KB-Splatting: Differentiable Kaiser-Bessel Splatting for Real X-ray Projection-Enabled CT Reconstruction

Sparse-view cone-beam computed tomography (CBCT) can reduce harmful X-ray patient exposure, but recovering an accurate three-dimensional attenuation field from limited X-ray projections remains severely ill-posed. To address this, recent differentiable CT reconstruction methods have adopted anisotropic Gaussian primitives. Yet CT volumes contain sharp attenuation transitions, whereas Gaussian profiles are smooth and couple spatial extent with kernel decay. Accurately representing these transitions can therefore require several small primitives, driven by adaptive control heuristics. Thus increasing memory and optimization cost. These methods are also evaluated mainly on synthetic digitally reconstructed radiographs (DRRs), so their performance on physical clinical scanners remains unclear. Consequently, we introduce KB-Splatting, a differentiable CT reconstruction framework based on anisotropic generalized Kaiser-Bessel primitives. Our KB primitives have exact compact support per kernel and independently control support size and profile concentration, decoupling where attenuation is represented from how it varies within that tissue region. Their analytic cone-beam projection also allows us to optimize these kernel parameters directly from real X-ray projections. We also introduce a simple reconstruction-guided population control scheme that uses volumetric residuals and local parent kernel selection to add and relocate primitives in poorly reconstructed regions. We evaluate KB-Splatting on established DRR benchmarks and introduce a paired multi-system CBCT dataset containing real measured projections, documented acquisition geometries with coordinate-convention checks, and reference CT volumes from one commercial CT system and one experimental laboratory system. Experiments compare KB-Splatting with neural-field and Gaussian-splatting baselines, where it surpasses current state-of-the-art (SOTA) methods in attenuation PSNR, with a mean gain of 0.93 dB at 2x training speed. Finally, we extend KB-Splatting to RGB novel-view synthesis, testing the same representation under both additive X-ray formation and occlusion-aware rendering.