Image denoising based on a mixture of circular symmetric Laplacian models in complex wavelet domain

For maximum a posteriori (MAP) estimation of noise-free data from noisy observation, it is necessary to consider a proper distribution for modeling probability density function (pdf) of noise-free data. Recently, it has been shown that bivariate pdfs, that exploit dependencies between coefficients in adjacent scales of wavelet coefficients, can better model the statistical property of wavelet coefficients. Thus wavelet based image denoising algorithms employing bivariate pdfs achieves better performance compared with the ones based on the independence assumption. In this paper, we design a bivariate MAP estimator which uses a mixture of circular symmetric Laplacian pdfs. This model not only is bivariate but also is mixture. Mixture pdf models the heavy-tailed natures of the data and the bivariate pdf model the interscale dependencies of wavelet coefficients. Experimental results show that our new algorithm achieves better results than several methods, such as denoising based on univariate mixture pdfs and denoising employing bivariate pdfs, visually and in terms of peak signal-to-noise ratio (PSNR).