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 filters for vector-valued observations. The coefficients of the proposed filters can be deduced so that the filters are optimal with respect to the output mean squared error. Expressions for the unconstrained, unbiased and location invariant optimal filter coefficients are derived. The calculation of moments of the R-ordered vectors that are involved in these expressions is also discussed. Experiments with noisy two-channel vector fields and noisy color images are presented in order to demonstrate the superiority of the proposed filters over other multichannel filters.