ABSTRACT We consider Bayesian approach to wavelet decomposition. We show how prior knowledge about a function's regularity can be incorporated into a prior model for its wavelet coefficients by establishing a relationship between the hyperparameters of the proposed model and the parameters of those Besov spaces within which realizations from the prior will fall. Such a relation may be seen as giving insight into the meaning of the Besov space parameters themselves. Furthermore, we consider Bayesian wavelet-based function estimation that gives rise to different types of wavelet shrinkage in non-parametric regression. Finally, we discuss an extension of the proposed Bayesian model by considering random functions generated by an overcomplete wavelet dictionary.
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1628
|
A theory for multiresolution signal decomposition: the wavelet representation
– Mallat
- 1989
|
|
496
|
Atomic decomposition by basis pursuit
– Chen, Donoho, et al.
- 1998
|
|
400
|
Ideal spatial adaptation by wavelet shrinkage
– Donoho, Johnstone
- 1994
|
|
391
|
Entropy-based algorithms for best basis selection
– Coifman, Wickerhauser
- 1992
|
|
372
|
Adapting to unknown smoothness via wavelet shrinkage
– Donoho, Johnstone
- 1995
|
|
210
|
Wavelet-based statistical signal processing using hidden Markov models
– Crouse, Nowak, et al.
- 1998
|
|
204
|
Wavelets and Operators
– Meyer
- 1992
|
|
179
|
Wavelets on the interval and fast wavelet transforms
– Cohen, Daubechies, et al.
- 1993
|
|
160
|
Translation-invariant de-noising
– Coifman, Donoho
- 1995
|
|
143
|
Wavelet thresholding via a Bayesian approach
– Abramovich, Sapatinas, et al.
- 1998
|
|
137
|
Wavelet threshold estimators for data with correlated noise
– Johnstone, Silverman
- 1997
|
|
122
|
Adaptive bayesian wavelet shrinkage
– Chipman, Kolaczyk, et al.
- 1997
|
|
122
|
Compression of wavelet decompositions
– DeVore, Jawerth, et al.
- 1992
|
|
88
|
Matching Pursuit in a time-frequency dictionary
– Mallat, Zhang
- 1993
|
|
83
|
The discrete wavelet transform in
– Nason, Silverman
- 1994
|
|
76
|
Multiple shrinkage and subset selection in wavelets
– Clyde, Parmigiani, et al.
- 1998
|
|
73
|
Interpolation of Besov spaces
– DeVore, Popov
- 1988
|
|
68
|
Noise reduction using an undecimated discrete wavelet transform
– Lang, Guo, et al.
- 1996
|
|
63
|
Wavelet Shrinkage Using Cross-Validation
– Nason
- 1996
|
|
51
|
Time-frequency localization operators: A geometric phase space approach
– Daubechies
- 1988
|
|
45
|
Wavelet decomposition approaches to statistical inverse problems
– Abramovich, Silverman
- 1998
|
|
32
|
Flexible empirical Bayes estimation for wavelets
– Clyde, George
- 2000
|
|
28
|
Generalized cross validation for wavelet thresholding
– Jansen, Malfait, et al.
- 1997
|
|
22
|
Adaptive thresholding of wavelet coefficients
– ABRAMOVICH, BENJAMINI
- 1996
|
|
17
|
Minimax Bayes, asymptotic minimax and sparse wavelet priors
– Johnstone
- 1994
|
|
14
|
Empirical bayes approaches to mixture problems and wavelet regression
– Johnstone, Silverman
- 1998
|
|
12
|
Adaptive time-frequency approximations with matching pursuit
– Davis, Mallat
- 1994
|
|
5
|
Stochastic expansions in an overcomplete wavelet dictionary . Probability Theory & Related Fields , to appear. logic in the wavelet framework
– Abramovich, Sapatinas, et al.
- 2000
|
|
2
|
Stochastic atomic decompositions in a wavelet dictionary
– Abramovich, Sapatinas
- 1998
|
|
1
|
Theofanis Sapatinas Daubechies, I
– Abramovich
- 1988
|
|
1
|
Approach To Wavelet Decomposition and Shrinkage 19
– Bayesian
- 1992
|
|
