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

This article primarily aims to unify the various formalisms of multivariate coefficients of variation, leveraging advanced concepts of generalized means, whether weighted or not, applied to the eigenvalues of covariance matrices. We highlight the existence of an infinite number of these coefficients and demonstrate that they are bounded. Moreover, 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. In this context, the coefficient of variation emerges as a key tool for detecting changes or identifying permanent scatterers, which are characterized by their remarkable temporal stability. The multidimensionality arises from the diversity of polarizations. The introduction of the various possible coefficients demonstrates how their selection impacts the detection of samples exhibiting specific temporal behaviors and underscores the contribution of polarimetry to dynamic speckle analysis.