Change detection (CD) for remotely sensed images of the Earth has been a popular subject of study in the past decades. With the increase in the number of spatial missions with embedded synthetic aperture radar (SAR) sensors, the amount of readily available observations has now reached the "big data" era. This chapter introduces several families of elliptical distributions that can be used to model multivariate SAR images. It describes several dissimilarity functions based on covariance matrices, which are then compared for CD on the considered datasets. The chapter presents an extension of a statistical detection methodology that allows us to account for low-rank structures in the covariance matrix, whose interest is also illustrated on the real dataset. The Kullback–Leibler divergence is a popular measure between probability density functions, encountered notably in SAR change detection problems. The local covariance matrix of pixel patches appears to be relevant feature to analyze multivariate image time series.