Image restoration by the family of signal adaptive parametric projection filters

Many of the image restoration techniques can roughly be classified into two types: those that are formulated as an optimization problem with regard to the restored image and those that are formulated as an optimization problem with regard to the restoration operator. The former has the advantage that the local information on the image can easily be expressed in the optimization reference. A problem is that the closeness of the image needs to be evaluated indirectly in the observation image space instead of the original image space. On the other hand, in the latter the closeness of the image can be evaluated in the original image space. However, because the optimization reference used to obtain the appropriate restoration operator does not include the information on the individual images, it is difficult to express the local information on the image, in contrast to the former type. Based on such a background, the objective of this paper is to propose a restoration method that can evaluate the closeness of images in the original image space while the local information on the images can be used systematically, based on improvement of the optimization reference of the parametric projection filter family belonging to the latter. The effectiveness of the proposed method is verified by numerical examples. (C) 2002 Wiley Periodicals, Inc.