Vector median filters

TLDR

The underlying probability densities are exponential, giving vector median operations properties similar to a median filter. The paper introduces two nonlinear vector‑median algorithms and studies their general properties and root signals. Derived via maximum‑likelihood from exponential multidimensional PDFs, the algorithms process vector samples exploiting component correlation, combine with linear filtering for enhanced noise attenuation and edge response, and an efficient implementation for long filters is provided. The filters achieve improved noise attenuation and are effective for velocity filtering.

Abstract

Two nonlinear algorithms for processing vector-valued signals are introduced. The 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. In the vector median approach, the samples of the vector-valued input signal are processed as vectors. The 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 for implementing long vector median filters is presented. The noise attenuation of the filters is discussed, and an application to velocity filtering is shown.