Image denoising via analytical form of adaptive generalized Gaussian random vectors in AWGN with MMSE estimator for local adaptive parameter

Abstract

In this paper, we present new Bayesian estimators for adaptive generalized Gaussian (GG) random vectors in additive white Gaussian noise (AWGN). The derivations are an extension of existing results for Pearson type VII random vectors in AWGN. Pearson type VII random vectors is one of the distribution that successfully use for image denoising. However, Pearson type VII distribution have higher-order moment in statistical parameter for fitted the data such as mean, variance and kurtosis. In our literature, where high-order statistics were used, better performance can be obtained but with much higher computational complexity. In fact, adaptive GG random vectors is similar to Pearson type VII random vectors. However, the special case of adaptive GG random vectors has only first few statistical moments such as adaptive parameter. So, the proposed method can be calculated very fast, without any complex step. In fact, the adaptive parameter of adaptive GG density is the function of standard deviation. Here, we employ minimum mean square error (MMSE) estimation to calculate local observed variances with gamma density prior for local observed variances and Gaussian distribution for noisy wavelet coefficients. In our experiments, our proposed method gives promising denoising results with moderate complexity.