Spatially adaptive image denoising based on joint image statistics in the curvelet domain

In this paper, we perform a statistical analysis of curvelet coefficients, making a distinction between two classes of coefficients: those representing useful image content and those dominated by noise. By investigating the marginal statistics, we develop a mixture prior for curvelet coefficients. Through analysis of the joint intra-band statistics, we find that white Gaussian noise is transformed by the curvelet transform into noise that is correlated in one direction and decorrelated in the perpendicular direction. This enables us to develop an appropriate local spatial activity indicator for curvelets. Finally, based on our findings, we develop a novel denoising method, inspired by a recent wavelet domain method ProbShrink. For textured images, the new method outperforms its wavelet-based counterpart and existing curvelet-based methods. For piecewise smooth images, performances are similar as existing methods.