Regularized iterative image restoration in a weighted Hilbert space

A regularized iterative algorithm is described which solves the ill-posed image restoration problem in a numerically stable way by incorporating a priori knowledge about the original image. Three kinds of a priori knowledge are used: the first type imposes an upperbound on the residual signal, and the second type restricts the high-frequency content of the (restored) signal. We show that by the use of weighted norms in defining the above-mentioned types of a priori knowledge the algorithm concentrates on restoration in the vicinity of edges, and on noise suppression in flat regions. In this way the algorithm is capable of handling spatially varying image statistics in a pleasing manner for the human observer. The third kind of a priori knowledge is a deterministic constraint, representing a closed convex set in the solution space. The convergence and the limiting solution of the proposed algorithm are established. In order to show the significance of our approach we present some preliminary experimental results.