This repository contains an implementation of EPLL and the implementation for the work Posterior Sampling for Image Restoration using Explicit Patch Priors in PyTorch.

Expected Patch Log-Likelihood (EPLL) is a well established image decorruption algorithm. EPLL uses a patch-denoiser in order to restore full images, using the Half-Quadratic Splitting algorithm. The original paper uses a Gaussian mixture model (GMM) in order to denoise patches, but in principal any patch-denoiser can be used. This implementation allows for any patch denoiser to be used in order to restore images.

denoise_demo.py shows how to denoise an image using the EPLL algorithm. Running it should produce the following images:

The first image is the noisy version and the second one is the denoised version, specifically under noise with $\sigma=35/255$. The patch-prior for these results is a GMM with 100 centers trained on ~5 million patches from the BSD300 train set.

This implementation follows the terminology of Posterior Sampling for Image Restoration using Explicit Patch Priors, which interprets the EPLL-loss as a loss of grids of the image. This allows for easily running faster versions of the same EPLL algorithm (using less grids), albeit at a slight cost of accuracy. For instance, the above images were produced using 16 grids, which takes ~5.2 seconds (with a GPU), while running on the same task with 4 grids takes ~1.3 seconds.

EPLL is widely known not for denoising, but for general image restorations. This implementation allows for that as well!

deblur_demo.py shows how to deblur an image using this implementations and should produce the following images:

Crucially, this implementation uses automatic differentiation in order to decorrupt images. Any corruption process $H$ can be restored, as long as $H$ is passed as a differentiable function to the function EPLL.decorrupt.

While a GMM is commonly used for EPLL, essentially any other patch-prior can be used. Specifically, all that is needed is a class with a function denoise which receives batches of patches as well as the noise variance and returns the denoised patches.