Total generalized variation-based Retinex image decomposition

Chunxue Wang, Huayan Zhang, Ligang Liu

Abstract: 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.