Calibrated Closed-Form Uncertainty for Radiative Gaussian Splatting in Sparse-View CT

Radiative Gaussian splatting has made sparse-view CT reconstruction fast, but existing methods output point estimates with no notion of where the reconstruction can be trusted. We exploit a property of transmissive X-ray imaging that RGB splatting cannot claim – projection and voxelization are strictly linear in the per-Gaussian densities – to equip radiative Gaussians with a variational density posterior whose predictive variance propagates in closed form, exactly, in a single forward pass, in both volume space (${\sigma }^2(x)={\sum }_i{g}_i(x{)}^2{s}_i^2$) and projection space ($\mathrm{V}\mathrm{a}\mathrm{r}[I_p]={\sum }_i{w}_{i,p}^2{s}_i^2$). We present the first systematic calibration study for Gaussian-splatting CT (Spearman / AUSE / ECE with temperature scaling), showing that the resulting per-voxel uncertainty ranks true reconstruction error on 14 of 15 scenes of the official benchmark across three view budgets – 9 of 15 additionally meeting our magnitude-calibration target after a single temperature – while the perturbation-ensemble heuristic of concurrent work, transplanted to voxel space under the same protocol on our development scenes, does not (rank correlation as low as $-0.08$). We then dissect why uncalibrated acquisition scores can nevertheless select acceptable views, identifying three regimes – flat (isotropic, balanced), pathological (degenerate coverage), and anisotropic – and showing, in controlled single-scene testbeds, that principled uncertainty earns a measurable premium only in the last, motivating a coverage-gated, maturity-scheduled acquisition policy; the same calibrated posterior further points toward a dose-adaptive stopping rule, whose experimental validation we leave to future work.