Remote sensing images are easily affected by noise in the process of acquisition and transmission. Based on the morphological component analysis (MCA) representation and the methods of inpainting to remote sensing images, the method of adaptive denoising on the basis of the MCA sparse decomposition and the method of denoising on the basis of image inpainting are both proposed. Compared with other classical denoising models, it is concluded that the former method can adaptivly remove the Gaussian white noise effectively, the latter method can adaptivly remove the salt and pepper noise of the gray or the colored remote sensing images effectively, especially can remove both salt noise and pepper noise at the same time. Both the subjective visual effects and the objective and quantitative evaluation of the methods are better than common models.