Modeling and extrapolation of prior scene information for set theoretic restoration and super-resolution of diffraction-limited images

We propose a novel image restoration and super-resolution algorithm based on a convex set theoretic approach. This procedure differs from the currently popular super-resolution algorithms, which typically are derived by employing statistical approaches, in offering a greater flexibility for incorporating scene-related prior information into the restoration processing. Novel methods for modeling and for extrapolation of scene information for efficient use in the restoration process are described. These include a border extraction method that permits a background-foreground separation of the image, a template-based information modeling and a method of extrapolating the image frequency content by a Taylor series expansion. A class of iterative projection algorithms for processing diffraction-limited images by using convex sets modeling various types of a priori information about the object or scene imaged is developed. The restoration and super-resolution performance of these algorithms are established through a variety of simulation experiments.