Image Denoising Based on a Mixture of Laplace Distributions with Local Parameters in Complex Wavelet Domain

Abstract

The performance of various estimators, such as maximum a posteriori (MAP) is strongly dependent on correctness of the proposed model for noise-free data distribution. Therefore, the selection of a proper model for distribution of wavelet coefficients is very important in the wavelet based image denoising. This paper presents a new image denoising algorithm based on the modeling of wavelet coefficients in each subband with a mixture of Laplace probability density functions (pdfs) that uses local parameters for the mixture model. The mixture model is able to capture the heavy-tailed nature of wavelet coefficients and the local parameters can model the empirically observed correlation between the coefficient amplitudes. Therefore, by using this relatively new model, we are able to model the statistical properties of wavelet coefficients. Within this framework, we describe a novel method for image denoising based on designing a MAP estimator, which relies on the mixture distributions with high local correlation. The simulation results show that our proposed technique achieves better performance than several published methods both visually and in terms of peak signal-to-noise ratio (PSNR).