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

arXiv: https://arxiv.org/abs/2609.29638 · HTML: https://mlsanity.com/paper/2609.29638/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 88 references that are in the map.
- First posted on arXiv 29 Aug 2026.

## Builds on (most cited first, 23 of 23)

- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [On hallucinations in tomographic image reconstruction](https://mlsanity.com/paper/2012.00646/) (2020)
- [R2-Gaussian: Rectifying Radiative Gaussian Splatting for Tomographic Reconstruction](https://mlsanity.com/paper/2405.20693/) (2024)
- [MedNeRF: Medical Neural Radiance Fields for Reconstructing 3D-aware CT-Projections from a Single X-ray](https://mlsanity.com/paper/2202.01020/) (2022)
- [Radiative Gaussian Splatting for Efficient X-ray Novel View Synthesis](https://mlsanity.com/paper/2403.04116/) (2024)
- [3DGR-CT: Sparse-View CT Reconstruction with a 3D Gaussian Representation](https://mlsanity.com/paper/2312.15676/) (2023)
- [Tensor-based formulation and nuclear norm regularization for multi-energy computed tomography](https://mlsanity.com/paper/1307.5348/) (2013)
- [Learning 3D Gaussians for Extremely Sparse-View Cone-Beam CT Reconstruction](https://mlsanity.com/paper/2407.01090/) (2024)
- [Core Imaging Library -- Part I: a versatile Python framework for tomographic imaging](https://mlsanity.com/paper/2102.04560/) (2021)
- [Deep Learning based Spectral CT Imaging](https://mlsanity.com/paper/2008.13570/) (2020)
- [SpectralGaussians: Semantic, spectral 3D Gaussian splatting for multi-spectral scene representation, visualization and analysis](https://mlsanity.com/paper/2408.06975/) (2024)
- [Systematic Review on Learning-based Spectral CT](https://mlsanity.com/paper/2304.07588/) (2023)
- [X-GRM: Large Gaussian Reconstruction Model for Sparse-view X-rays to Computed Tomography](https://mlsanity.com/paper/2505.15235/) (2025)
- [A material decomposition method for dual-energy CT via dual interactive Wasserstein generative adversarial networks](https://mlsanity.com/paper/2007.11247/) (2020)
- [Sparse-View Spectral CT Reconstruction Using Deep Learning](https://mlsanity.com/paper/2011.14842/) (2020)
- [Ray-driven Spectral CT Reconstruction Based on Neural Base-Material Fields](https://mlsanity.com/paper/2404.06991/) (2024)
- [AC-IND: Sparse CT reconstruction based on attenuation coefficient estimation and implicit neural distribution](https://mlsanity.com/paper/2409.07171/) (2024)
- [X-Field: A Physically Grounded Representation for 3D X-ray Reconstruction](https://mlsanity.com/paper/2503.08596/) (2025)
- [CT Material Decomposition using Spectral Diffusion Posterior Sampling](https://mlsanity.com/paper/2402.03476/) (2024)
- [Volumetric Material Decomposition Using Spectral Diffusion Posterior Sampling with a Compressed Polychromatic Forward Model](https://mlsanity.com/paper/2503.22392/) (2025)
- [ADJUST: A Dictionary-Based Joint Reconstruction and Unmixing Method for Spectral Tomography](https://mlsanity.com/paper/2112.11406/) (2021)
- [Direct Iterative Reconstruction of Multiple Basis Material Images in Photon-counting Spectral CT](https://mlsanity.com/paper/2309.13397/) (2023)
- [End-to-End Model-based Deep Learning for Dual-Energy Computed Tomography Material Decomposition](https://mlsanity.com/paper/2406.00479/) (2024)

## Built on by (most cited first, 1 of 1)

- [Gaussian Material Fields for Volumetric Multi-Energy CT Decomposition](https://mlsanity.com/paper/2610.09492/) (2026)

## Abstract (arXiv)

Spectral computed tomography (CT) extends conventional CT by measuring attenuation across multiple energy channels, allowing improved modeling of physical X-ray interactions and energy-dependent material behavior and leading to richer scene understanding. We present a novel method for spectral CT reconstruction and basis material decomposition using 3D Gaussian Splatting by adding per-Gaussian basis material fractions to the set of learnable parameters, which together with a set of energy-dependent basis functions define the attenuation across the full spectral range. The basis functions represent various physical attenuation models such as photoelectric absorption and Compton scattering, and are jointly optimized across all energy channels through a differentiable polychromatic forward model, with material decomposition performed via mean-shift clustering of the resulting coefficients. We evaluate our method on a baseline real-world dataset as well as a synthetic dataset that we introduce, comparing against traditional reconstruction algorithms and state-of-the-art learning-based CT reconstruction methods. Our approach outperforms all traditional baselines in novel view synthesis and achieves the best PSNR among all compared methods for spectral CT volume reconstruction, while describing all energy channels with a single shared representation that requires a number of Gaussians comparable to single-channel Gaussian splatting-based CT reconstruction approaches. For basis material decomposition, no traditional or learning-based baseline offers one-step decomposition with direct RGB material segmentation, and our method additionally recovers the photoelectric basis with higher PSNR than traditional pipelines.