# A Bayesian Hyperprior Approach for Joint Image Denoising and Interpolation, with an Application to HDR Imaging

arXiv: https://arxiv.org/abs/1706.03261 · HTML: https://mlsanity.com/paper/1706.03261/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jun 2017.

## Built on by (most cited first, 7 of 7)

- [Bayesian imaging using Plug & Play priors: when Langevin meets Tweedie](https://mlsanity.com/paper/2103.04715/) (2021)
- [Denoising: A Powerful Building-Block for Imaging, Inverse Problems, and Machine Learning](https://mlsanity.com/paper/2409.06219/) (2024)
- [Solving Inverse Problems by Joint Posterior Maximization with Autoencoding Prior](https://mlsanity.com/paper/2103.01648/) (2021)
- [Self-Supervised Super-Resolution for Multi-Exposure Push-Frame Satellites](https://mlsanity.com/paper/2205.02031/) (2022)
- [NF-ULA: Langevin Monte Carlo with Normalizing Flow Prior for Imaging Inverse Problems](https://mlsanity.com/paper/2304.08342/) (2023)
- [Sampling Strategies in Bayesian Inversion: A Study of RTO and Langevin Methods](https://mlsanity.com/paper/2406.16658/) (2024)
- [Riemannian Patch Assignment Gradient Flows](https://mlsanity.com/paper/2504.13024/) (2025)

## Abstract (arXiv)

Recently, impressive denoising results have been achieved by Bayesian approaches which assume Gaussian models for the image patches. This improvement in performance can be attributed to the use of per-patch models. Unfortunately such an approach is particularly unstable for most inverse problems beyond denoising. In this work, we propose the use of a hyperprior to model image patches, in order to stabilize the estimation procedure. There are two main advantages to the proposed restoration scheme: Firstly it is adapted to diagonal degradation matrices, and in particular to missing data problems (e.g. inpainting of missing pixels or zooming). Secondly it can deal with signal dependent noise models, particularly suited to digital cameras. As such, the scheme is especially adapted to computational photography. In order to illustrate this point, we provide an application to high dynamic range imaging from a single image taken with a modified sensor, which shows the effectiveness of the proposed scheme.