A closed form solution of MMSE using multivariate radial-exponential priors for wavelet-based image denoising

The Performance of various estimators, such as 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 (pdfs) with local variance. Generally these multivariate extensions do not result in a closed form expression, and the solution requires numerical solutions as in . However, we drive a closed form MMSE shrinkage functions for a radial exponential random vector in Gaussian noise. Experimental results show that for images of structural textures, for example dasiaBarbarapsila and texture image, our proposed method, MMSE_TriShrink_Radial, have better PSNR than MMSE_TriShrink_Laplace , CauchyShrinkL and BayeShrink .