Application of the UPRE method to optimal parameter selection for large scale regularization problems

Proceedings of the IEEE Southwest Symposium on Image Analysis and Interpretation

Volumn , Issue , 2008, Pages 89-92

  Lin, Youzuo ^a   Wohlberg, Brendt ^b  

^a ARIZONA STATE UNIVERSITY   (United States)

^b LOS ALAMOS NATIONAL LABORATORY   (United States)

Author keywords

Inverse problem; Large scale problem; Parameter selection; Tikhonov regularization; Total variation regularization

Indexed keywords

COMPUTATIONAL REQUIREMENTS; DEBLURRING; LARGE-SCALE PROBLEM; LINEAR PROBLEMS; OPTIMAL PARAMETER SELECTION; OPTIMAL REGULARIZATION; RECONSTRUCTED IMAGE; RISK ESTIMATORS; TIKHONOV REGULARIZATION; TOTAL VARIATION REGULARIZATION;

DIFFERENTIAL EQUATIONS; IMAGE ANALYSIS; OPTIMIZATION; RISK PERCEPTION;

INVERSE PROBLEMS;

EID: 67349245416     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/SSIAI.2008.4512292     Document Type: Conference Paper

References (14)

1. A. N. Tikhonov, "Regularization of incorrectly posed problems," Soviet Math. Dokl., vol. 4, pp. 1624-1627, 1963.
2. L. Rudin, S. Osher, and E. Fatemi, "Nonlinear total variation based noise removal algorithms," Physica D, 60, pp. 259-268, 1992.
3. V. A. Morozov, "Methods for solving incorrectly posed problems," Springer-Verlag, New York, 1984.
4. G. H. Golub, M. T. Heath, and G. Wahba, "Generalized cross-validation as a method for choosing a good ridge parameter," Technometrics, vol. 21, pp. 215-223, 1979.
5. G. Wahba, "Practical approximate solutions to linear operator equations when the data are noisy," SIAM J. Numer. Anal., vol. 14, pp. 651-667, 1977.
6. P. C. Hansen, "Rank-deficient and discrete ill-posed problems," SIAM, 1997.
7. P. C. Hansen and D. P. O'Leary, "The use of the L-curve in the regularization of discrete ill-posed problems," SIAM J. Sci. Comput., vol. 14, pp. 1487-1503, 1993.
8. p," Technometrics, vol. 15, no. 4, pp. 661-675, November 1973.
9. C. R. Vogel, Computational Methods for Inverse Problems. SIAM, 2002.
10. M. E. Kilmer and D. P. O'Leary, "Choosing regularization parametres in iterative methods for ill-posed problems," Journal on Matrix Analysis and Applications, vol. 22, no. 4, pp. 1204-1221, 2001. (Pubitemid 33341775)
11. L, procedures: Comments, new results, and application to image recovery problems," Computational Statistics, vol. 10, pp. 205-231, 1995.
12. G. H. Golub and U. von Matt, "Generalized cross-validation for large-scale problems," Journal of Computational and Graphical Statistics, vol. 6, pp. 1-34, 1997. (Pubitemid 127175935)
13. H. Guo, "Computing trace of function of matrix," Numerical Mathematics, vol. 2, pp. 204-215, 2000.
14. M. F. Hutchinson, "A stochastic estimator of the trace of the influence matrix for laplacian smoothing splines," Communications in Statistics, Simulation, and Computation, vol. 19, pp. 433-450, 1990.