D Gaussians, has demonstrated both high reconstruction quality and fast convergence in cone-beam sparse-view CT. However, when deployed in real CT systems with limited and non-uniform view distributions, we observe distinctive streak and strip artifacts that are far more pronounced than in conventional reconstruction methods. Through detailed analysis, we show that these artifacts primarily originate from pose inaccuracies in the acquisition geometry rather than from view sparsity itself. We revisit pose sensitivity in the splatting formulation and derive a stable gradient-based framework that jointly refines geometric parameters during reconstruction. Our study not only identifies how pose perturbations propagate through the differentiable projection operator but also reveals why splat-based CT is particularly vulnerable to geometric misalignment. The resulting formulation remains lightweight and easily integrable into existing pipelines while substantially improving reconstruction fidelity under real-world sparse-view conditions.

This work introduces a continuous soft near-orthogonality score and a resolution-aware saturated coverage objective for projection selection in region-of-interest focused cone-beam CT, grounded in Tuy's completeness theory. Replacing the binary hit-or-miss model of classical Tuy completeness with a graded, differentiable formulation preserves a direct link to achievable feature sizes while enabling both efficient approximate and exact optimisation. We establish that the underlying discrete decision problems are NP-complete via polynomial-time reductions from Set Cover, motivating a submodular greedy algorithm with proven $(1-1/\mathrm{e})$ approximation guarantees and a mixed-integer linear program (MILP) that provides certified optimality bounds. The MILP serves as a quality certificate for the greedy solution rather than a competing optimiser. The primary empirical finding confirms this relationship: across a systematic benchmark spanning six target regions, multiple projection budgets, and four controlled occlusion conditions, the pooled median greedy-to-MILP objective ratio was 0.998, with a substantial fraction of cases certified globally optimal. A binary formulation is included as a diagnostic baseline; it strengthens hard directional completeness but is weaker on the continuous coverage scale. We additionally introduce Effective Spatial Resolution (ESR), a physically interpretable trajectory-level diagnostic that maps directional sampling gaps to achievable feature sizes. ESR correlates reliably with matched reconstruction quality across projection budgets and occlusion levels, providing a practical bridge between the selection stage and the image domain without requiring reconstruction.

Sparse-view computed tomography (CT) is critical for reducing radiation exposure to patients. Recent advances in radiative 3D Gaussian Splatting (3DGS) have enabled fast and accurate sparse-view CT reconstruction. Despite these algorithmic advancements, practical reconstruction fidelity remains fundamentally bounded by the quality of the captured data, raising the crucial yet underexplored problem of X-ray active view selection. Existing active view selection methods are primarily designed for natural-light scenes and fail to capture the unique geometric ambiguities and physical attenuation properties inherent in X-ray imaging. In this paper, we present Perturbed Gaussian Ensemble, an active view selection framework that integrates uncertainty modeling with sequential decision-making, tailored for X-ray Gaussian Splatting. Specifically, we identify low-density Gaussian primitives that are likely to be uncertain and apply stochastic density scaling to construct an ensemble of plausible Gaussian density fields. For each candidate projection, we measure the structural variance of the ensemble predictions and select the one with the highest variance as the next best view. Extensive experimental results on arbitrary-trajectory CT benchmarks demonstrate that our density-guided perturbation strategy effectively eliminates geometric artifacts and consistently outperforms existing baselines in progressive tomographic reconstruction under unified view selection protocols.