Multivariate Bayes wavelet shrinkage and applications

被引:10
|
作者
Huerta, G [1 ]
机构
[1] Univ New Mexico, Dept Math & Stat, Albuquerque, NM 87131 USA
关键词
Bayes shrinkage; wavelets; discrete wavelet transformation; data de-noising; MCMC methods;
D O I
10.1080/02664760500079662
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
In recent years, wavelet shrinkage has become a very appealing method for data denoising and density function estimation. In particular, Bayesian modelling via hierarchical priors has introduced novel approaches for Wavelet analysis that had become very popular, and are very competitive with standard hard or soft thresholding rules. In this sense, this paper proposes a hierarchical prior that is elicited on the model parameters describing the wavelet coefficients after applying a Discrete Wavelet Transformation (DWT). In difference to other approaches, the prior proposes a multivariate Normal distribution with a covariance matrix that allows for correlations among Wavelet coefficients corresponding to the same level of detail. In addition, an extra scale parameter is incorporated that permits an additional shrinkage level over the coefficients. The posterior distribution for this shrinkage procedure is not available in closed form but it is easily sampled through Markov chain Monte Carlo (MCMC) methods. Applications on a set of test signals and two noisy signals are presented.
引用
收藏
页码:529 / 542
页数:14
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