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 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 RGB/depth upsampling, on RGB/NIR image restoration, and in a comparison with related regularization by denoising approaches.

中文翻译：

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逆成像问题的自适应分位数稀疏图像 (AQuaSI) 先验

逆问题在许多经典的计算机视觉和图像处理任务中起着核心作用。许多逆问题是不适定的，因此需要先验对解空间进行正则化。然而，许多现有的先验，如总变异，都是基于临时假设，难以表示自然图像的实际分布。因此，图像处理研究的一个关键挑战是找到更合适的先验来表示自然图像。在本文中，我们先提出了自适应分位数稀疏图像 (AQuaSI)。它基于分位数滤波器，可用作引导数据的联合滤波器，并可轻松插入各种数值优化算法。我们证明了所提出的先验在联合 RGB/深度上采样中对 RGB/NIR 图像恢复的功效，