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

## TL;DR

This paper introduces a Bayesian hyperprior method for joint image denoising and interpolation, enhancing stability and adaptability for inverse problems like HDR imaging from single, sensor-modified images.

## Contribution

It proposes a hyperprior-based Bayesian approach that stabilizes patch modeling, especially for diagonal degradation and signal-dependent noise, improving HDR imaging applications.

## Key findings

- Effective inpainting and zooming for missing data
- Handles signal-dependent noise in digital cameras
- Demonstrates improved HDR imaging results

## Abstract

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.