An adaptative, nonlinear edge-preserving filter

An adaptative filter whose main feature is to preserve edges and impulses present in the signal is analyzed by the computation of the mean-square error (MSE) of its output sequence. The filter in its more general form is highly nonlinear, resembling the M-type estimators used in robust statistics. A simplified form used here allows the exact computation of the MSE when the filter length is finite. This MSE can be compared to the ones obtained for a median filter and a mean filter. It is shown that for a wide range of the filter and signal parameters such as filter length, edge heights, and impulse width, the performance of the filter proposed in this paper is superior to the other filters mentioned above. An additional advantage of the simplified version of the filter is that in most cases, its computation amounts to a linear adaptative averaging. This contrasts with the amount of calculation required to implement the median filter and any other filter based on the order statistics of the measured samples.