Closest-to-mean filter: An edge preserving smoother for Gaussian environments

Median based filters have gained wide-spread use because of their ability to preserve edges and suppress impulses. In this paper, we introduce the Closest-to-Mean (CTM) filter, which outputs the input sample closest to the sample mean. The CTM filtering framework offers lower computational complexity and better performance in near Gaussian environments than median filters. The formulation of the CTM is derived from the theory of S-filters, which form a class of generalized selection-type filters with the features of edge preservation and impulse suppression. S-filters can play a significant role in image processing, where edge and detail preservation are of paramount importance. We compare the performance of CTM, median, and mean filters in the smoothing of edges and impulses immersed in Gaussian noise. A sufficient condition for a signal to be a root of the CTM filter is included. Data, figures and source code utilized in this paper are available at http://www.ee.udel.edu/signals/robust.