Deterministic/stochastic wavelet decomposition for recovery of signal from noisy data

Technometrics

Volumn 42, Issue 3, 2000, Pages 262-276

  Huang, H C ^a   Cressie, N ^b  

^a INSTITUTE OF STATISTICAL SCIENCE   (Taiwan)

^b OHIO STATE UNIVERSITY   (United States)

Author keywords

EM algorithm; Empirical Bayes; Image denoising; Multiscale graphical model; Nonparametric regression; Normal probability plot

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; DIGITAL SIGNAL PROCESSING; GRAPHIC METHODS; NORMAL DISTRIBUTION; RANDOM PROCESSES; REGRESSION ANALYSIS; SPURIOUS SIGNAL NOISE;

DETERMINISTIC WAVELET DECOMPOSITION; EMPIRICAL BAYES; EXPECTATION-MAXIMIZATION (EM) ALGORITHMS; IMAGE DENOISING; NONPARAMETRIC REGRESSION; SIGNAL RECOVERY; STOCHASTIC WAVELET DECOMPOSITION;

WAVELET TRANSFORMS;

EID: 0034247954     PISSN: 00401706     EISSN: 15372723     Source Type: Journal    
DOI: 10.1080/00401706.2000.10486047     Document Type: Article

References (42)

1. Abramovich, F., and Benjamini, Y. (1995), “Thresholding of Wavelet Coefficients as Multiple Flypotheses Testing Procedure,” in Wavelets and Statistics (Lecture Notes in Statistics, 103), eds. A. Antoniadis and G. Oppenheim, New York: Springer-Verlag, pp. 5-14.
2. Abramovich, F., and Benjamini, Y. (1996), “Adaptive Thresholding of Wavelet Coefficients,” Computational Statistics and Data Analysis, 22, 351-361.
3. Abramovich, F., Sapatinas, F., and Silverman, B. W. (1998), “Wavelet Thresholding via a Bayesian Approach,” Journal of the Royal Statistical Society, Ser. B, 60, 725-749.
4. Alsberg, B. K., Woodward, A. M., and Kell, D. B. (1997), “An Introduction to Wavelet Transforms for Chemometricians: A Time-Frequency Approach,” Chemometrics and Intelligent Laboratory Systems, 37, 215- 239.
5. Box, G. E. P., and Jenkins, G. M. (1970), Time Series Analysis: Forecasting and Control, San Francisco: Holden-Day.
6. Boyles, R. A. (1983), “On the Convergence of the EM Algorithm,” Journal of the Royal Statistical Society, Ser. B, 45, 47-50.
7. Bruce, A., and Gao, H.-Y. (1994), S+ Wavelets User’s Manual, Seattle: StatSci.
8. Chipman, H. A., Kolaczyk, E. D., and McCulloch, R. E. (1997), “Adaptive Bayesian Wavelet Shrinkage,” Journal of the American Statistical Association, 92, 1413-1421.
9. Chou, K. C., Willsky, A. S., and Nikoukhah, R. (1994), “Multiscale Systems, Kalman Filters, and Riccati Equations,” IEEE Transactions on Automatic Control, 39, 479-492.
10. Chui, C. K. (1992), An Introduction to Wavelets, New York: Academic Press.
11. Clyde, M., Parmigiani, G., and Vidakovic, B. (1996), “Bayesian Strategies for Wavelet Analysis,” Statistical Computing and Statistical Graphics Newsletter, 1, 3-9.
12. Clyde, M., Parmigiani, G., and Vidakovic, B. (1998), “Multiple Shrinkage and Subset Selection in Wavelets,” Biometrika, 85, 391-401.
13. Cohen, A., Daubechies, I., and Vial, P. (1993), “Wavelets on the Interval and Fast Wavelet Transforms,” Applied and Computational Harmonic Analysis, 1, 54-81.
14. Cressie, N. (1993), Statistics for Spatial Data (rev. ed.), New York: Wiley
15. Crouse, M., Nowak, R., and Baraniuk, R. (1998), “Wavelet-based Statistical Signal Processing Using Hidden Markov Models,” IEEE Transactions on Signal Processing, 46, 886-902.
16. Daubechies, I. (1992), Ten Lectures on Wavelets, Philadelphia: Society foi Industrial and Applied Mathematics.
17. Dempster, A. P., Laird, N. M., and Rubin, D. B. (1977), “Maximum Likelihood From Incomplete Data via the EM Algorithm,” Journal of the Royal Statistical Society, Ser. B, 39, 1-38.
18. Donoho, D. L., and Johnstone, I. M. (1994), “Ideal Spatial Adaptation by Wavelet Shrinkage,” Biometrika, 81, 425-455.
19. Donoho, D. L., and Johnstone, I. M. (1995), “Adapting to Unknown Smoothness via Wavelet Shrinkage,” Journal of the American Statistical Association, 90, 1200-1224.
20. Donoho, D. L., and Johnstone, I. M. (1998), “Minimax Estimation via Wavelet Shrinkage,” The Annah of Statistics, 26, 879-921.
21. Donoho, D. L., Johnstone, I. M., Kerkyacharian, G., and Picard, D. (1995) “Wavelet Shrinkage: Asymptopia?” (with discussion), Journal of the Royal Statistical Society, Ser. B, 57, 301-369.
22. George, E. I., and McCulloch, R. (1993), “Variable Selection via Gibbs Sampling,” Journal of the American Statistical Association, 88, 881.
23. George, E. I., and McCulloch, R. (1997), “Approaches to Bayesian Variable Selection,” Statistica Sinica, 1, 339-373.
24. Gong, G., and Samaniego, F. J. (1981), “Pseudo Maximum Likelihood Estimation: Theory and Applications,” The Annals of Statistics, 9, 861-869.
25. Hall, P., and Patil, P. (1996), “Effect of Threshold Rules on Performance of Wavelet-Based Curve Estimators,” Statistica Sinica, 6, 331-345.
26. Harvey, A. C. (1989), Forecasting, Structural Time Series Models and the Kalman Filter, Cambridge, U.K.: Cambridge University Press.
27. Huang, H.-C., and Cressie, N. (1997), “Multiscale Spatial Modeling,” in Proceedings of the Section on Statistics and the Environment, American Statistical Association, pp. 49-54.
28. Jawerth, B., and Sweldens, W. (1994), “An Overview of Wavelet Based Multiresolution Analysis,” SIAM Review, 36, 3774-12.
29. Johnstone, I. M., and Silverman, B. W. (1997), “Wavelet Threshold Estimators for Data With Correlated Noise,” Journal of the Royal Statistical Society, Ser. B, 59, 319-351.
30. Lu, H. H.-C., Huang, S.-Y., and Tung, Y.-C. (1997), “Wavelet Shrinkage for Nonparametric Mixed-Effects Models,” technical report, National Chiao-Tung University, Institute of Statistics.
31. Mallat, S. (1989), “A Theory for Multiresolution Signal Decomposition: The Wavelet Representation,” IEEE Transactions on Pattern Analysis and Machine Intelligence, 11, 674-693.
32. Meyer, Y. (1992), Wavelets and Operators, Cambridge, U.K.: Cambridge University Press.
33. Meyer, Y. (1993), Wavelets: Algorithms and Applications, Philadelphia: Society for Industrial and Applied Mathematics.
34. Nason, G. P. (1995), “Choice of the Threshold Parameter in Wavelet Function Estimation,” in Wavelets and Statistics (Lecture Notes in Statistics 103), eds. A. Antoniadis and G. Oppenheim, New York: Springer-Verlag, pp. 261-279.
35. Nason, G. P. (1996), “Wavelet Shrinkage Using Cross-validation,” Journal of the Royal Statistical Society, Ser. B, 58, 463-479.
36. Ogden, R. T. (1997), Essential Wavelets for Statistical Applications and Data Analysis, Boston: Birkhauser.
37. Ogden, R. T., and Parzen, E. (1996a), “Change-point Approach to Data Analytic Wavelet Thresholding,” Statistics and Computing, 6, 93-99.
38. Ogden, R. T., and Parzen, E. (1996b), “Data Dependent Wavelet Thresholding in Nonparametric Regression With Change-point Applications,” Computational Statistics and Data Analysis, 22, 53-70.
39. Ruggeri, F., and Vidakovic, B. (1999), “A Bayesian Decision Theoretic Approach to Wavelet Thresholding,” Statistica Sinica, 9, 183-197.
40. Vidakovic, B. (1998), “Nonlinear Wavelet Shrinkage With Bayes Rules and Bayes Factors,” Journal of the American Statistical Association, 93, 173-179.
41. Vidakovic, B., and Muller, P. (1995), “Wavelet Shrinkage With Affine Bayes Rules With Applications,” Discussion Paper 95-24, ISDS, Duke University, Dept, of Statistics.
42. Wu, C. F. (1983), “On the Convergence of the EM Algorithm,” The Annals of Statistics, 11, 95-103.