Prototype image constraints for set-theoretic image restoration

Constraints based on prototype images are developed and used in set-theoretic image restoration. A prototype can be obtained as a result of applying a predetermined operator to the observed image. In this case, the operator and the bound, which limits the variation of the restored image from the prototype, are the two defining quantities of a prototype constraint. General guidelines for rigorously estimating the defining bound of a prototype constraint under certain simplifying conditions are discussed. The authors provide two examples of prototype constraints where the prototypes are obtained by the Wiener filtering operator and a local averaging operator. The projection onto convex sets algorithm using the prototype constraints is applied to both monochrome and color images degraded by out-of-focus blur at different noise levels. The results show significant improvement over the Wiener restoration in reducing the restoration artifacts