A Novel Directionlet-Based Image Denoising Method Using MMSE Estimator and Laplacian Mixture Distribution

Abstract

A novel method based on directionlet transform is proposed for image denoising under Bayesian framework. In order to achieve noise removal, the directionlet coefficients of the uncorrupted image are modeled independently and identically by a two-state Laplacian mixture model with zero mean. The expectation-maximization algorithm is used to estimate the parameters that characterize the assumed prior model. Within the framework of Bayesian theory, the directionlet coefficients of noise-free image are estimated by a nonlinear shrinkage function based on weighted average of the minimum mean square error estimator. We demonstrate through simulations with images contaminated by additive white Gaussian noise that the proposed method is very competitive when compared with other methods in terms of both peak signal-to-noise ratio and visual quality.