Image restoration by a novel method of parallel projection onto constraint sets

Abstract

Image restoration from degraded observations and from properties that the image is supposed to satisfy has been approached by the method of projections onto convex constraint sets. Previous attempts have incorporated only partially the knowledge that we possess about the image to be restored because of difficulties in the implementation of some of the projections. In the parallel-projection algorithm presented here the a priori knowledge can be fully exploited. Moreover, the algorithm operates well even if the constraints are nonconvex and/or if the constraints have an empty intersection, without a limitation on the (finite) number of constraint sets.