Statistically optimal control of a blending - Type filter with its application to old film restoration

The blending-type filter, widely used for several image-processing tasks, is composed of multiple component filters, and it gives out a dividing value between the component filters´ outputs in a certain ratio, referred to as a blending coefficient, that can be defined as a function of some observable parameters measured for a given input image. The propriety of the blending-type filter depends on how to define the blending coefficient as a function of the observable parameters. So far, to define the blending-coefficient function, heuristic design methods such as a steepest descent method using a training sequence of data are often employed. On the contrary, we present a new well-grounded design method that optimizes the blending coefficient statistically as a function of the observable parameters by taking into account their statistics and the posterior probability model of the events for which the component filters are prepared. Our new design method provides the theoretical framework that nicely explains the propriety of the blending-type filter to the practical image-processing task. We apply our new design method to the statistically optimal control of the blending-type blotch repair filter for old film restoration.