Retinex by Higher Order Total Variation L1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^{1}$$\end{document} Decomposition

In this paper, we propose a reflectance and illumination decomposition model for the Retinex problem via high-order total variation and L1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^{1}$$\end{document} decomposition. Based on the observation that illumination varies smoother than reflectance, we propose a convex variational model which can effectively decompose the gradient field of images into salient edges and relatively smoother illumination field through the first- and second-order total variation regularizations. The proposed model can be efficiently solved by a primal–dual splitting method. Numerical experiments on both grayscale and color images show the strength of the proposed model with applications to Retinex illusions, medical image bias field removal, and color image shadow correction.