Abstract
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.