Method of convex projections for image enhancement and restoration

The method of projections onto convex sets (POCS) is an interative method that finds a feasible solution consistent with a number of a priori constraints. POCS has found applications in numerous fields ranging from astronomy to neural networks. Here we focus on the application of POCS in image restoration and enhancement. In image restoration and enhancement problems, a priori constraints are defined on the basis of the measured data as well as on the degradation operator, the noise statistics, and the actual image distribution itself. For each constraint, a closed convex set is defined. An estimate of the actual image distribution is defined as a member of the intersection set and is determined by successively projecting an initial estimate onto the constraint sets. After a brief review of the fundamentals of POCS, we discuss the application of POCS to two problems: (i) restoration of images degraded by both blur and noise, and (ii) resolution enhancement of image sequences by reconstructing high-resolution still frames from a sequence of images at a lower spatial resolution.