Image denoising employing a closed form solution of MMSE using multivariate radial-exponential priors with approximate MAP estimate for statistical parameter

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 (pdf) with approximated MAP estimation for statistical parameter (local variance) using exponential priori. 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 vector in Gaussian noise. Experimental results show that our proposed method, MMSE_TriShrink_Radial, outperforms several exiting methods in terms of peak signal-to-noise ratio (PSNR).