DiffCT: Differentiable Computed Tomography Operators

A high-performance, CUDA-accelerated library for circular orbits CT reconstruction with end-to-end differentiable operators, enabling advanced optimization and deep learning integration.

⭐ Please star this project if you find it useful!

✨ Features

• Fast: CUDA-accelerated projection and backprojection operations
• Differentiable: End-to-end gradient propagation for deep learning workflows

📐 Supported Geometries

• Parallel Beam: 2D parallel-beam geometry
• Fan Beam: 2D fan-beam geometry
• Cone Beam: 3D cone-beam geometry

🧩 Code Structure

diffct/
├── diffct/
│   ├── __init__.py            # Package initialization
│   ├── non_differentiable.py  # CUDA implementation
│   ├── differentiable.py      # Differentiable implementation
├── examples/                  # Example usages
│   ├── non_differentiable     # Non-differentiable examples
│   │   ├── parallel.py        
│   │   ├── fan.py             
│   │   ├── cone.py            
│   ├── differentiable         # Differentiable examples
│   │   ├── parallel.py        
│   │   ├── fan.py             
│   │   ├── cone.py            
├── pyproject.toml             # Project metadata
├── README.md                  # README
├── LICENSE                    # License
├── requirements.txt           # Dependencies

🚀 Quick Start

Prerequisites

• CUDA-capable GPU
• Python 3.10+
• PyTorch, NumPy, Numba with CUDA support

Installation

# Create and activate environment
conda create -n diffct python=3.10
conda activate diffct

# Install CUDA support
conda install cudatoolkit

git clone https://github.com/sypsyp97/diffct.git
cd diffct

pip install -r requirements.txt
pip install diffct

📚 Usage Examples

Non-Differentiable CUDA Implementation

import torch
import numpy as np
from diffct.non_differentiable import forward_parallel_2d, back_parallel_2d

# Create phantom
phantom = shepp_logan_2d(256, 256)

# Configure geometry
angles = np.linspace(0, 2*np.pi, 360, endpoint=False)

# Forward projection
sinogram = forward_parallel_2d(
    phantom, 
    num_views=360,
    num_detectors=512, 
    detector_spacing=1.0, 
    angles=angles, 
    step=0.5
)

# Reconstruction
sinogram_filtered = ramp_filter(torch.from_numpy(sinogram)).numpy()
reconstruction = back_parallel_2d(
    sinogram_filtered, 
    Nx=256, Ny=256,
    detector_spacing=1.0, 
    angles=angles, 
    step=0.5
) / 360  # Normalize by number of angles

Differentiable Implementation

import torch
from diffct.differentiable import ParallelProjectorFunction, ParallelBackprojectorFunction

# Setup device
device = torch.device('cuda' if torch.cuda.is_available() else 'cpu')

# Create phantom tensor with gradient tracking
phantom = torch.tensor(shepp_logan_2d(256, 256), device=device, requires_grad=True)
angles = torch.linspace(0, 2*np.pi, 360, device=device)

# Forward projection
sinogram = ParallelProjectorFunction.apply(
    phantom, 
    angles, 
    num_detectors=512, 
    detector_spacing=1.0, 
    step_size=0.5
)

# Filtered backprojection
sinogram_filtered = ramp_filter(sinogram).requires_grad_(True)
reconstruction = ParallelBackprojectorFunction.apply(
    sinogram_filtered,
    angles, 
    detector_spacing=1.0, 
    step_size=0.5, 
    Nx=256, Ny=256
) / 360  # Normalize

# Compute loss and gradients
loss = torch.mean((reconstruction - phantom)**2)
loss.backward()  # Gradients flow through the entire pipeline

📊 HU Calibration

1. With Original Image:

   • Normalize image before forward projection
   • Apply inverse transformation to restore HU range
   • Consider histogram matching if needed

2. With Sinogram Only:

   • Reconstruct to get raw values
   • Calibrate using reference points (air ≈ -1000 HU, water ≈ 0 HU)
   • Or use calibration markers with known attenuation coefficients

📝 Citation

If you use this library in your research, please cite:

@software{DiffCT2025,
  author       = {Yipeng Sun},
  title        = {DiffCT: Differentiable Computed Tomography 
                 Reconstruction with CUDA},
  year         = 2025,
  publisher    = {Zenodo},
  doi          = {10.5281/zenodo.14999333},
  url          = {https://doi.org/10.5281/zenodo.14999333}
}

📄 License

This project is licensed under the Apache 2.0 - see the LICENSE file for details.

🙏 Acknowledgements

This project was highly inspired by:

• PYRO-NN
• geometry_gradients_CT

Issues and contributions are welcome!