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High‐resolution image reconstruction with displacement errors: A framelet approach
Author(s) -
Chan Raymond H.,
Riemenschneider Sherman D.,
Shen Lixin,
Shen Zuowei
Publication year - 2004
Publication title -
international journal of imaging systems and technology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.359
H-Index - 47
eISSN - 1098-1098
pISSN - 0899-9457
DOI - 10.1002/ima.20012
Subject(s) - computer science , displacement (psychology) , artificial intelligence , image (mathematics) , resolution (logic) , computer vision , psychology , psychotherapist
Abstract High‐resolution image reconstruction arises in many applications, such as remote sensing, surveillance, and medical imaging. The Bose and Boo (1998) model can be viewed as the passage of the high‐resolution image through a blurring kernel built from the tensor product of a univariate low‐pass filter of the form [½ + ϵ, 1, …, 1, ½ − ϵ], where ϵ is the displacement error. When the number L of low‐resolution sensors is even, tight‐frame symmetric framlet filters were constructed (Chan et al., 2004b) from this low‐pass filter using Ron and Shen's (1997) unitary extension principle. The framelet filters do not depend on ϵ, and hence the resulting algorithm reduces to that of the case where ϵ = 0. Furthermore, the framelet method works for symmetric boundary conditions. This greatly simplifies the algorithm. However, both the design of the tight framelets and extension to symmetric boundary are only for even L and cannot, be applied to the case when L is odd. In this article, we design tight framelets and derive a tight‐framelet algorithm with symmetric boundary conditions that work for both odd and even L . An analysis of the convergence of the algorithms is also given. The details of the implementations of the algorithm are also given. © 2004 Wiley Periodicals, Inc. Int J Imaging Syst Technol 14, 91–104, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ima.20012