We present a study of some image resoration techniques based on partial differential equations. We study separately the denoising problem and the restoration of discontinuities. We analyze the capabilities of the differential operators to restore images. In particular, we analyze a number of models present in the literature, and we present comparative results. Finally, we present a model based in the combination of the anisotropic diffusion of Alvarez, Lions, and Morel and the shock filters of Osher and Rudin.