Shift-Invariant Image Denoising Using Mixture of Laplace Distributions in Wavelet-Domain

In this paper, we propose a new method for denoising of images based on the distribution of the wavelet transform. We model the discrete wavelet coefficients as mixture of Laplace distributions. Redundant, shift invariant wavelet transform is made use of in order to avoid aliasing error that occurs with critically sampled filter bank. A simple Expectation Maximization algorithm is used for estimating parameters of the mixture model of the noisy image data. The noise is considered as zero-mean additive white Gaussian. Using the mixture probability model, the noise-free wavelet coefficients are estimated using a maximum a posteriori estimator. The denoising method is applied for general category of images and results are compared with that of wavelet-domain hidden Markov tree method. The experimental results show that the proposed method gives enhanced image estimation results in the PSNR sense and better visual quality over a wide range of noise variance.