Gaussian Material Fields for Volumetric Multi-Energy CT Decomposition

Computed Tomography (CT) carries significant ionizing radiation risks, driving the need for sparse-view reconstruction. Implicit scene representations (ISRs) address this by recovering continuous volumetric attenuation fields directly from sparse projections, and recent geometry-aware extensions jointly model surface geometry alongside attenuation to improve fidelity and enable clean tissue segmentation without manual thresholding. However, these methods remain limited by manually tuned attenuation bounds and rigid two-material constraints. This paper proposes $K$-NeAS, a unified and scalable architecture for automated, multi-material surface reconstruction. We replace independent material networks with a shared latent backbone and introduce a fully differentiable $K$-material sequential soft selector to model an arbitrary number of overlapping tissues. To eliminate manual tuning, we automate attenuation bounding using a Gaussian Mixture Model (GMM) and implement a scheduled auxiliary floater loss to mitigate geometric hallucinations common under extreme sparsity. Evaluated across four clinical Cone-Beam CT (CBCT) datasets, $K$-NeAS successfully scales to arbitrary material counts, achieving superior 3D volumetric fidelity at $K=3$ materials on complex multi-tissue regions such as the Abdomen ($33.28\text{ dB}$ 3D PSNR vs. $31.40\text{ dB}$ single-material NeAS baseline, a $+1.88\text{ dB}$ improvement). Furthermore, our model exhibits enhanced robustness under sparse-sampling conditions, outperforming baseline 3D PSNR by up to $1.17\text{ dB}$ under 5- and 10-view constraints.

Dual-energy CT (DECT) exploits attenuation differences across different X-ray spectra to provide richer material information and has been widely used in medical imaging. While sparse-view acquisition can lower radiation exposure, it makes DECT material decomposition even more challenging, as the problem is nonlinear and ill-posed. Existing deep unrolling approaches generally do not explicitly incorporate the Jacobian operator induced by the nonlinear forward model, and their sparsity priors are still mainly built on conventional convolutions, which are insufficient for modeling global structural information. This study addresses the challenge of DECT multi-material decomposition in sparse-view settings by representing it as a sparse-regularized nonlinear least-squares problem. To solve it, we propose an iterative dual-domain refinement network (DECT-DRNet). In each iteration, the filtered back-projection (FBP)-based Jacobian approximation module is used first to generate an intermediate material decomposition result. Here, we characterize the forward process of material decomposition using a nonlinear operator, and then construct a theoretically grounded learnable approximation of the adjoint Jacobian operator by integrating the FBP algorithm with a U-Net into the backward process. In addition, to address the limitation of existing deep learning-based decomposition methods in globally suppressing noise and artifacts, we introduce a learnable sparse dual domain regularization term that incorporates Fourier convolutional residual blocks. This refinement block combines geometric feature extraction in the image domain with noise suppression in the frequency domain, allowing the model to capture both global and local features while maintaining structural details. DECT-DRNet demonstrates its ability to achieve more accurate material decomposition under sparse-view conditions.

Sparse-view computed tomography is a severely ill-posed inverse problem, where recent 3D Gaussian Splatting methods offer an efficient explicit representation for tomographic reconstruction. However, we find that projection-domain optimization can be misleading in this setting: the rendered projections may continue to improve while the reconstructed volume deteriorates. We identify this failure mode as Projection-Volume Fidelity Divergence (PVFD), a representation-level optimization drift caused by anisotropic Gaussian deformation and view-specific primitive co-adaptation under sparse Radon constraints. To characterize this behavior, we introduce geometry- and volume-level diagnostics that measure needle-like Gaussian degeneration and the stability of the voxelized density field. Based on these observations, we propose LADES, a ground-truth-free optimization controller for sparse-view Gaussian tomography. LADES combines Linearly Annealed Dropout, which applies strong stochastic masking in early training to disrupt premature primitive co-adaptation and gradually restores full capacity for structural consolidation, with Structure-Aware Early Stopping, which terminates densification according to the saturation of Gaussian population growth rather than validation PSNR. Experiments on sparse-view CT reconstruction show that LADES improves volumetric fidelity, suppresses structural degeneration, and substantially reduces training time while maintaining competitive projection accuracy. These results suggest that robust Gaussian-based tomography requires monitoring and controlling volumetric structure, rather than optimizing projection fit alone.