Signal de-noising using adaptive Bayesian wavelet shrinkage

H. Chipman, E.D. Kolacxyk, R. McCulloch
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引用次数: 11

Abstract

Shrinkage of the empirical wavelet coefficients is an effective way to de-noise signals possessing sparse wavelet transforms. This article outlines a Bayesian approach to wavelet shrinkage, in which the form of the shrinkage function is induced by a particular choice of prior distributions placed on the wavelet coefficients. Our priors are chosen to be mixtures of two normal distributions, one wide and the other narrow, so as to effectively model the sparseness inherent in the wavelet representations of many signals. This particular choice of prior also allows us to obtain a closed-form expression for the shrinkage function (posterior mean) and for the corresponding uncertainty (posterior variance). This uncertainty information is used in turn to generate uncertainty bands for the full signal reconstruction. An automatic, level-dependent scheme is used to adapt the shrinkage functions to each resolution level of coefficients, although subjective information may be incorporated quite easily.
基于自适应贝叶斯小波收缩的信号去噪
经验小波系数的缩减是对具有稀疏小波变换的信号进行去噪的有效方法。本文概述了小波收缩的贝叶斯方法,其中收缩函数的形式由放置在小波系数上的特定先验分布的选择引起。我们的先验被选择为两个正态分布的混合物,一个宽一个窄,以便有效地模拟许多信号的小波表示中固有的稀疏性。这种特殊的先验选择还允许我们获得收缩函数(后验均值)和相应的不确定性(后验方差)的封闭形式表达式。这些不确定性信息依次用于生成完整信号重构的不确定性频带。一个自动的,水平相关的方案被用来适应收缩函数的每个分辨率水平的系数,虽然主观信息可以很容易地纳入。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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