《Chp1 Space-Variant Image Restoration with Running Sinusoidal Transforms》.pdf

1 Space-Variant Image Restoration with Running Sinusoidal Transforms Vitaly Kober Computer Science Department, CICESE, Mexico 1. Introduction Various restoration methods (linear, nonlinear, iterative, noniterative, deterministic, stochastic, etc.) optimized with respect to different criteria have been introduced (Bertero Boccacci, 1998; Biemond et al., 1990; Kundur, Hatzinakos, 1996; Banham Katsaggelos, 1997; Jain, 1989; Bovik, 2005; Gonzalez Woods, 2008). These techniques may be broadly divided in two classes: (i) fundamental algorithms and (ii) specialized algorithms. One of the most popular fundamental techniques is a linear minimum mean square error (LMMSE) method. It finds the linear estimate of the ideal image for which the mean square error between the estimate and the ideal image is minimum. The linear operator acting on the observed image to determine the estimate is obtained on the basis of a priori second-order statistical information about the image and noise processes. In the case of stationary processes and space-invariant blurs, the LMMSE estimator takes the form of the Wiener filter (Jain, 1989). The Kalman filter determines the causal LMMSE estimate recursively. Specialized algorithms can be viewed as extensions of the fundamental algorithms to specific restoration problems. It is based on a state-space rep