Affine equivariance in multichannel OS-filtering

Nonlinear multichannel filters have successfully been applied to biomedical signals, multichannel images as well as processing of vector fields. In multichannel signals, component variances and correlations among components may be unequal and time-varying. Such changes can be expressed as an affine transformation of the input signal. In this paper, we investigate how the performance and statistical properties of multichannel filters stemming from order statistics (OS) change under affine transformations. An affine equivariant multichannel filter is introduced and the use of the affine equivariant performance metric replacing the mean square error is proposed. Advantages of affine equivariance are demonstrated in simulation, and filtering examples using real data are given