A trust region-CG algorithm for deblurring problem in atmospheric image reconstruction

Science in China, Series A: Mathematics, Physics, Astronomy

Volumn 45, Issue 6, 2002, Pages 731-740

  Wang, Yanfei ^a   Yuan, Yaxiang ^a   Zhang, Hongchao ^a  

^a INSTITUTE OF COMPUTATIONAL MATHEMATICS AND SCIENTIFIC ENGINEERING COMPUTING   (China)

Author keywords

Ill posed problems; Image reconstruction; Truncated CG; Trust region

Indexed keywords

EID: 0345795720     PISSN: 10069283     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (20)

1. Roggemann, M., Welsh, B., Imaging Through Turbulence, Boca Raton: CRC Press, 1996.
2. Vogel, C. R., Oman, M. E. et al., Fast, robust total variation-based reconstruction of noisy, blurred images, IEEE Transactions on Image Processing, 1998, 7: 813-824.
3. Michael, K. N. Plemmons, R. J., Qiao San-zheng et al., Regularized blind deconvolution using recursive inverse filtering, in Proc. HK97 Conference on Scientific Computation (eds. Golub, G., Liu, S., Luk, F. et al.), Berlin: Springer-Verlag, 1997.
4. Hanke, M., Iterative regularization techniques in image reconstruction, in Proceedings of the Conference Mathematical Methods in Inverse Problems for Partial Differential Equations, Mt. Holyoke: Springer-Verlag, 1998.
5. Tikhonov, A. N., Arsenin, V. Y. et al., Solutions of Ill-posed Problems, New York: Wiley, 1977.
6. Engl, H. W., Neubauer, H. M. et al., Regularization of Inverse Problems, Dordrecht: Kluwer, 1996.
7. Fletcher, R., Practical Methods of Optimization, 2nd ed. Chichester: John Wiley and Sons, 1987.
8. Fletcher, R., A model algorithm for composite NDO problem, Math. Prog. Study, 1982, 17: 67-76.
9. Moré, J. J., Recent developments in algorithms and software for trust region methods, Mathematical Programming: The State of the Art (eds. Bachem, A., Grötschel, K. B.), Berlin: Springer-Verlag, 1983: 258-287.
10. Powell, M. J. D., Nonconvex minimization calculations and the conjugate gradient method, in Lecture Notes in Mathematics 1066: Numerical Analysis, Berlin: Springer-Verlag, 1984, 122-141.
11. Powell, M. J. D., Convergence properties of a class of minimization algorithms, in Nonlinear Programming, New York: Academic Press, 1975, 2: 1-27.
12. Duff, I. S., Nocedal, J., Reid, J. K. et al., The use of linear programming for the solution of sparse sets of nonlinear equations, SIAM J. Sci. Stat. Comput., 1987, 8: 99-108.
13. Sorensen, D. C., Newton's method with a model trust region modification, SIAM J. Numer. Anal., 1982, 19: 409-426.
14. Moré, J. J., Sorensen, D. C. et al., Computing a trust region step, SIAM J. Sci. Stat. Comput., 1983, 4: 553-572.
15. Gay, D. M., Computing optimal local constrained step, SIAM J. Sci. Stat. Comp., 1981, 2: 186-197.
16. Toint, P. L., Towards an efficient sparsity exploiting Newton method for minimization, in Sparse Matrices and Their Uses (ed. Duff, I.), Berlin: Academic Press, 1981, 57-88.
17. Steihaug, T., The conjugate gradient method and trust regions in large scale optimization, SIAM J. Numer. Anal., 1983, 20: 626-637.
18. Yuan, Y., On the truncated conjugate gradient method, Math. Prog., 2000, 87: 561-571.
19. Vogel, C. R., A limited memory BFGS method for an inverse problem in atmospheric imaging, in Lecture Notes in Earth Sciences: Methods and Applications of Inversion (eds. Hansen, P. C., Jacobsen, B. H., Mosegaard, K.), Berlin: Springer-Verlag, 2000, 92: 292-304.
20. Vogel, C. R., Computational Methods for Inverse Problems, Frontiers in Applied Mathematics, Philadelphia: SIAM, 2002, in press.