ANZIAM J. 49 (2007), no. 2, pp. 171–185.

Deblurring and denoising of images with minimization of variation and negative norms

A. Cherid M. A. El-Gebeily
Department of Mathematical Sciences
King Fahd University of Petroleum and Minerals
Dhahran 31261
Department of Mathematical Sciences
King Fahd University of Petroleum and Minerals
Dhahran 31261
Donal O'Regan Ravi Agarwal
Department of Mathematics
National University of Ireland
Department of Mathematical Sciences
Florida Institute of Technology
150 West University Blvd
Melbourne FL 32901-6975
Received March 28, 2007; revised October 16, 2007


A method based on the minimization of variation is presented for the identification of a completely unknown blur operator. We assume the knowledge of a blurred image and its original version. The class of blurring operators is identified in the class of compact operators. A variational method with negative norms is then used for the restoration of a blurred and noised image. The restoration method works for a wide class of blurring operators and we do not assume that the blur operator commutes with the Laplacian.

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2000 Mathematics Subject Classification: primary 68U10; secondary 94A08
(Metadata: XML, RSS, BibTeX) MathSciNet: MR2376???
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