# External Patch-Based Image Restoration Using Importance Sampling

arXiv: https://arxiv.org/abs/1807.03018 · HTML: https://mlsanity.com/paper/1807.03018/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jul 2018.

## Built on by (most cited first, 3 of 3)

- [BR-SNIS: Bias Reduced Self-Normalized Importance Sampling](https://mlsanity.com/paper/2207.06364/) (2022)
- [Patch-Based Image Restoration using Expectation Propagation](https://mlsanity.com/paper/2106.15327/) (2021)
- [Fast Scalable Image Restoration using Total Variation Priors and Expectation Propagation](https://mlsanity.com/paper/2110.01585/) (2021)

## Abstract (arXiv)

This paper introduces a new approach to patch-based image restoration based on external datasets and importance sampling. The Minimum Mean Squared Error (MMSE) estimate of the image patches, the computation of which requires solving a multidimensional (typically intractable) integral, is approximated using samples from an external dataset. The new method, which can be interpreted as a generalization of the external non-local means (NLM), uses self-normalized importance sampling to efficiently approximate the MMSE estimates. The use of self-normalized importance sampling endows the proposed method with great flexibility, namely regarding the statistical properties of the measurement noise. The effectiveness of the proposed method is shown in a series of experiments using both generic large-scale and class-specific external datasets.