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. Many inverse problems are illposed, and hence require a prior to regularize the solution space. However, many of the existing priors, like total variation, are based on adhoc 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 article, 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 RGBdepth upsampling, on RGBNIR image restoration, and in a comparison with related regularization by denoising approaches.

A convex single image dehazing model via sparse dark channel prior Abstract   In this paper, we present a convex model for single image dehazing via a sparse dark channel prior. Our work is based on an observation that the number of bright pixels is very small in the dark channel of a hazefree image, but significantly increases in that of a hazy image due to the existence of bright atmosphere light. Since the dehazing problem is inherently ambiguous, we first reformulate the degradation model of hazy images into an equivalent form where the transmission and the image variable are decoupled. With the above formulation and observation, we propose the convex model to recover the hazefree image whose dark channel is assumed to be sparse. The proposed objective function consists of four terms: a datafitting term, an l1 regularization term for the dark channel of the hazefree image, and two total variation regularization terms for both the hazefree image and the transmission map. We develop an efficient alternating direction method of multipliers (ADMM) to tackle the proposed convex model. Extensive experiments on real hazy images illustrate that our method outperforms the stateoftheart methods.