Multichannel signal processing using spatial rank covariance matrices

This paper addresses the problem of estimating the covariance matrix reliably when the assumptions, such as Gaussianity, on the probabilistic nature of multichannel data do not necessarily hold. Multivariate spatial sign and rank functions, which are generalizations of univariate sign and centered rank, are introduced. Furthermore, spatial rank covariance matrix and spatial Kendall’s tau covariance matrix based new robust covariance matrix estimators are proposed. Efficiency of the estimators is discussed and their qualitative robustness is demonstrated using a empirical influence function concept. The use and reliable performance of the proposed methods is demonstrated in color image filtering, image analysis, principal component analysis and blind source separation tasks.