Optimum Image restoration and generalized Inverses of operators

Abstract

optimum image restoration filter is a filter which minimizes or maximizes some objective function. There are close relations between those optimum image restoration filters and generalized inverses of operators. These relations help us to understand optimum restoration filters and generalized inverses of operators. This paper clarifies t hat optimum filters such as the projection filter and the averaged Projection filter become generalized inverses of the degraded operator under some restrictions. It is slso shown that the wiener filter behaves like a generalize inverse to some specific set of images, In order to discuss above problems, we introduce the notion of Pseudo-projection operators which minimize mean square error.