Covariance estimation in multivariate OS-filtering

In this paper, covariance estimation and consequently reduced ordering in multivariate order statistic (OS) filters are studied. The robustness of covariance estimators is characterized by plotting the sensitivity surfaces that describe the change caused by outliers in the condition number of the covariance matrix. The efficiency of the estimators under nominal noise distribution is studied. The estimation of correlations and component variances are addressed separately through eigendecomposition of the covariance matrix. The results indicate that correlations and ratios of component variances are estimated rather accurately using robust estimators whereas a constant correction factor is often necessary to get consistent estimates, The minimum volume ellipsoid (MVE) and minimum covariance determinant (MCD) algorithms based on random sampling do not perform reliably for small sampled or when too few elemental subsets are drawn. The qualitative comparison is performed in a RGB color image filtering task. The filter employing the iterative minimum covariance determinant (IMCD) estimate preserves the edges the best whereas the M-estimator smooths out noise effectively on homogeneous regions. The robustness of the IMCD filter and the efficiency of an M-estimator can be combined using a final refinement step as in the case of S-IMCD filters