FaCT-GS: Fast and Scalable CT Reconstruction with Gaussian Splatting

1. Problem Statement

X-ray Computed Tomography (CT) reconstruction, particularly in sparse-view scenarios (where the number of projection images is limited to reduce radiation dose or acquisition time), faces a critical trade-off between reconstruction quality and computational cost.

• Classical Algebraic Methods (e.g., FISTA, SIRT): Fast and effective but often suffer from residual artifacts and reduced fidelity in sparse-view settings.
• Learning-Based Methods (e.g., NeRFs, IntraTomo): Offer superior image quality but are computationally prohibitive, often requiring 15–30 minutes per scan, making them impractical for high-resolution (1k–2k) or time-sensitive applications.
• Existing Gaussian Splatting (GS) Approaches (e.g., R2-Gaussian): While promising, previous GS-based CT methods still lag behind classical methods in speed (e.g., R2-Gaussian takes ~9 minutes vs. FISTA's ~1 minute for standard 512² projections) and lack scalability for modern high-resolution scanners.

The core challenge is to develop a GS-based reconstruction pipeline that matches the quality of advanced learning-based methods while achieving the speed and scalability required for clinical and industrial adoption.

2. Methodology: FaCT-GS

The authors propose FaCT-GS, a framework that re-engineers the Gaussian Splatting pipeline specifically for CT reconstruction. The method models the 3D attenuation field as a collection of learnable 3D Gaussian kernels.

Key Technical Components:

• Optimized Rasterization and Voxelization:
  • Bounding Box Optimization: Replaces inefficient square bounding boxes with axis-aligned rectangular boxes factoring in density to reduce overestimation of affected regions.
  • Backward Pass Reformulation: Shifts from a per-pixel backward pass (prone to write conflicts) to a per-Gaussian backward pass, eliminating warp stalls and memory conflicts.
  • Ordering Removal: Removes unnecessary view-dependent occlusion ordering logic, as X-ray integration order does not affect the measured signal in CT.
  • Memory Efficiency: Coalesces function parameters into compact float4 structs to reduce memory traffic.
• Fused Loss Kernels:
  • Implements custom CUDA kernels to fuse loss calculations, significantly reducing memory traffic and launch overhead.
  • 2D SSIM: Accelerated by 5–8× using fused-ssim logic.
  • 3D SSIM: Introduces a novel fused kernel using a ring buffer for the depth dimension, achieving an 11× speedup.
  • 3D Total Variation (TV): Custom fused kernel for homogeneity regularization, achieving a 3× speedup.
• Initialization Strategies:
  • Gradient-Based Sampling: Instead of sampling Gaussian means based on intensity, the method samples based on the gradient magnitude of an initial FDK reconstruction. This places Gaussians near high-frequency features (edges) more effectively.
  • Volume Prior (Warm Start): Introduces a novel "Volume Fitting" stage where Gaussians are fitted directly to a pre-existing volumetric prior (e.g., a previous scan or a low-res reconstruction). This allows the optimization to start closer to the solution, mimicking the "warm start" capabilities of classical algebraic methods.

3. Key Contributions

1. Significant Speedup: FaCT-GS is >4× faster than the State-of-the-Art (R2-Gaussian) on standard 512² projections and >13× faster on 2k projections. It achieves competitive results in under 45 seconds and full optimization in ~2 minutes for standard scans.
2. Scalability: The method scales exceptionally well with increasing projection and volume sizes. Unlike algebraic methods where cost grows cubically with volume size, FaCT-GS scales primarily with projection resolution, making it highly efficient for high-resolution (1k–2k) data.
3. Novel Initialization: The introduction of gradient-based sampling and volume-prior fitting bridges the gap between learning-based and classical methods, enabling efficient warm-starts that were previously difficult in GS frameworks.
4. Data Compression: The authors demonstrate that the fitted Gaussian representation serves as a highly efficient compression format. Storing a volume as Gaussians (quantized to float16) yields a compression ratio comparable to or better than zipped uint8 volumes and JPEG stacks, with high fidelity (SSIM ~0.976).

4. Experimental Results

The method was evaluated on the R2-Gaussian dataset (15 real CT volumes) and real projection data (FIPS dataset) across 25, 50, and 75 view settings.

• Performance vs. Quality:
  • FaCT-GS achieves the highest SSIM (0.949) and second-highest PSNR (38.80) among all tested methods on 75-view 512² data.
  • It outperforms FISTA (a fast classical method) in both speed and quality, a rare feat for learning-based approaches.
  • Compared to R2-Gaussian, FaCT-GS is 4.5× faster for the same number of iterations and reaches R2-Gaussian's quality level in only 150 iterations (vs. 400).
• Scalability:
  • On 2k projections, FaCT-GS is 31.5× faster than FISTA and 13× faster than R2-Gaussian.
  • While FISTA converges quickly on small data, its per-iteration cost rises steeply with resolution, whereas FaCT-GS maintains a low per-iteration cost.
• Initialization Impact:
  • Gradient-based initialization outperforms intensity-based sampling.
  • The Volume Prior (Warm Start) strategy significantly accelerates convergence, requiring ~40% fewer iterations to reach the same quality as a cold start.
• Compression:
  • Fitted Gaussians (0.84 MB) offer a higher compression ratio than zipped uint8 (4.52 MB) and JPEG stacks (0.92 MB) while maintaining high structural similarity (SSIM 0.976).

5. Significance and Impact

FaCT-GS represents a major step forward in making Gaussian Splatting a practical tool for medical and industrial CT.

• Clinical Viability: By reducing reconstruction times from minutes to seconds/low-minutes for high-resolution scans, it enables time-sensitive applications like in-line industrial inspection and real-time patient monitoring.
• Bridging the Gap: It successfully addresses the "performance-quality trade-off" that has prevented learning-based methods from replacing classical algorithms. It offers the quality of NeRFs/GS with the speed of algebraic methods.
• Versatility: Beyond reconstruction, the method provides a unified framework for volumetric compression and warm-starting reconstructions using prior knowledge, which is crucial for longitudinal studies and repetitive scanning.

In conclusion, FaCT-GS demonstrates that with deep optimization of the rendering and voxelization pipelines, Gaussian Splatting can become the new standard for fast, high-fidelity, and scalable CT reconstruction.