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Abstract and Applied Analysis
Volume 2013, Article ID 129652, 9 pages
Research Article

Two New Efficient Iterative Regularization Methods for Image Restoration Problems

School of Mathematical Sciences/Institute of Computational Science, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, China

Received 4 March 2013; Revised 2 June 2013; Accepted 10 June 2013

Academic Editor: Marco Donatelli

Copyright © 2013 Chao Zhao 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.


Iterative regularization methods are efficient regularization tools for image restoration problems. The IDR() and LSMR methods are state-of-the-arts iterative methods for solving large linear systems. Recently, they have attracted considerable attention. Little is known of them as iterative regularization methods for image restoration. In this paper, we study the regularization properties of the IDR() and LSMR methods for image restoration problems. Comparative numerical experiments show that IDR() can give a satisfactory solution with much less computational cost in some situations than the classic method LSQR when the discrepancy principle is used as a stopping criterion. Compared to LSQR, LSMR usually produces a more accurate solution by using the -curve method to choose the regularization parameter.