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Journal of Mathematics
Volume 2013 (2013), Article ID 274573, 11 pages
http://dx.doi.org/10.1155/2013/274573
Research Article

Restoring Poissonian Images by a Combined First-Order and Second-Order Variation Approach

1School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 610054, China
2School of Science, Huaihai Institute of Technology, Lianyungang, Jiangsu 222005, China

Received 6 December 2012; Accepted 27 January 2013

Academic Editor: Kaleem R. Kazmi

Copyright © 2013 Le Jiang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The restoration of blurred images corrupted by Poisson noise is an important topic in imaging science. The problem has recently received considerable attention in recent years. In this paper, we propose a combined first-order and second-order variation model to restore blurred images corrupted by Poisson noise. Our model can substantially reduce the staircase effect, while preserving edges in the restored images, since it combines advantages of the first-order and second-order total variation. We study the issues of existence and uniqueness of a minimizer for this variational model. Moreover, we employ a gradient descent method to solve the associated Euler-Lagrange equation. Numerical results demonstrate the validity and efficiency of the proposed method for Poisson noise removal problem.