An image NSCT-HMT model based on copula entropy multivariate Gaussian scale mixtures

Abstract

As an important multiscale geometric analysis tool, the nonsubsampled contourlet transform (NSCT) has a strong ability in capturing anisotropy and directional features of images. This paper proposes a copula entropy multivariate Gaussian scale mixtures based nonsubsampled contourlet transform hidden Markov tree model (CE-NSCT-HMT). First, we study the probability density distribution of the NSCT coefficients and observe that they exhibit a sharp peak at the zero amplitude and two heavy tails on both sides of the peak. Second, we redefine the generalized neighborhood relationship of the NSCT coefficients and then analyze the joint statistical property among them. We get that the NSCT coefficients have the strongest correlation with their newly defined ‘four neighborhood’ coefficients. Third, we use the Gaussian copula function to model the NSCT coefficients with their ‘four neighborhood’ coefficients. Based on the copula entropy value, the copula entropy multivariate Gaussian scale mixtures distribution is proposed, the application of copula entropy helps the contourlet a lot in localizing textures. In addition, we combine these studies with the hidden Markov tree model and propose the CE-NSCT-HMT model. Finally, the proposed model is applied to image denoising and achieve a good performance. The copula entropy is first applied to the correlation measurement of multiscale decomposition coefficients in this paper, which provides a way to further extend the application of copula entropy to other image processing area.