A study on image denoising in contourlet domain using the alpha-stable family of distributions

In the past decade, several image denoising techniques have been developed aiming at recovering signals from noisy data as much as possible along with preserving the features of an image. This paper proposes a new image denoising method in the contourlet domain by using the alpha-stable family of distributions as a prior for contourlet image coefficients. The univariate symmetric alpha-stable distribution (SαS) is mostly suited for modeling of the i.i.d. contourlet coefficients with high non-Gaussian property and heavy tails. In addition, the bivariate SαS exploits the dependencies between the coefficients across scales. In this paper, using the univariate and bivariate priors, Bayesian minimum mean absolute error and maximum a posteriori estimators are developed in order to estimate the noise-free contourlet coefficients. To estimate the parameters of the alpha-stable distribution, a spatially-adaptive method using fractional lower order moments is proposed. It is shown that the proposed parameter estimation method is superior to the maximum likelihood method. An extension to color image denoising is also developed. Experiments are carried out using noise-free images corrupted by additive Gaussian noise, and the results show that the proposed denoising method outperforms other existing methods in terms of the peak signal-to-noise ratio and mean structural similarity index, as well as in visual quality of the denoised images. & 2016 Elsevier B.V. All rights reserved.