HerKry: A Hermite–Gaussian Hierarchy with Recurrent Krylov Trajectory Modeling for Robust Sparse-View CT Reconstruction

Sparse-view computed tomography (SVCT) relies heavily on learned priors, leaving it vulnerable to clinical distribution shifts. While a coarse-to-fine hierarchy can regularize early reconstruction by restricting weakly constrained degrees of freedom, directly extending data consistency (DC) to coarse scales is nontrivial. Image and sinogram downsampling do not generally commute with fan-beam projection, introducing geometry-dependent inconsistencies. To resolve this, we propose Hermite-Krylov CT (HerKry), which models images via a continuous Hermite–Gaussian (HG) hierarchy shifting from sparse, high-order primitives to dense, lower-order ones. This parameterization decouples representation resolution from measurement scale, enabling geometry-consistent DC directly against native sinograms. Crucially, higher-order HG modes can absorb complex spatial deformations via linear coefficient combination. This allows DC to freeze nonlinear parameters and optimize exclusively in linear coefficient space via Hermite-Coefficient CGLS (HC-CGLS), slashing DC latency by over $90\%$ with better fidelity. A Krylov-Trajectory GRU (KT-GRU) further encodes intermediate solver iterates to propagate optimization dynamics across stages. Extensive evaluations across cross-organ transfer, varying noise, and extreme sparsity demonstrate superior robustness, outperforming competing methods by up to $4\text{ dB}$. The code is available at https://anonymous.4open.science/r/Code-for-HerKry-DB40https://anonymous.4open.science/r/Code-for-HerKry-DB40.