This article focuses on the complex version of the Bertozzi–Esedoglu–Gillete–Cahn–Hilliard equation for grayscale image inpainting as well as on the multicomponent Cahn–Hilliard systems for image inpainting. That is, the objective is to outline an extension approach for color image inpainting. We study into the well-posedness of the steady state problem associated with the complex Bertozzi–Esedoglu–Gillete–Cahn–Hilliard equation and with the Bertozzi–Esedoglu–Gillete–Cahn Hilliard systems. Then, backward Euler discretization in time is considered in both the models mentioned. We succeed in proving the stability of the backward Euler scheme. Finally, some numerical simulations are performed that confirm the theoretical results and show the efficiency of the scheme. The simulations are done using FreeFem++.