{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,25]],"date-time":"2023-10-25T15:41:36Z","timestamp":1698248496682},"reference-count":17,"publisher":"Wiley","issue":"5","license":[{"start":{"date-parts":[[2007,3,21]],"date-time":"2007-03-21T00:00:00Z","timestamp":1174435200000},"content-version":"vor","delay-in-days":5192,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Systems &amp;amp; Computers in Japan"],"published-print":{"date-parts":[[1993,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>An optimum image restoration filter is defined by an objective function. Its objective function is given using a topology in a space. Therefore, when another topology in a space is used, a different restoration filter may be obtained.<\/jats:p><jats:p>In this paper the change of the topology in a space is restricted to a homeomorphic change of the inner product in a Hilbert space and the following two are discussed: (1) some optimum image restoration filters are independent of the inner product in a space; (2) When a Mahalanobis space is used, some of the optimum image restoration filters coincide with each other.<\/jats:p><jats:p>The former property can be used in practical situations as follows. The inner product in a space generally must be chosen to suit the problem at hand, but in many cases this is a very difficult task. However, if a restoration filter is independent of the inner product in a space, there is no need to search for such an optimal inner product. Therefore, such inner product independent filters are very useful in practice.<\/jats:p>","DOI":"10.1002\/scj.4690240505","type":"journal-article","created":{"date-parts":[[2007,7,8]],"date-time":"2007-07-08T00:45:31Z","timestamp":1183855531000},"page":"53-63","source":"Crossref","is-referenced-by-count":1,"title":["Optimum image restoration and topological invariance"],"prefix":"10.1002","volume":"24","author":[{"given":"Yukihiko","family":"Yamashita","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hidemitsu","family":"Ogawa","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2007,3,21]]},"reference":[{"key":"e_1_2_1_2_2","volume-title":"Digital Image Restoration","author":"Andrews H. 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(D)","volume":"74","author":"Yamashita Y.","year":"1991","journal-title":"I.E.I.C.E."},{"issue":"2","key":"e_1_2_1_14_2","first-page":"142","article-title":"Properties of averraged projection filter for image restoration. Trans. (D)","volume":"74","author":"Yamashita Y.","year":"1991","journal-title":"I.E.I.C.E."},{"issue":"6","key":"e_1_2_1_15_2","first-page":"593","article-title":"Image and signal restoration [III]\u2010Traditional optimum restoration filters","volume":"71","author":"Ogawa H.","year":"1988","journal-title":"Proc. I.E.I.C.E."},{"issue":"7","key":"e_1_2_1_16_2","first-page":"739","article-title":"Image and signal restoration [III]\u2014A family of projection filters for optimum restoration","volume":"71","author":"Ogawa H.","year":"1988","journal-title":"Proc. I.E.I.C.E."},{"issue":"7","key":"e_1_2_1_17_2","first-page":"739","article-title":"Image and signal restoration [IV]\u2010Nonlinear restoration","volume":"71","author":"Ogawa H.","year":"1988","journal-title":"Proc. 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