Contents I. Introduction
Image denoising is an essential part of many image processing systems, since images are often degraded by noise. A number of recent works on image denoising have focused on wavelet domain techniques due to locality, multi-resolution and compression properties of wavelet coefficients. The wavelet-domain Bayesian denoising methods impose a prior distribution on wavelet coefficients and build a non-linear mapping function for processing the noisy wavelet coefficients. In these methods, the prior distribution of the wavelet coefficients has a substantial effect on their performance. The wavelet subband coefficients have been formerly assumed to be independent and modeled simply by marginal statistics such as Gaussian [1], generalized Gaussian (GG) [2] or Cauchy [3]. However, it has been shown that the wavelet coefficients of an image have strong dependencies across scales and within scale resulting in the introduction of joint statistical models in the wavelet domain. Crouse et al. [4] have developed a framework for statistical signal processing based on wavelet-domain hidden Markov model to capture both the non-Gaussian statistics of individual wavelet coefficients and their inter-scale and intra-scale dependencies. In [5] and [6], a bivariate shrinkage function has been proposed for the purpose of image denoising by considering the parent to child dependencies of the wavelet coefficients. In [7], an image denoising algorithm based on a Gaussian scale mixture model has been proposed in which the covariance between neighboring coefficients have been considered as the dependencies. The multivariate generalized Gaussian distribution has been introduced in [8] to exploit the coefficients dependencies across scales. In [9], a wavelet shrinkage function has been obtained using the neighboring and level dependencies. The three-scale dependency of wavelet coefficients has been considered for a denoising scheme in [10].
