Retinex theory is introduced to show how the human visual system perceives the color and the illumination effect such as Retinex illusions, medical image intensity inhomogeneity and color shadow effect etc.. Many researchers have studied this ill-posed problem based on the framework of the variation energy functional for decades. However, to the best of our knowledge, the existing models via the sparsity of the image based on the nonconvex $ \ell^p $-quasinorm were limited. To deal with this problem, this paper considers a TV$ _p $-HOTV$ _q $-based retinex model with $ p, q\in(0, 1) $. Specially, the TV$ _p $ term based on the total variation(TV) regularization can describe the reflectance efficiently, which has the piecewise constant structure. The HOTV$ _q $ term based on the high order total variation(HOTV) regularization can penalize the smooth structure called the illumination. Since the proposed model is non-convex, non-smooth and non-Lipschitz, we employ the iteratively reweighed $ \ell_1 $ (IRL1) algorithm to solve it. We also discuss some properties of our proposed model and algorithm. Experimental experiments on the simulated and real images illustrate the effectiveness and the robustness of our proposed model both visually and quantitatively by compared with some related state-of-the-art variational models.

中文翻译：

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基于非凸TV型正则化的图像retinex

引入Retinex理论来说明人类视觉系统如何感知颜色和照明效果，例如Retinex幻觉，医学图像强度不均匀性和色影效果等。许多研究人员基于变化的框架研究了不适的问题。能源功能数十年。但是，据我们所知，基于非凸$ \ ell ^ p $ -quasinorm的图像稀疏性的现有模型是有限的。为了解决这个问题，本文考虑了基于TV $ _p $ -HOTV $ _q $的retinex模型，其中$ p，q \ in（0，1）$。特别地，基于总变化量（TV）正则化的TV $ _p $项可以有效地描述反射率，该反射率具有分段常数结构。基于高阶总变化量（HOTV）正则化的HOTV $ _q $项会惩罚称为照明的平滑结构。由于所提出的模型是非凸的，非平滑的和非Lipschitz的，因此我们使用迭代重新称重的\ \ ell_1 $（IRL1）算法来解决它。我们还讨论了我们提出的模型和算法的一些属性。通过与一些相关的最新变分模型进行比较，在模拟图像和真实图像上进行的实验实验从视觉和定量上说明了我们提出的模型的有效性和鲁棒性。