Regularized iterative image restoration with ringing reduction

Linear space-invariant image restoration algorithms often introduce ringing effects near sharp intensity transitions. It is shown that these artifacts are attributable to the regularization of the ill-posed image restoration problem. Two possible methods to reduce the ringing effects in restored images are proposed. The first method incorporates deterministic a priori knowledge about the original image into the restoration algorithm. The second method locally regulates the severity of the noise magnification and the ringing phenomenon, depending on the edge information in the image. A regularized iterative image restoration algorithm is proposed in which both ringing reduction methods are included by making use of the theory of the projections onto convex sets and the concept of norms in a weighted Hilbert space. Both the numerical performance and the visual evaluation of the results are improved by the use of ringing reduction.>