Human visual system (HVS) can perceive color under varying illumination conditions, and Retinex theory is precisely aimed to simulate and explain how the HVS perceives reflectance regardless of different illumination conditions. In this paper, we introduce a reflectance and illumination decomposition model for the Retinex problem via total generalized variation regularization and $$H^{1}$$ H 1 decomposition. The total generalized variation regularization ameliorates the staircasing artifacts that appear in the reflectance component of existing total variation-based models and $$H^{1}$$ H 1 norm guarantees smoother illumination. We analyze the existence and uniqueness of the proposed model and employ an alternating minimization scheme based on split Bregman iteration. We present numerous numerical experiments on both grayscale and color images to make comparisons with several state-of-the-art methods and demonstrate that our method is comparable both quantitatively and qualitatively.

中文翻译：

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基于总广义变异的 Retinex 图像分解

人类视觉系统 (HVS) 可以在不同光照条件下感知颜色，而 Retinex 理论正是旨在模拟和解释 HVS 如何在不同光照条件下感知反射率。在本文中，我们通过总广义变异正则化和 $$H^{1}$$ H 1 分解为 Retinex 问题引入了反射和光照分解模型。总广义变异正则化改善了现有基于总变异的模型的反射分量中出现的阶梯伪影，并且 $$H^{1}$$ H 1 范数保证了更平滑的照明。我们分析了所提出模型的存在性和唯一性，并采用了基于分裂 Bregman 迭代的交替最小化方案。