Image denoising employing a bivariate Cauchy distribution with local variance in complex wavelet domain

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 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 bivariate Cauchy probability density functions (pdfs) with local variance. The bivariate pdf takes into account the statistical dependency among wavelet coefficients and the local variance model the empirically observed correlation between the coefficient amplitudes. Therefore, by using this statistical model, we are able to better model statistical property of wavelet coefficients. Within this framework, we propose a novel method for image denoising employing a bivariate MAP estimator, which relies on the bivariate distribution with high local correlation. The simulation results show that our proposed technique outperforms several exiting methods both visually and in terms of peak signal-to-noise ratio (PSNR).