Weighted median filters for multichannel signals

This paper focuses on extending the weighted median for use with multidimensional (multichannel) signals. Sorting multicomponent (vector) values and selecting the middle value is not well defined as in the scalar case. This paper introduces two median based multivariate filtering structures inspired by ML estimates of location in multivariate spaces. Unlike Astola´s weighted vector median filter, the multichannel weighted median filter structures introduced in this paper are able to exploit the spatial and cross-channel correlations embedded in the data. Adaptive optimization algorithms for the filters are derived. The effectiveness of these algorithms is shown through image and array processing experiments.