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

Published online by Cambridge University Press:  17 February 2009

A. Cherid ,
M. A. El-Gebeily ,
Donal O′Regan  and
Ravi Agarwal
A. Cherid
Affiliation:
department of Mathematical Sciences King Fahd University of Petroleum and Minerals, Dhahran 31261 KSA.
M. A. El-Gebeily
Affiliation:
department of Mathematical Sciences King Fahd University of Petroleum and Minerals, Dhahran 31261 KSA.
Donal O′Regan
Affiliation:
department of Mathematics National University of Ireland, Galway Ireland.
Ravi Agarwal
Affiliation:
department of Mathematical Sciences Florida Institute of Technology, 150 West University Blvd Melbourne FL 32901-6975 USA; email: agarwal@fit.edu.
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Abstract

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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.

Keywords

image deblurringimage restorationvariation minimizationnegative norms.
Type
Articles
Information
The ANZIAM Journal , Volume 49 , Issue 2 , October 2007 , pp. 171 - 185
Copyright
Copyright © Australian Mathematical Society 2007

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