Gaussian Material Fields for Volumetric Multi-Energy CT Decomposition

2026-10-07

AI Summary

Multi-energy CT material decomposition requires precise characterization of diverse material distributions and their local structural variations within a unified spatial domain. This work proposes Gaussian Material Fields, which jointly optimize geometry and composition through shared anisotropic 3D Gaussian primitives with independent non-negative coefficients. By incorporating material-aware adaptive density control, the method flexibly balances reconstruction demands between prevalent compositions and sparse structural details. Furthermore, a differentiable spectral forward model combined with Gaussian path tracing enables end-to-end joint optimization. Compared to the strongest baseline, the proposed approach achieves a 4.03 dB improvement in PSNR, a 4.96% increase in SSIM, and a 33.45% reduction in NRMSE, demonstrating significantly enhanced local structure recovery with high computational efficiency.

Abstract

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.

Problem

• Multi-energy CT
• Volumetric material decomposition
• Material fields
• 3D reconstruction

Innovation

• Gaussian Material Fields
• Multi-Energy CT
• Volumetric Material Decomposition
• Differentiable Spectral Forward Model
• Adaptive Density Control