The Estimation of Radial Exponential Random Vectors in Additive White Gaussian Noise

Image signals are always disturbed by noise during their transmission, such as in mobile or network communication. The received image quality is significantly influenced by noise. Thus, image signal denoising is an indispensable step during image processing. As we all know, most commonly used methods of image denoising is Bayesian wavelet transform estimators. The Performance of various estimators, such as maximum a posteriori (MAP), or minimum mean square error (MMSE) is strongly dependent on correctness of the proposed model for original data distribution. Therefore, the selection of a proper model for distribution of wavelet coefficients is important in wavelet-based image denoising. This paper presents a new image denoising algorithm based on the modeling of wavelet coefficients in each subband with multivariate Radial Exponential probability density function (PDF) with local variances. Generally these multivariate extensions do not result in a closed form expression, and the solution requires numerical solutions. However, we drive a closed form MMSE shrinkage functions for a Radial Exponential random vectors in additive white Gaussian noise (AWGN). The estimator is motivated and tested on the problem of wavelet-based image denoising. In the last, proposed, the same idea is applied to the dual-tree complex wavelet transform (DT-CWT), This Transform is an over-complete wavelet transform.