Block Coordinate Relaxation Methods for Nonparametric Wavelet Denoising

Journal of Computational and Graphical Statistics

Volumn 9, Issue 2, 2000, Pages 361-379

  Sardy, Sylvain ^a   Bruce, Andrew G ^b   Tseng, Paul ^c  

^a EPFL   (Switzerland)

^b Parametric Technology Corporation   (United States)

^c UNIVERSITY OF WASHINGTON   (United States)

Author keywords

Basis pursuit; Block coordinate relaxation; Function estimation; Interior point; Optimization

Indexed keywords

EID: 23044521122     PISSN: 10618600     EISSN: 15372715     Source Type: Journal    
DOI: 10.1080/10618600.2000.10474885     Document Type: Article

References (25)

1. Alliney, S., and Ruzinsky, S. A. (1994), “An Algorithm for the Minimization of Mixed l\ and 1.2 Norms with Application to Bayesian Estimation,” IEEE Transactions on Signal Processing, 42, 618-627.
2. Bishop, Y. M. M., Fienberg, S. E., and Holland, P. W. (1975), Discrete Multivariate Analysis: Theory and Practice, Cambridge, MA: MIT Press.
3. Bruce, A. G., and Gao, H.-Y. (1994), S+ WAVELETS User’s Manual, Seattle, WA: StatSci (Division of Math-Soft, Inc., 1700 Westlake Ave. N, 98109-9891).
4. Chen, S., Donoho, D., and Saunders, M. (1999), “Atomic Decomposition by Basis Pursuit,” SIAM Journal on Scientific Computing, 20, 33-61.
5. Clarke, F. (1990), Optimization and Nonsmooth Analysis, Philadelphia: Society for Industrial and Applied Mathematics.
6. Coifman, R. R., and Donoho, D. L. (1995), “Time-Invariant Wavelet Denoising,” in Wavelets and Statistics, Lecture Notes in Statistics (vol. 103), Berlin/New York: Springer-Verlag, pp. 125-150.
7. Coifman, R., and Wickerhauser, V. (1992), “Entropy-Based Algorithms for Best Basis Selection,” IEEE Transactions on Information Theory, 38, 713-718.
8. Daubechies, I. (1992), Ten Lectures on Wavelets, Philadelphia: Society for Industrial and Applied Mathematics.
9. Donoho, D. L., and Johnstone, I. M. (1994), “Ideal Spatial Adaptation via Wavelet Shrinkage,” Biometrika, 81, 425-455.
10. Fu, W. (1998), “Penalized Regression: The Bridge Versus the Lasso,” Journal of Computational and Graphical Statistics, 7, 397-416.
11. Golub, G. H., and Van Loan, C. F. (1989), Matrix Computations, Baltimore, MD: Johns Hopkins University Press.
12. Hastie, T., and Tibshirani, R. (1990), Generalized Additive Models, London: Chapman and Hall.
13. Herman, G. T. (1980), Image Reconstruction from Projections: The Fundamentals of Computerized Tomography, New York: Academic Press.
14. Kojima, M., Megiddo, N., and Mizuno, S. (1993), “A Primal-Dual Exterior Point Algorithm for Linear Programming,” Mathematical Programming, 61, 261-280.
15. Lina, J.-M., and Mayrand, M. (1995), “Complex Daubechies Wavelets,” Applied and Computational Harmonic Analysis, 2, 219-229.
16. Mann, S., and Haykin, S. (1992), “Adaptive ‘Chirplet’ Transform and Adaptive Generalization of the Wavelet Transform,” Optical Engineering, 31, 1243-1256.
17. Meyer, F. G., and Coifman, R. (1997), “Brushlets: A Tool for Directional Image Analysis and Image Compression,” in Applied and Computational Harmonic Analysis (vol. 4), New York: Academic Press, pp. 147-187.
18. Nason, G. P. (1995), “Wavelet Function Estimation Using Cross-Validation,” in Wavelets and Statistics, eds. A. Antoniadis, and G. Oppenheim, New York: Springer-Verlag, pp. 261-280.
19. Nesterov, Y., and Todd, M. (1997), “Self-Scaled Barriers and Interior-Point Methods for Convex Programming,” Mathematics of Operations Research, 22, 1-42.
20. Osborne, M. (1995), Finite Algorithms in Optimization and Data Analysis, Chichester: Wiley.
21. Osbome, M., Presnell, B., and Turlach, B. (1998), “Knot Selection for Regression Splines via the Lasso,” in Dimension Reduction, Computational Complexity, and Information, ed. S. Weisberg, Vol. 30 of Computing Science and Statistics, Fairfax Station, VA: Interface Foundation of North America, Inc., pp. 44-49.
22. Sardy, S. (2000), “Minimax Threshold for Denoising Complex Signals with WaveShrink,” IEEE Transactions on Signal Processing, 48, 1023-1028.
23. Shiskin, J., Young, A. H., and Musgrave, J. C. (1967), “The X-ll Variant of the Census Method 11 Seasonal Adjustment Program,” Technical Paper 15, U.S. Bureau of the Census, Washington, DC: U.S. Government Printing Office.
24. Tibshirani, R. (1996), “Regression Shrinkage and Selection via the Lasso,” Journal of the Royal Statistical Society, Series B, 58, 267-288.
25. Tseng, P. (1993), “Dual Coordinate Ascent Methods for Non-Strictly Convex Minimization,” Mathematical Programming, 59, 231-247.