发表机构
Nanchang University; Fudan University; Southeast University（南昌大学; 复旦大学; 东南大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出高斯材料场，通过共享各向异性高斯基元和独立系数实现多能CT体积材料分解，联合优化几何与成分，在15个案例中显著提升重建质量。
AI 中文摘要
多能计算机断层扫描中的体积材料分解需要一种表示，该表示在共同的空间域中组织多个三维材料场，同时保留组成和局部结构的差异。我们观察到空间基元可以在不同材料之间共享，而无需绑定其系数，但其局部容量必须响应特定材料的重建需求。我们引入了高斯材料场，它使用共享的各向异性三维高斯基元和独立的非负材料系数来表示多种材料分布。共享几何体定义了一个连续的空间基，而系数决定了每个基元对各个材料场的贡献。为了从多能投影重建这种表示，一个可微分的谱前向模型将高斯材料路径积分与校准的基矩阵相结合，使得空间几何和材料组成的联合优化成为可能。材料感知的自适应密度控制保留特定材料的细化证据，然后进行聚合，并调整局部表示容量以适应空间上广泛的组件和稀疏细节。实验使用从公开可用的CT数据通过常规方法构建的伪参考材料图生成的合成多能投影。在15个案例中，我们的方法在平均PSNR上比最强基线提高了4.03 dB，SSIM提高了4.96%，同时NRMSE降低了33.45%。材料层面的比较和组件消融支持对局部结构的改进恢复，而运行时和内存测量显示了有利的计算扩展性。这些结果确立了高斯材料场作为体积多材料重建的显式、自适应表示。
英文摘要
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.
Comments13 pages, 12 figures
