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http://dx.doi.org/10.14317/jami.2017.399

PERFORMANCE OF Gℓ-PCG METHOD FOR IMAGE DENOISING PROBLEMS  

YUN, JAE HEON (Department of Mathematics, College of Natural Sciences, Chungbuk National University)
Publication Information
Journal of applied mathematics & informatics / v.35, no.3_4, 2017 , pp. 399-411 More about this Journal
Abstract
We first provide the linear operator equations corresponding to the Tikhonov regularization image denoising problems with different regularization terms, and then we propose how to choose Kronecker product preconditioners which are required for accelerating the $G{\ell}$-PCG method. Next, we provide how to apply the $G{\ell}$-PCG method with Kronecker product preconditioner to the linear operator equations. Lastly, we provide numerical experiments for image denoisng problems to evaluate the effectiveness of the $G{\ell}$-PCG with Kronecker product preconditioner.
Keywords
$G{\ell}$-PCG method; Tikhonov regularization; Image denoising; Kronecker product preconditioner; Linear operator equation;
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Times Cited By KSCI : 1  (Citation Analysis)
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1 P.C. Hansen, J.G. Nagy and D.P. O'Leary, Deblurring Images: Matrices, Spectra, and Filtering, SIAM, Philadelphia, 2006.
2 M.R. Hestense, E. Stiefel, Methods of conjugate gradients for solving linear systems, J. Res. Nat. Bur. Standards, 49 (1952), 409-436.   DOI
3 K. Jbilou, A. Messaoudi and H. Sadok, Global FOM and GMRES algorithms for matrix equations, Appl. Numer. Math. 31 (1999), 49-63.   DOI
4 E. Kreyszig, Introductory functional analysis with applications, John Wiley & Sons. Inc., New York, 1978.
5 A.J. Laub, Matrix Analysis for Scientists and Engineers, SIAM, Philadelphia, 2005.
6 S. Oh, S. Kwon and J.H. Yun, Image restoration by the global conjugate gradient least squares method, J. Appl. Math. & Informatics 31 (2013), 353-363.   DOI
7 D.K. Salkuyeh, CG-type algorithms to solve symmetrics matrix equations, Appl. Math. Comput. 172 (2006), 985-999.