Adaptive Quantile Sparse Image (AQuaSI) Prior for Inverse Imaging Problems

TL;DR

This paper introduces the AQuaSI prior, a novel regularization method for inverse imaging problems that leverages quantile filtering to better model natural image distributions, improving tasks like upsampling and restoration.

Contribution

The paper presents the AQuaSI prior, a new adaptive quantile-based regularizer that can be integrated into various optimization algorithms for inverse imaging tasks.

Findings

Effective in joint RGB/depth upsampling

Improves RGB/NIR image restoration quality

Outperforms related denoising regularization methods

Abstract

Inverse problems play a central role for many classical computer vision and image processing tasks. Many inverse problems are ill-posed, and hence require a prior to regularize the solution space. However, many of the existing priors, like total variation, are based on ad-hoc assumptions that have difficulties to represent the actual distribution of natural images. Thus, a key challenge in research on image processing is to find better suited priors to represent natural images. In this work, we propose the Adaptive Quantile Sparse Image (AQuaSI) prior. It is based on a quantile filter, can be used as a joint filter on guidance data, and be readily plugged into a wide range of numerical optimization algorithms. We demonstrate the efficacy of the proposed prior in joint RGB/depth upsampling, on RGB/NIR image restoration, and in a comparison with related regularization by denoising approaches.