Medical Volume Noise Reduction Employing a Laplace Distribution with Local Variance for Modeling Contourlet Coefficients

In this paper we introduce a simple shrinkage function employing local Laplace distribution for medical volume noise reduction in contourlet transform domain. Since we implement our denoising algorithm in contourlet domain, we are able to preserve the important details of noise-free images that for medical volume may contain important diagnostic information. It is clear that using maximum a posteriori (MAP) estimator for denoising problem, needs a prior distribution for noise-free data. In this paper we propose a Laplace probability density function (pdf) to model the statistical properties of contourlet coefficients. This distribution is able to simultaneously model the heavy-tailed nature and spatially clustering property of coefficients. We use the produced thresholding function from MAP estimator for denoising of a sequence of CT images corrupted with additive Gaussian noise in various noise levels. The simulation results show that our method has better performance visually and in terms of peek signal-to-noise ratio (PSNR) in comparison with several denoising methods.