Novel Form of MMSE Estimation via Exact Moment Value of Noise and Higher Order Taylor Series in AWGN

Minimum mean-square-error (MMSE) and maximum a posteriori (MAP) estimations are considered basic approaches commonly used in denoising methods. In most cases, MMSE estimation yields better performance in reducing noise than MAP estimation does. However, the calculation according to MMSE estimation is more difficult than that of MAP estimation, because MMSE estimation relies on integration and its results mainly contain special functions, while MAP estimation relies on differentiation. The previous research work presented MMSE estimation in the form of differentiation, which is in the approximation form. But in this letter, we will present MMSE estimation in the differentiation form by using the actual moment value of the probability density function of Gaussian noise together with the higher order Taylor series. This will provide higher efficiency of noise reduction than the formerly presented method.