VECTOR MEDIAN FILTERS

Two nonlinear algorithms for processing vector-valued signals are introduced. These algorithms, called vector median operations, are derived from two multidimensional probability density functions using the maximum likelihood estimate approach. The underlying probability densities are exponential and the resulting operations have properties very similar to those of the median filter. These include zero impulse response and preserving of edges in the vector-valued input signal. The vector median filters also have root signals, as does the median filter. In the vector median approach, the samples of the vector-valued input signal are processed as vectors as opposed to componentwise scalar processing. The vector median operation inherently utilizes the correlation between the signal components giving the filters some desirable properties. General properties as well as the root signals of the vector median filters are studied. The vector median operation is combined with linear filtering, resulting in filters with improved noise attenuation and filters with very good edge response. An efficient algorithm to implement long vector median filters is presented. The noise attenuation of the filters is discussed and an application to velocity filtering is shown. © 1990 IEEE