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Multivariate Bayes Wavelet shrinkage and applications

机译：多元贝叶斯小波收缩及其应用

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In recent years, wavelet shrinkage has become a very appealing method for data de-noising 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.
机译：近年来，小波收缩已经成为用于数据去噪和密度函数估计的非常有吸引力的方法。特别是，通过分层先验的贝叶斯建模为小波分析引入了新颖的方法，这种方法已经非常流行，并且与标准的硬阈值或软阈值规则竞争非常激烈。从这个意义上讲，本文提出了一种分层先验，该先验是在应用离散小波变换（DWT）之后，在描述小波系数的模型参数上引起的。与其他方法不同的是，现有技术提出了一种具有协方差矩阵的多元正态分布，该协方差矩阵允许与相同细节水平相对应的小波系数之间的相关性。另外，并入了一个额外的比例参数，该参数允许在系数上增加收缩率。该收缩过程的后验分布不是封闭形式，但可以通过马尔可夫链蒙特卡洛（MCMC）方法轻松进行采样。介绍了一组测试信号和两个噪声信号的应用。

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