Adaptive mean/median filtering

The use of median and averaging filters is fairly routine in signal processing applications. One problem in using such algorithms is the lack of objective criteria by which to decide whether an averager or a median filter is more appropriate. We formulate an L_p (1⩽p⩽2) normed filter where p is chosen as a function of the kurtosis of the residual vector; we restrict attention in this work to a mean filter (p=2) and a median filter (p=1). In order to highlight the effectiveness of this filtering algorithm we demonstrate reduced sum squared error by adaptively filtering a sinusoid and a test image in the presence of both additive white Gaussian noise and an impulsive noise component