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

Inverse problems play a central role for many classical computer vision and image processing tasks. A key challenge in solving an inverse problem is to find an appropriate prior to convert an ill-posed problem into a well-posed task. 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. 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.