In order to enhance efficiency of artificial intelligence (AI) tools such as classification or pattern recognition, it is important to have noise-free data to be processed with AI tools. Therefore, the study of algorithms used for reducing noise is also very significant. In thermal condition, Gaussian noise is important problem in analog circuit and image processing. Therefore, this paper focuses on the study of an algorithm for Gaussian noise reduction. In recent year, Bayesian with wavelet-based methods provides good efficiency in noise reduction and spends short time in processing. In Bayesian method, mixture density is more flexible than non-mixture density. Therefore, we proposed novel form of minimum mean square error (MMSE) estimation for mixture model, Pearson type VII and logistic densities, in Gaussian noise. The expectation-maximization (EM) algorithm is most deeply used for computing statistical parameters of mixture model. However, the EM estimator for the proposed method does not have the closed-form. Numerical methods are required to implement an EM algorithm. Therefore, we employ maximum a posteriori (MAP) estimation to compute local noisy variances with half-normal distribution prior for local noisy variances and Gaussian density for noisy wavelet coefficients. Here, the proposed method is expressed in closed-form. The denoising results present that our proposed algorithm outperforms the state-of-the-art method qualitatively and quantitatively.
Split and merge EM algorithm for improving Gaussian mixture density estimates
