SpectralCTGaussians: Projection-Domain Reconstruction and Basis Material Decomposition for Spectral CT using 3D Gaussian Splatting

Sparse-view spectral computed tomography (CT) reconstructs energy-resolved attenuation volumes from limited projection views, requiring simultaneous handling of angular undersampling and spectral coupling. We propose a SharedStructure 4D Spectral Gaussian Representation (4D-SG) that learns shared Gaussian geometry from full spectrum structural projections and uses a Gaussian-wise Spectral Density Curve Network (GSC-Net) to predict Gaussian raw density transformations. This factorization separates shared spatial structure from spectral attenuation variation, avoids independent channel geometry optimization, and establishes a continuous 4D-SG representation from discrete spectral measurements for unobserved spectral channel queries. Experiments on six synthesized, simulated projection, and real projection datasets with 50 views demonstrate the best average performance. Compared with the strongest Gaussian baseline, 4D-SG improves PSNR from 35.56 dB to 36.61 dB, increases SSIM from 0.909 to 0.914, and reduces LPIPS from 0.208 to 0.194, demonstrating its effectiveness for sparse-view spectral CT reconstruction.

Volumetric material decomposition in multi-energy computed tomography requires a representation that organizes multiple three-dimensional material fields in a common spatial domain while retaining differences in composition and local structure. We observe that spatial primitives can be shared across materials without tying their coefficients, but their local capacity must respond to material-specific reconstruction needs. We introduce Gaussian material fields, which represent multiple material distributions with shared anisotropic 3D Gaussian primitives and independent nonnegative material coefficients. The shared geometry defines a continuous spatial basis, while the coefficients determine each primitive's contribution to the individual material fields. To reconstruct this representation from multi-energy projections, a differentiable spectral forward model combines Gaussian material path integrals with a calibrated basis matrix, enabling joint optimization of spatial geometry and material composition. Material-aware adaptive density control retains material-specific refinement evidence before aggregation and adjusts local representation capacity to accommodate both spatially extensive components and sparse details. Experiments use synthesized multi-energy projections generated from pseudo-reference material maps constructed by conventional methods from publicly available CT data. Across 15 cases, our approach improves average PSNR by 4.03 dB and SSIM by 4.96% over the strongest baseline, while reducing NRMSE by 33.45%. Material-wise comparisons and component ablations support improved recovery of localized structures, while runtime and memory measurements show favorable computational scaling. These results establish Gaussian material fields as an explicit, adaptive representation for volumetric multi-material reconstruction.

While 3D Gaussian splatting (3DGS) offers explicit and efficient scene representations for cone-beam computed tomography reconstruction, conventional photometric optimization inherently suffers from spectral bias under ultra sparse-view conditions, leading to over-smoothing and a loss of high-frequency anatomical details. Since wavelet transforms provide rich high-frequency information and have been widely utilized to enhance sparse reconstruction, this work integrates wavelet multi-resolution analysis with 3DGS. To circumvent the mathematical mismatch between the strict non-negativity of physical X-ray attenuation and the bipolar nature of high-frequency wavelet coefficients, we propose Residual Gaussian Splatting (RGS). Methodologically, we introduce a spectrally-decoupled Gaussian representation that stratifies the volumetric field into a geometric base component and a residual detail component. This decomposition systematically transforms explicit high-frequency fitting into a physically consistent, implicit residual compensation task. Furthermore, we devise a spectral-spatial collaborative optimization strategy to coordinate the interplay between geometric anchoring and texture refinement, effectively preventing spectral crosstalk. Extensive experiments on clinical datasets demonstrate that RGS enables the reconstructed images to capture highly refined geometric textures. It successfully resolves the trade-off between artifact suppression and detail preservation, yielding superior visual fidelity in complex trabecular and vascular structures compared to existing neural rendering baselines.