Browse > Article
http://dx.doi.org/10.14317/jami.2018.317

PARALLEL PERFORMANCE OF THE Gℓ-PCG METHOD FOR IMAGE DEBLURRING PROBLEMS  

YUN, JAE HEON (Department of Mathematics, College of Natural Sciences, Chungbuk National University)
Publication Information
Journal of applied mathematics & informatics / v.36, no.3_4, 2018 , pp. 317-330 More about this Journal
Abstract
We first provide how to apply the global preconditioned conjugate gradient ($G{\ell}-PCG$) method with Kronecker product preconditioners to image deblurring problems with nearly separable point spread functions. We next provide a coarse-grained parallel image deblurring algorithm using the $G{\ell}-PCG$. Lastly, we provide numerical experiments for image deblurring problems to evaluate the effectiveness of the $G{\ell}-PCG$ with Kronecker product preconditioner by comparing its performance with those of the $G{\ell}-CG$, CGLS and preconditioned CGLS (PCGLS) methods.
Keywords
Image deblurring; $G{\ell}-PCG$ method; Kronecker product preconditioner; Point spread function;
Citations & Related Records
연도 인용수 순위
  • Reference
1 A. Bjorck, Numerical methods for least squares problems, SIAM, Philadelphia, 1996.
2 M. Donatelli, D. Martin and L. Reichel, Arnoldi methods for image deblurring with antireflextive boundary conditions, Appl. Math. Comput. 253 (2015), 135-150.
3 R.W. Freund, G.H. Golub and N.M. Nachtigal, Iterative solutions of linear systems, Acta Numerica 1 (1991), 57-100.
4 M. Hankey and J.G. Nagy, Restoration of atmospherically blurred images by symmetric indefinite conjugate gradient, Inverse Problems 12 (1996), 157-173.   DOI
5 P.C. Hansen, J.G. Nagy and D.P. O'Leary, Deblurring Images: Matrices, Spectra, and Filtering, SIAM, Philadelphia, 2006.
6 M.R. Hestenes, E. Stiefel, Methods of conjugate gradients for solving linear systems, J. Res. Nat. Bur. Standards 49 (1952), 409-436.   DOI
7 E. Kreyszig, Introductory functional analysis with applications, John Wiley & Sons. Inc., New York, 1978.
8 J.G. Nagy, K.M. Palmer and L. Perrone, Iterative methods for image deblurring: A MAT-LAB object oriented approach, Numerical Algorithms 36 (2004), 73-93.   DOI
9 J. Kamn and J.G. Nagy, Optimal kronecker product approximation of block Toeplitz matrices, SIAM J. Matrix Anal. Appl. 22 (2000), 155-172.   DOI
10 J.G. Nagy, M.N. Ng and L. Perrone, Kronecker product approximations for image restoration with reflexive boundary conditions, SIAM J. Matrix Anal. Appl. 25 (2004), 829-841.
11 C.C. Paige and M.A. Saunders, LSQR. An algorithm for sparse linear equations and sparse least squares, ACM Trans. Math. Software 8 (1982), 43-71.   DOI
12 Y. Saad, Iterative methods for sparse linear systems, PWS Publishing Company, Boston, 1996.
13 D.K. Salkuyeh, CG-type algorithms to solve symmetrics matrix equations, Appl. Math. Comput. 172 (2006), 985-999.