Towards a Unified Formalism of Multivariate Coefficients of Variation: Application to the Analysis of Polarimetric Speckle Time Series

The main aim of this article is to unify the different formalisms of multivariate coefficients of variation, based on the advanced concepts of generalized averages - weighted or unweighted - applied to the eigenvalues of covariance matrices. We highlight the existence of an infinite number of these coefficients and demonstrate that they are bounded. Furthermore, we link the various coefficients of variation identified in the literature to specific instances within our unified formalism. We illustrate the utility of our method by applying it to a time series of polarimetric radar imagery, where the coefficient of variation emerges as a key tool for detecting changes or identifying permanent scatterers characterized by remarkable temporal stability. Multidimensionality arises from the diversity of polarizations. The introduction of various possible coefficients shows how their selection impacts the detection of samples exhibiting specific temporal behaviors, underlining the contribution of polarimetry to dynamic speckle analysis.