# Patch-Based Image Restoration using Expectation Propagation

arXiv: https://arxiv.org/abs/2106.15327 · HTML: https://mlsanity.com/paper/2106.15327/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 61 references that are in the map.
- First posted on arXiv 18 Jun 2021.

## Builds on (most cited first, 14 of 14)

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [The Little Engine that Could: Regularization by Denoising (RED)](https://mlsanity.com/paper/1611.02862/) (2016)
- [Expectation Propagation for approximate Bayesian inference](https://mlsanity.com/paper/1301.2294/) (2013)
- [DeepRED: Deep Image Prior Powered by RED](https://mlsanity.com/paper/1903.10176/) (2019)
- [Efficient Bayesian computation by proximal Markov chain Monte Carlo: when Langevin meets Moreau](https://mlsanity.com/paper/1612.07471/) (2016)
- [Scalable Bayesian uncertainty quantification in imaging inverse problems via convex optimization](https://mlsanity.com/paper/1803.00889/) (2018)
- [Maximum-a-posteriori estimation with Bayesian confidence regions](https://mlsanity.com/paper/1602.08590/) (2016)
- [Efficient Covariance Approximations for Large Sparse Precision Matrices](https://mlsanity.com/paper/1705.08656/) (2017)
- [External Patch-Based Image Restoration Using Importance Sampling](https://mlsanity.com/paper/1807.03018/) (2018)
- [Compressed sensing reconstruction using Expectation Propagation](https://mlsanity.com/paper/1904.05777/) (2019)
- [Non-convex image reconstruction via Expectation Propagation](https://mlsanity.com/paper/1809.03958/) (2018)
- [A Gaussian Mixture MRF for Model-Based Iterative Reconstruction with Applications to Low-Dose X-ray CT](https://mlsanity.com/paper/1605.04006/) (2016)

## Built on by (most cited first, 4 of 4)

- [The split Gibbs sampler revisited: improvements to its algorithmic structure and augmented target distribution](https://mlsanity.com/paper/2206.13894/) (2022)
- [Accelerated Bayesian imaging by relaxed proximal-point Langevin sampling](https://mlsanity.com/paper/2308.09460/) (2023)
- [Fast Scalable Image Restoration using Total Variation Priors and Expectation Propagation](https://mlsanity.com/paper/2110.01585/) (2021)
- [Learning Sparse Codes with Entropy-Based ELBOs](https://mlsanity.com/paper/2311.01888/) (2023)

## Abstract (arXiv)

This paper presents a new Expectation Propagation (EP) framework for image restoration using patch-based prior distributions. While Monte Carlo techniques are classically used to sample from intractable posterior distributions, they can suffer from scalability issues in high-dimensional inference problems such as image restoration. To address this issue, EP is used here to approximate the posterior distributions using products of multivariate Gaussian densities. Moreover, imposing structural constraints on the covariance matrices of these densities allows for greater scalability and distributed computation. While the method is naturally suited to handle additive Gaussian observation noise, it can also be extended to non-Gaussian noise. Experiments conducted for denoising, inpainting and deconvolution problems with Gaussian and Poisson noise illustrate the potential benefits of such flexible approximate Bayesian method for uncertainty quantification in imaging problems, at a reduced computational cost compared to sampling techniques.