Optimum image restoration filters and generalized inverses of operators

✍ Scribed by Yukihiko Yamashita; Hidemitsu Ogawa

• Publisher: John Wiley and Sons
• Year: 1993
• Tongue: English
• Weight: 651 KB
• Volume: 24
• Category: Article
• ISSN: 0882-1666
• DOI: 10.1002/scj.4690240607

✦ Synopsis

Abstract

An optimal restoration filter is a restoration filter which meets some optimization criterion. It is known that a close relationship exists between optimal image restoration filters and generalized inverses of operators. By clarifying this relationship, the understanding of both optimal image restoration filters and generalized inverse is deepened.

This paper clarifies the following points concerning the aforementioned relationship. First, the projection filter and averaged projection filter satisfy an optimal criterion in some restricted subspace. Furthermore, it is shown that whether that optimal criterion is evaluated in the original image space or the observed image space, the same result is achieved. Finally, it is shown clearly how the Wiener filter behaves as a generalized inverse.