Wavelet thresholding for some classes of non-gaussian noise

Statistica Neerlandica

Volumn 56, Issue 4, 2002, Pages 434-453

  Antoniadis, A ^a,b   Leporini, D ^a,b   Pesquet, J C ^a,b  

^a UNIV GRENOBLE ALPES   (France)

^b UNIVERSITÉ GUSTAVE EIFFEL   (France)

Author keywords

Cauchy distribution; Denoising; Exponential power distributions; MAP; Non Gaussian noises; Regularization; Wavelets

Indexed keywords

EID: 0036873311     PISSN: 00390402     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9574.00211     Document Type: Article

References (44)

1. ABRAMOVICH, F. and Y. BENJAMINI (1996), Adaptive thresholding of wavelet coefficients, Computational Statistics and Data Analysis 22, 351-361.
2. ABRAMOVICH, F., T. SAPATINAS and B. W. SILVERMAN (1998), Wavelet thresholding via a Bayesian approach, Journal of the Royal Statistic Society Series B 60, 725-749.
3. ANTONIADIS, A., I. GIJBELS and G. GRÉGOIRE (1997), Model selection using wavelet decomposition and applications, Biometrika 84, 751-763.
4. AVERKAMP, R. and C. HOUDRÉ (1999), Wavelet thresholding for non (necessarily) Gaussian noise: idealism. Internal report, Georgia Institute of Technology, Atlanta.
5. BUCCIGROSSI, R. W. and E. P. SIMONCELLI (1997), Progressive wavelet image coding based on a conditional probability model in: Proceedings of the IEEE Conference on Acoustics, Speech, Signal Processing, pages IV.2957-IV.2960, Munich, Germany.
6. CHAMBOLLE, A., R. A. DEVORE, N.-Y. LEE and B. J. LUCIER (1998), Nonlinear wavelet image processing: variational problems, compression and noise removal through wavelet shrinkage. IEEE Transactions on Image Processing 7, 319-335.
7. CHIPMAN, H. A., E. D. KOLACZYCK and R. E. MCCULLOCH (1997), Adaptive Bayesian wavelet shrinkage, Journal of the American Statistical Association 22, 1413-1421.
8. CLYDE, M., G. PARMIGIANI and B. VIDAKOVIC (1998), Multiple shrinkage and subset selection in wavelets, Biometrika 85, 391-401.
9. COIFMAN, R. and D. DONOHO (1995), Translation-invariant de-noising: in ANTONIADIS, A. and G. OPPENHEIM, (eds.), Wavelets and statistics. Lecture Notes in Statistics, Springer Verlag.
10. DECHEVSKY, L. T. and S. I. PENEV (1998), On penalized wavelet estimation, Report No. S98-15, Department of Statistics, The University of New South Wales.
11. DELYON, B. and A. JUDITSKY (1996), On minimax wavelet estimators, Applied and Computational Harmonic Analysis 3, 215-228.
12. DONOHO, D. L. (1995), Denoising by soft-thresholding. IEEE Transactions on Information Theory 41, 613-627.
13. DONOHO, D. L. and I. M. JOHNSTONE (1994), Ideal spatial adaptation by wavelet shrinkage, Biometrika 81, 425-455.
14. DONOHO, D. L. and I. M. JOHNSTONE (1995), Adapting to unknown smoothness via wavelet shrinkage, Journal of the American Statistical Association 90, 1200-1224.
15. DONOHO, D. L. and I. M. JOHNSTONE (1998), Minimax estimation via wavelet shrinkage, Annals of Statistics 26, 879-921.
16. DONOHO, D. L., I. M. JOHNSTONE, G. KERKYACHARIAN and D. PICARD (1995), Wavelet shrinkage: asymptopia? (with discussion), Journal of the Royal Statistical Society Series B 57, 301-369.
17. FANG, K. T., S. KOTZ and K. W. NG (1989), Symmetric multivariate and related distributions, Chapman and Hall, London and New York.
18. FRANK, I. and J. H. FRIEDMAN (1993), A statistical view of some chemometrics regression tools, Technometrics 35, 109-148.
19. FU, W. J. (1998), Penalized regressions: the Bridge versus the Lasso, Journal of Computational and Graphical Statistics 7, 397-416.
20. GEORGE, E. I. and R. MCCULLOGH (1997), Approaches to Bayesian variable selection, Statistica Sinica 7, 339-373.
21. JOHNSTONE, I. M and B. W. SILVERMAN (1998), Empirical Bayes approaches to mixture problems and wavelet regression, Technical Report, University of Bristol and Stanford University.
22. JÙDITSKY, A. (1997), Wavelet estimators: adapting to unknown smoothness, Mathematical Methods of Statistics 6, 1-25.
23. KRIM, H. and I.-C. SCHICK (1999), Minimax description length for signal denoising and optimized respresentation, IEEE Transactions on Information Theory 45, 898-908.
24. LEPORINI, D. (1998), Modélisation statistique et paquets d'Ondelettes : application au débruitage de signaux transitoires d'Acoustique sous-marine, Thèse de Doctorat de l'Université Paris XI, Orsay.
25. LÈPORINI D. and J.-C. PESQUET (1999), High-order wavelet packets and cumulant field analysis, IEEE Transaction on Information Theory 45, 863-877.
26. LEPORINI, D. and J.-C. PESQUET (2001), Bayesian wavelet denoising: Besov priors and non-Gaussian noises, Signal Processing 81, 55-67.
27. 2(ℝ), Transactions of the American Mathematical Society 315, 69-87.
28. MALLAT, S. (1989b), A theory for multiresolution signal decomposition: the wavelet representation, IEEE Transactions on Pattern Analysis and Machine Intelligence PAMI-11, 674-693.
29. NASON, G. P. (1995), Choice of the threshold parameter in wavelet function estimation, in: A. ANTONIADIS and G. OPPENHEIM (eds.), Wavelets and statistics, 261-280, Lecture Notes in Statistics, Springer Verlag.
30. NASON, G. P. (1996), Wavelet shrinkage using cross-validation, Journal of the Royal Statistical Society Series B 58, 463-479.
31. NASON, G. P. and B. W. SILVERMAN (1995), The stationary wavelet transform and some statistical applications, in: A. ANTONIADIS and G. OPPENHEIM (eds.), Wavelets and statistics, 281-299. Lecture Notes in Statistics, Springer Verlag.
32. NEUMANN, M. H. and R. VON SACHS (1995), Wavelet thresholding: beyond the Gaussian i.i.d situation, in: A. ANTONIADIS and G. OPPENHEIM (eds.), Wavelets and statistics, Lecture Notes in Statistics, Springer Verlag, 301-330.
33. NG, K. W. and D. A. S. FRASER (1994), Inference for linear models with radially decomposable error in: Multivariate analysis and its applications, 359-367 IMS Lecture notes, Vol 24.
34. NIKIAS, C. L. and M. SHAO (1995), Signal processing with alpha-stable distributions and applications, Wiley-Interscience, New York.
35. NIKOLOVA, M. (1997), Estimées localement fortement homogènes, Comptes Rendus de l'Academie des Sciences Serie 1 325, 665-670.
36. OGDEN, R. T. and E. PARZEN (1996a), Change-point approach to data analytic wavelet thresholding, Statistics and Computing, 63, 93-99.
37. OGDEN, R. T. and E. PARZEN (1996b), Data dependent wavelet thresholding in nonparametric regression with change-point applications, Computational Statistics 22, 53-70.
38. RUGGERI, F. and B. VIDAKOVIC (1999), A Bayesian decision theoretic approach to wavelet thresholding, Statistica Sinica 9, 183-197.
39. SIMONCELLI, E. (1999), Bayesian denoising of visual images in the wavelet domain, in: P. MULLER and B. VIDAKOVIC (eds.), Bayesian inference in wavelet-based models, Lecture Notes in Statistics, Springer Verlag.
40. SIMONCELLI, E. P. and E. H. ADELSON (1996), Noise removal via Bayesian wavelet coring, in: Proceedings of the IEEE International Conference on Image Processing, Lausanne, Switzerland, I.379-I.382.
41. SMITH, A. and G. ROBERTS (1993), Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods, Journal of the Royal Statistical Society Series B 55, 3-23.
42. TIBSHIRANI, R. (1996), Regression shrinkage and selection via the Lasso. Journal of the Royal Statistical Society Series B 58, 267-288.
43. TIERNEY, L. (1994), Markov chains for exploring posterior distributions, Annals of Statistics 227 1701-1762.
44. VIDAKOVIC, B. (1998), Nonlinear wavelet shrinkage with Bayes rules and Bayes factors, Journal of the American Statistical Association 93, 173-179.