Noise Variance Estimation In Signal Processing

We present a new method of estimating noise variance. The method is applicable for 1D and 2D signal processing. The essence of this method is estimation of the scatter of normally distributed data with high level of outliers. The method is applicable to data with the majority of the data points having no signal present. The method is based on the shortest half sample method. The mean of the shortest half sample (shorth) and the location of the least median of squares are among the most robust measures of the location of the mode. The length of the shortest half sample has been used as the measurement of the data scatter of uncontaminated data. We show that computing the length of several sub samples of varying sizes provides the necessary information to estimate both the scatter and the number of uncontaminated data points in a sample. We derive the system of equations to solve for the data scatter and the number of uncontaminated data points for the Gaussian distribution. The data scatter is the measure of the noise variance. The method can be extended to other distributions.