Discretized Gaussian Representation for Tomographic Reconstruction

TL;DR

This work introduces Discretized Gaussian Representation (DGR) for end-to-end CT reconstruction by modeling the volume as a set of discretized isotropic Gaussians and aligning their contributions on a voxel grid. A highly parallel Fast Volume Reconstruction (FVR) module accelerates Gaussian aggregation, while a global optimization loop projects the volume to the projection domain using a multi-term, projection-space loss, augmented by adaptive density control. Across Cone-Beam Sparse-View, Fan-Beam Sparse-View, and Limited-Angle CT tasks, DGR achieves state-of-the-art image quality with substantially reduced reconstruction time, often without requiring training data for inference. The approach unifies representation, reconstruction, and optimization in a scalable framework, with code available for reproduction and deployment in diverse CT configurations.

Abstract

Computed Tomography (CT) enables detailed cross-sectional imaging but continues to face challenges in balancing reconstruction quality and computational efficiency. While deep learning-based methods have significantly improved image quality and noise reduction, they typically require large-scale training data and intensive computation. Recent advances in scene reconstruction, such as Neural Radiance Fields and 3D Gaussian Splatting, offer alternative perspectives but are not well-suited for direct volumetric CT reconstruction. In this work, we propose Discretized Gaussian Representation (DGR), a novel framework that reconstructs the 3D volume directly using a set of discretized Gaussian functions in an end-to-end manner. To further enhance efficiency, we introduce Fast Volume Reconstruction, a highly parallelized technique that aggregates Gaussian contributions into the voxel grid with minimal overhead. Extensive experiments on both real-world and synthetic datasets demonstrate that DGR achieves superior reconstruction quality and runtime performance across various CT reconstruction scenarios. Our code is publicly available at https://github.com/wskingdom/DGR.

Figures (6)

• Figure 1: I: CT imaging workflow: X-ray projections are acquired from multiple angles. II: Deep Learning-based Reconstruction (DLR): Networks are trained on paired projection-image datasets to reconstruct volumes, requiring extensive pre-training. III: Instance reconstruction (exemplified by 3DGS): Instance-adaptive optimization of 3D Gaussians via differentiable rendering, tailored for each instance without the need for training datasets.
• Figure 2: Pipeline of DGR. The 3D volume is initially represented by a set of continuous Gaussians, with each Gaussian's contribution confined to a local region surrounding the voxel. The Gaussians are then discretized onto the 3D grid, where their contributions are aligned to directly reconstruct the entire volume. Fast Volume Reconstruction technique gathers these contributions in a highly parallelized manner. Within each iteration, these Gaussians are reconstructed and then projected into the measurement domain for optimization.
• Figure 3: Qualitative Comparison of our DGR with previous state-of-the-art instance reconstruction methods SAX-NeRF and R$^2$-Gaussian, with major differences highlighted in Red boxes. Please zoom in for better visibility.
• Figure 4: This figure illustrates the reconstruction process by iterations of Fan-Beam 60-view CT. The positions of Gaussians are initialized using Filtered Back Projection, as described in the experimental settings.
• Figure 5: This figure illustrates the reconstruction process by iterations of Fan-Beam 90$^\circ$ Limited-Angle CT. The positions of Gaussians are randomly initialized for visualization comparison.