Projected Barzilai-Borwein method for large-scale nonnegative image restoration

Inverse Problems in Science and Engineering

Volumn 15, Issue 6, 2007, Pages 559-583

  Wang, Yanfei ^a   Ma, Shiqian ^b  

^a INSTITUTE OF GEOLOGY AND GEOPHYSICS   (China)

^b CHINESE ACADEMY OF SCIENCES   (China)

Author keywords

65F22; 65J10; 65K10

Indexed keywords

AEROSOLS; CCD CAMERAS; OPTIMIZATION; PARAMETERIZATION; PROBLEM SOLVING; QUADRATIC PROGRAMMING;

NONNEGATIVE CONSTRAINTS; PROJECTED BARZILAI BORWEIN (PBB) METHOD; UNCONSTRAINED OPTIMIZATION PROBLEMS;

IMAGE RECONSTRUCTION;

EID: 34548368566     PISSN: 17415977     EISSN: 17415985     Source Type: Journal    
DOI: 10.1080/17415970600881897     Document Type: Article

References (32)

1. Bardsley, J. and Vogel, C.R., 2003, A nonnegatively constrained convex programming method for image reconstruction. SIAM Journal on Scientific Computing, 25, 1326-1343.
2. Barzilai, J. and Borwein, J., 1988, Two-point step size gradient methods. IMA Journal of Numerical Analysis, 8, 141-148.
3. Bertero, M. and Boccacci, P., 1998, Introduction to Inverse Problems in Imaging (Philadelphia: Institute of Physics Publishing).
4. Dai, Y.H. and Fletcher, R., 2003, Projected Barzilai-Borwein methods for large-scale box-constrained quadratic programming, University of Dundee Report NA/215.
5. Eicke B., 1992, Iteration methods for convexly constrained ill-posed problems in Hilbert space. Numerical Functional Analysis Optimization, 13, 413-429.
6. Fletcher, R., 1987, Practical Methods of Optimization 2nd Edn (Chichester: John Wiley and Sons).
7. Gonzalez, R.C. and Woods, R.E., 2002, Digital Image Processing, 2nd Edn (Beijing: Publishing Hourse of Electronics Industry).
8. Hanke, M., Nagy, J. and Vogel, C.R., 2000, Quasi-Newton approach to nonnegative image restorations. Linear Algebra and its Applications, 316, 223-236.
9. Hanke, M. and Nagy, J., 1996, Restoration of atmospherically blurred images by symmetric indefinite conjugate gradient techniques. Inverse Problems, 12, 157-173.
10. Hansen, P.C., 1998, Rank-deficient and Discrete Ill-posed Problems: Numerical Aspects of Linear Inversion (Philadelphia: SIAM).
11. Koptelova, E., Shimanovskaya, E., Artamonov, B., Sazhin, M., Yagola, A., Bruevich, V. and Burkhonov, O., 2005, Image reconstruction technique and optical monitoring of the QSO2237+0305 from Maidanak Observatory in 2002-2003, Monthly Notices of Royal Astronomical Society, 356, 323-330.
12. Lee, K.P. and Nagy, J.G., 2003, Steepest descent, CG and iterative regularization of ill-posed problems. BIT, 43, 1003-1017.
13. Moré, J. and Toraldo, G., 1991, On the solution of large quadratic programming problems with bound constraints, SIAM Journal of Optimization, 1, 93-113.
14. Nagy, J. and Strakos, Z., 2000, Enforcing nonnegativity in image reconstruction algorithms, In: David C Wilson, et al (Eds) Mathmatical Modeling, Estimation, and Imaging, Vol. 4121, pp. 182-190.
15. Nagy, J. and Perrone, L., 2004, Kronecker products in image restoration, In: Franklin T. Luk (Ed.) Advanced Signal Processing Algorithms, Architectures, and Implementations VIII, Vol. 5205, pp. 369-379.
16. Nashed, M.Z., 1970, Steepest descent for singular linear operator equations. SIAM Journal on Numerical Analysis, 7, 358-362.
17. Raydan, M., 1993, On the Barzilai and Borwein choice of steplength for the gradient method. IMA Journal of Numerical Analysis, 13, 321-326.
18. Rojas, M. and Steihaug, T., 2002, An Interior-Point Trust-Region-Based Method for Large-Scale Nonnegative Regularization, CERFACS Technical Report TR/PA/01/11, July 6 2001, Revised June 3, 2002.
19. Rudin, L., Osher, S. and Fatemi, E., 1992, Nonlinear total variation based noise removal algorithms. Physica D, 60, 259-268.
20. Tikhonov, A.N., Arsenin, V. Y., 1977, Solutions of Ill-posed Problems (New York: John Wiley and Sons).
21. Tikhonov, A.N., Goncharsky, A.V., Stepanov, V.V., and Yagola, A.G., 1995, Numerical Methods for the Solution of Ill-posed Problems (Dordrecht: Kluwer Academic Publishers).
22. Barrett, R., Berry, M., Chan, T.F., Demmel, J., Donato, J., Dongarra, J., Eijkhout, V., Pozo, R., Romine, C., and Van der Vorst, H., 1994 Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods (Philadelphia: SIAM).
23. Toint, Ph. L., 1997, A non-monotone trust region algorithm for nonlinear optimzation subject to convex constraints, Mathematical Programming, 77, 69-94.
24. Vogel, C.R. and Oman, M.E., 1998, A fast, robust algorithm for total variation based reconstruction of noisy, blurred images, IEEE Transactions On Image Processing, 7, 813-824.
25. Vogel, C.R., 2002, Computational Methods for Inverse Problems (Philadelphia: SIAM).
26. Wang, Y.F., Yuan, Y.X. and Zhang, H.C., 2002, A trust region-CG algorithm for deblurring problem in atmospheric image reconstruction, Science in China A, 45, 731-740.
27. Wang, Y. F., 2003, On the regularity of trust region-CG algorithm: with application to deconvolution problem, Science in China A, 46, 312-325.
28. Wang, Y.W., Wang, Y.F., Xue, Y. and Gao, W., 2004, A new algorithm for remotely sensed image texture classification and segmentation, International Journal of Remote Sensing, 25, 4043-4050.
29. Wen, Z.W. and Wang, Y.F., 2004, A trust region method for large scale inverse problems in atmospheric image restoration. In: Y. Yuan (Ed.) Numerical Linear Algebra and Optimization (Beijing/New York: Science Press), pp. 275-287.
30. Wen, Z.W. and Wang, Y.F., 2005, A new trust region algorithm for image restoration, Science in China A, 48, 169-184.
31. Xiao, T.Y., Yu, Y.S. and Wang, Y.F., 2003, Numerical Methods for Inverse Problems (Beijing: Science Press).
32. Yuan, Y.X., 1993, Numerical Methods for Nonliear Programming (Shanghai: Shanghai Science and Technology Publication).