In this paper, we study the Papoulis-Gerchberg (PG) method and its applications to domains of image restoration such as super-resolution (SR) and inpainting. We show that the method performs well under certain conditions. We then suggest improvements to the method to achieve better SR and inpainting results. The modification applied to the SR process also allows us to apply the method to a larger class of images by doing away with some of the restrictions inherent in the classical PG method. We also present results to demonstrate the performance of the proposed techniques.