We consider a model of wavelet shrinkage with two normal distributions where the variance of the noise is estimated using exponential distribution. Instead of normal and double exponential distributions on the parameters domain of wavelet coefficients, which is usually the case in the existing literature, the $∊$-contamination prior distribution is involved that is particularly attractive to work with when one seeks robust priors in Bayesian analysis. The proposed method starts with computing the posterior mean and the posterior mean under the mass point. This article covers the major topic of theoretical approaches. Wavelet methods are applied, involving decimated wavelet transform with a single parameter for each level. The proposed method is illustrated on the standard test functions of Donoho and Johnstone, where the level of noise corrupts these functions. This procedure can be explained as a type of inverse problem. We compared some standard wavelet-based methods with the existing process. Extensive simulation is implemented to perform the proposed method and improve signal’s reconstruction using average mean-squared error to compare different approaches. As a practical illustration, we present an application to a real-life data set. The main interest of the paper is to compare two different likelihoods-the first is the normal distribution, and the other is the double exponential distribution.

我们考虑具有两个正态分布的小波收缩模型，其中使用指数分布估计噪声的方差。与现有文献中通常采用的小波系数参数域上的正态分布和双指数分布不同，$∊$- 涉及污染先验分布，当人们在贝叶斯分析中寻求稳健的先验时，这种分布特别有吸引力。所提出的方法从计算质点下的后验平均值和后验平均值开始。本文涵盖了理论方法的主要主题。应用了小波方法，涉及每个级别具有单个参数的抽取小波变换。所提出的方法在 Donoho 和 Johnstone 的标准测试函数上进行了说明，其中噪声水平会破坏这些函数。这个过程可以解释为一种逆问题。我们将一些基于小波的标准方法与现有过程进行了比较。实施广泛的模拟以执行所提出的方法并使用平均均方误差来比较不同的方法来改进信号的重建。作为一个实际的例子，我们展示了一个真实数据集的应用。这篇论文的主要兴趣是比较两种不同的似然——第一种是正态分布，另一种是双指数分布。