Modified special HSS method for discrete ill-posed problems and image restoration

References

• N. Aghazadeh, M. Bastani, and D.K. Salkuyeh, Generalized Hermitian and skew-Hermitian splitting iterative method for image restoration, Appl. Math. Model. 39 (2015), pp. 6126–6138. doi: 10.1016/j.apm.2015.01.042
   Web of Science ®Google Scholar
• H. Aminikhah and M. Yousefi, A special generalized HSS method for discrete ill-posed problems, Comput. Appl. Math. 37 (2018), pp. 1507–1523. doi: 10.1007/s40314-016-0408-7
   Google Scholar
• O. Axelsson, Z.Z. Bai, and S.X. Qiu, A class of nested iteration schemes for linear systems with a coefficient matrix with a dominant positive definite symmetric part, Numer. Algor. 35 (2004), pp. 351–372. doi: 10.1023/B:NUMA.0000021766.70028.66
   Web of Science ®Google Scholar
• Z.Z. Bai, G.H. Golub, and M.K. Ng, Hermitian and skew-Hermitian splittingmethods for non-Hermitian positive definite linear systems, SIAM J. Matrix Anal. Appl. 24 (2003), pp. 603–626. doi: 10.1137/S0895479801395458
   Web of Science ®Google Scholar
• Z.Z. Bai, G.H. Golub, and M.K. Ng, On successive-overrelaxation acceleration of the Hermitian and skew-Hermitian splitting iterations, Numer. Linear Algebra Appl. 14 (2007), pp. 319–335. doi: 10.1002/nla.517
   Web of Science ®Google Scholar
• M. Benzi, A generalization of the Hermitian and skew-Hermitian splitting iteration, SIAM J. Matrix Anal. Appl. 31 (2009), pp. 360–374. doi: 10.1137/080723181
   Web of Science ®Google Scholar
• G.H. Cheng, X. Rao, and X.G. Lv, The comparisons of two special Hermitian and skew-Hermitian splitting methods for image restoration, Appl. Math. Model. 39 (2015), pp. 1275–1280. doi: 10.1016/j.apm.2014.08.002
   Web of Science ®Google Scholar
• H.T. Fan, M. Bastani, and X.Y. Zhu, A class of upper and lower triangular splitting iteration methods for image restoration, Appl. Math. Model. 54 (2018), pp. 82–111. doi: 10.1016/j.apm.2017.09.033
   Web of Science ®Google Scholar
• G.H. Golub, M. Heath, and G. Wahba, Generalized cross-validation as a method for choosing a good ridge parameter, Technometrics 21 (1979), pp. 215–223. doi: 10.1080/00401706.1979.10489751
   Web of Science ®Google Scholar
• C.W. Groetsch, The Theory of Tikhonov Regularization for Fredholm Integral Equations of the First Kind, Pitman, Boston, 1984.
   Google Scholar
• X.X. Guo and S. Wang, Modified HSS iteration methods for a class of non-Hermitian positive-definite linear systems, Appl. Math. Comput. 218 (2012), pp. 10122–10128.
   Web of Science ®Google Scholar
• P.C. Hansen, Analysis of discrete ill-posed problems by means of the L-curve, SIAM Rev. 34 (1992), pp. 561–580. doi: 10.1137/1034115
   Web of Science ®Google Scholar
• P.C. Hansen, Regularization tools: A MATLAB package for analysis and solution of discrete ill-posed problems, Numer. Algor. 6 (1994), pp. 1–35. doi: 10.1007/BF02149761
   Google Scholar
• P.C. Hansen, Rank-deficient and Discrete Ill-posed Problems. Numerical Aspects of Linear Inversion, SIAM, Philadelphia, 1997.
   Google Scholar
• P.C. Hansen, J.G. Nagy, and D.P. OLeary, Deblurring Images: Matrices Spectra and Filtering, SIAM, Philadelphia, 2006.
   Google Scholar
• L. Li, T.Z. Huang, and X.P. Liu, Modified Hermitian and skew-Hermitian splitting methods for non-Hermitian positive-definite linear systems, Numer. Linear Algebra Appl. 14 (2007), pp. 217–235. doi: 10.1002/nla.528
   Web of Science ®Google Scholar
• X.G. Lv, T.Z. Huang, Z.B. Xu, and X.L. Zhao, A special Hermitian and skew-Hermitian splitting method for image restoration, Appl. Math. Model. 37 (2013), pp. 1069–1082. doi: 10.1016/j.apm.2012.03.019
   Web of Science ®Google Scholar
• V. Morozov, On the solution of functional equations by the method of regularization, Soviet Math. Dokl. 7 (1966), pp. 414–417.
   Google Scholar
• L. Perrone, Kronecker product approximations for image restoration with anti-reflective boundary conditions, Numer. Linear Algebra Appl. 13 (2006), pp. 1–22. doi: 10.1002/nla.458
   Web of Science ®Google Scholar
• D.L. Phillips, A technique for the numerical solution of certain integral equations of the first kind, J. Assoc. Comput. Mach. 9 (1962), pp. 84–97. doi: 10.1145/321105.321114
   Web of Science ®Google Scholar
• A.N. Tikhonov and V.Y. Arsenin, Solutions of Ill-posed Problems, Winston, Washington, DC, 1977.
   Google Scholar
• R.S. Varga, Matrix Iteration Analysis, 2nd ed., Springer, New York and London, 2000.
   Google Scholar