Image retinex based on the nonconvex TV-type regularization

Abstract

<p style='text-indent:20px;'>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 <inline-formula><tex-math id="M1">\begin{document}$ \ell^p $\end{document}</tex-math></inline-formula>-quasinorm were limited. To deal with this problem, this paper considers a TV<inline-formula><tex-math id="M2">\begin{document}$ _p $\end{document}</tex-math></inline-formula>-HOTV<inline-formula><tex-math id="M3">\begin{document}$ _q $\end{document}</tex-math></inline-formula>-based retinex model with <inline-formula><tex-math id="M4">\begin{document}$ p, q\in(0, 1) $\end{document}</tex-math></inline-formula>. Specially, the TV<inline-formula><tex-math id="M5">\begin{document}$ _p $\end{document}</tex-math></inline-formula> term based on the total variation(TV) regularization can describe the reflectance efficiently, which has the piecewise constant structure. The HOTV<inline-formula><tex-math id="M6">\begin{document}$ _q $\end{document}</tex-math></inline-formula> term based on the high order total variation(HOTV) regularization can penalize the smooth structure called the illumination. Since the proposed model is non-convex, non-smooth and non-Lipschitz, we employ the iteratively reweighed <inline-formula><tex-math id="M7">\begin{document}$ \ell_1 $\end{document}</tex-math></inline-formula> (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.</p>