Wavelet-Based Bayesian Denoising Using Bernoulli-Gaussian Mixture Model

In general, wavelet coefficients are composed of a few large coefficients and a lot of small ones. Therefore, each wavelet coefficient is efficiently modeled as a random variable of a Bernoulli-Gaussian mixture distribution with unknown parameters. The Bernoulli-Gaussian mixture is composed of the multiplication of the Bernoulli random variable and the Gaussian mixture random variable. In this paper, we propose a denoising algorithm using the BernoulliGaussian mixture model based on sparse characteristics of the wavelet coefficient. The denoising is performed with Bayesian estimation. We present an effective denoising method through simplified parameter estimation for the Bernoulli random variable using a local expected square error. Simulation results showed that our method outperformed the states of the art denoising methods.