Yuji Koide

A unified theory of the family of projection filters for signal and image estimation

In an image restoration problem, there are many problems involved in accurate estimation of the original form from the restricted form. The family of projection filters, comprising the projection filter, the partial projection filter, and the averaged projection filter, has a good performance in such estimation problems. To construct these filters, we have to solve a system of operator equations. These operator equations have been solved in several ways and there were subtle differences between each expression of the form of solution. Besides, there were some properties already known for one filter, while not known for another filter. If we can discuss these three filters together, we can clarify unknown properties at the same time and give the unified form for each filter. One of authors has in fact had some success in this regard. However, the filter forms obtained there were more complicated than the original forms obtained respectively. To solve this problem, we propose another system of operator equations which can give almost the same form as the original and discuss the unified theory of the family of projection filter.