Identifying Optimal Gaussian Filter for Gaussian Noise Removal

In this paper we show that the knowledge of noise statistics contaminating a signal can be effectively used to choose an optimal Gaussian filter to eliminate noise. Very specifically, we show that the additive white Gaussian noise (AWGN) contaminating a signal can be filtered best by using a Gaussian filter with specific characteristics. The design of the Gaussian filter bears relationship with the noise statistics in addition to some basic information about the signal. We first derive a relationship between the properties of the Gaussian filter, the noise statistics and the signal and later show through experiments that this relationship can be used effectively to identify the optimal Gaussian filter that can effectively filter noise.