# Accelerating GMM-based patch priors for image restoration: Three ingredients for a 100× speed-up

arXiv: https://arxiv.org/abs/1710.08124 · HTML: https://mlsanity.com/paper/1710.08124/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Oct 2017.

## Built on by (most cited first, 5 of 5)

- [PatchNR: Learning from Very Few Images by Patch Normalizing Flow Regularization](https://mlsanity.com/paper/2205.12021/) (2022)
- [Learning Regularization Functionals for Inverse Problems: A Comparative Study](https://mlsanity.com/paper/2510.01755/) (2025)
- [Wasserstein Patch Prior for Image Superresolution](https://mlsanity.com/paper/2109.12880/) (2021)
- [WPPNets and WPPFlows: The Power of Wasserstein Patch Priors for Superresolution](https://mlsanity.com/paper/2201.08157/) (2022)
- [Learning from small data sets: Patch-based regularizers in inverse problems for image reconstruction](https://mlsanity.com/paper/2312.16611/) (2023)

## Abstract (arXiv)

Image restoration methods aim to recover the underlying clean image from corrupted observations. The Expected Patch Log-likelihood (EPLL) algorithm is a powerful image restoration method that uses a Gaussian mixture model (GMM) prior on the patches of natural images. Although it is very effective for restoring images, its high runtime complexity makes EPLL ill-suited for most practical applications. In this paper, we propose three approximations to the original EPLL algorithm. The resulting algorithm, which we call the fast-EPLL (FEPLL), attains a dramatic speed-up of two orders of magnitude over EPLL while incurring a negligible drop in the restored image quality (less than 0.5 dB). We demonstrate the efficacy and versatility of our algorithm on a number of inverse problems such as denoising, deblurring, super-resolution, inpainting and devignetting. To the best of our knowledge, FEPLL is the first algorithm that can competitively restore a 512x512 pixel image in under 0.5s for all the degradations mentioned above without specialized code optimizations such as CPU parallelization or GPU implementation.