Multichannel L filters based on reduced ordering

Nonlinear multichannel signal processing is an emerging research topic with numerous applications. In this paper we use the so-called reduced ordering (R-ordering) principle to introduce a new family of L lters for vector-valued observations. The coeecients of the proposed lters can be deduced so that the lters are optimal with respect to the output mean squared error. Expressions for the unconstrained, unbiased and location invariant optimal lter coeecients are derived. The calculation of moments of the R-ordered vectors that are involved in these expressions is also being considered. Experiments with noisy two-channel vector elds and noisy color images are presented in order to demonstrate the superiority of the proposed lters over other multichannel lters.