Adaptive image restoration with artifact suppression using the theory of convex projections

The authors develop an iterative, adaptive, space-variant restoration incorporating both regularization and artifact-suppression constraints. The algorithm is formulated using the method of projections onto convex sets (POCS). They introduce a closed-convex regularization constraint set called the partial Wiener solution set. Projection onto this set forces the solution to be equal to the Wiener solution over a predetermined set of frequencies that lie outside the neighborhoods of the zeros of the degradation transfer function. In the neighborhoods of the zeros, the Wiener solution contains significant errors that contribute to artifacts. Hence, in these neighborhoods the Wiener solution is discarded, and the missing frequency components are determined so that the entire solution is consistent with the artifact-suppression constraints and other a priori information. The proposed artifact-suppression constraints bound the norm of the variation of the image from its local mean using regionally adaptive bounds. The high quality of the resulting restorations is noteworthy