Plug-and-play Split Gibbs Sampler (PnP-SGS)

A PyTorch implementation of the "Plug-and-play split Gibbs sampler: integrating deep generative priors into Bayesian inference" paper, focused on solving inverse imaging problems using DDPM-based regularization.

Overview

This repository implements the PnP-SGS algorithm, which combines:

• Split Gibbs Sampling
• Denoising Diffusion Probabilistic Models (DDPM)
• Variable splitting optimization techniques

The implementation currently supports image inpainting, with the potential to extend to other inverse problems like deblurring and super-resolution.

Algorithm

Features

• Full posterior distribution sampling for inverse imaging problems
• Integration with pre-trained DDPM models
• Sparse matrix operations for efficient computation
• Support for RGB image inpainting
• Adaptive noise estimation and denoising steps
• Configurable sampling parameters

Parameter Tuning

The algorithm is sensitive to parameter selection. Here are recommended ranges:

• rho: Coupling parameter [0.1, 0.5] (0.33 recommended)
• sigma: Noise level [0.05, 0.2] (0.1 recommended)
• n_steps: Total MCMC steps [100, 200]
• burn_in: Burn-in period [30, 50]

Results

Expected reconstruction quality for image inpainting (75% masked pixels):

• PSNR: ~25-30 dB
• SSIM: ~0.8-0.9
• Computation time: ~7 minutes (NVIDIA RTX 3080)

Known Limitations

1. Computational overhead compared to simpler methods like DPS (Diffusion Posterior Sampling).
2. Sensitive to parameter rho
3. Background reconstruction may be less accurate than foreground
4. Memory intensive for large images

Citation

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

@article{coeurdoux2023plug,
  title={Plug-and-play split Gibbs sampler: integrating deep generative priors into Bayesian inference},
  author={Coeurdoux, Florentin and Dobigeon, Nicolas and Chainais, Pierre},
  year={2023}
}