Image retinex based on the nonconvex TV-type regularization

<p style='text-indent:20px;'>Retinex theory is introduced to show how the human visual system perceives color and illumination effect such as Retinex illusions, medical image intensity inhomogeneity shadow etc.. Many researchers have studied this ill-posed problem based on framework of variation energy functional for decades. However, best our knowledge, existing models via sparsity nonconvex <inline-formula><tex-math id="M1">\begin{document}$ \ell^p $\end{document}</tex-math></inline-formula>-quasinorm were limited. To deal with problem, paper considers a TV<inline-formula><tex-math id="M2">\begin{document}$ _p $\end{document}</tex-math></inline-formula>-HOTV<inline-formula><tex-math id="M3">\begin{document}$ _q $\end{document}</tex-math></inline-formula>-based retinex model id="M4">\begin{document}$ p, q\in(0, 1) $\end{document}</tex-math></inline-formula>. Specially, id="M5">\begin{document}$ $\end{document}</tex-math></inline-formula> term total variation(TV) regularization can describe reflectance efficiently, which has piecewise constant structure. The HOTV<inline-formula><tex-math id="M6">\begin{document}$ high order variation(HOTV) penalize smooth structure called illumination. Since proposed non-convex, non-smooth non-Lipschitz, we employ iteratively reweighed id="M7">\begin{document}$ \ell_1 (IRL1) algorithm solve it. We also discuss some properties algorithm. Experimental experiments simulated real images illustrate effectiveness robustness both visually quantitatively by compared related state-of-the-art variational models.</p>