General Choice of the Regularization Functional in Regularized Image Restoration

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196 Citations (Scopus)


The determination of the regularization parameter is an important issue in regularized image restoration, since it controls the trade-off between fidelity to the data and smoothness of the solution. A number of approaches have been developed in determining this parameter. In this paper, a new paradigm is adopted, according to which the required prior information is extracted from the available data at the previous iteration step, i.e., the partially restored image at each step. We propose the use of a regularization functional instead of a constant regularization parameter. The properties such a regularization functional should satisfy are investigated, and two specific forms of it are proposed. An iterative algorithm is proposed for obtaining a restored image. The regularization functional is defined in terms of the restored image at each iteration step, therefore allowing for the simultaneous determination of its value and the restoration of the degraded image. Both proposed iteration adaptive regularization functionals are shown to result in a smoothing functional with a global minimum, so that its iterative optimization does not depend on the initial conditions. The convergence of the algorithm is established and experimental results are shown.

Original languageEnglish
Pages (from-to)594-602
Number of pages9
JournalIEEE Transactions on Image Processing
Issue number5
Publication statusPublished - 1995 May

Bibliographical note

Funding Information:
Manuscript received August 18, 1993; revised April 5, 1994. This work was supported by a grant from the Space Telescope Science Institute, Baltimore, MD. The associate editor coordinating the review of this paper and approving it for publication was Prof. Xinhua Zhuang. M. G. Kang is with the Department of Elelctrical and Computer Engineering, University of Minnesota, Duluth, MN 55812 USA. A. K. Katsaggelos is with the Department of Electrical Engineering and Computer Science, McCormick School of Engineering and Applied Science, Northwestern University, Evanston, IL 60208-31 18 USA. IEEE Log Number 9410201.

All Science Journal Classification (ASJC) codes

  • Software
  • Computer Graphics and Computer-Aided Design


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