Optimal nonlinear filter to remove random impulses from Gaussian noise

This paper investigates the problem of removing random impulse noise from a white signal of Gaussian distribution. A nonlinear polynomial filter is used, whose coefficients are optimised using an exact least squares method. The method relies on exploiting the differing probability distributions of the impulsive noise and the Gaussian signal. The paper then looks at the effect of both the polynomial order and the normalised spike amplitude on the mean squared error and signal to noise ratio. The results are compared to the results found using a simple clipping filter. The results show that the optimal filter gives a much improved performance over the simple clipping filter in reducing the mean square error.