Image Denoising in Curvelet Transform Domain Using Gaussian Mixture Model with Local Parameters for Distribution of Noise-Free Coefficients

This paper proposes a new statistical model for curvelet coefficients of images to characterize both leptokurtic behavior and spatially clustering property of them. We employ a mixture of Gaussian probability density functions (pdfs) with local parameter to model the distribution of noise-free curvelet coefficients. This pdf is mixture and so it is able to model the heavy-tailed nature of curvelet coefficients. Since we use local parameters for mixture model, the proposed pdf can capture the clustering property of curvelet coefficients in spatial adjacent. This model is employed for noise reduction in a Bayesian framework using maximum a posteriori (MAP) estimator. We examine this method for denoising of several grayscale images such as CT image corrupted with additive Gaussian noise in various noise levels. The simulation results show that the proposed method has better performance visually and in terms of peek signal-to-noise ratio (PSNR) from several denoising methods in wavelet and curvelet domain.