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We develop the information geometry of scaled Gaussian distributions forwhich the covariance matrix exhibits a Kronecker product structure. This modeland its geometry are then used to propose an online change detection (CD)algorithm for multivariate image times series (MITS). The proposed approachrelies mainly on the online estimation of the structured covariance matrixunder the null hypothesis, which is performed through a recursive (natural)Riemannian gradient descent. This approach exhibits a practical interestcompared to the corresponding offline version, as its computational costremains constant for each new image added in the time series. Simulations showthat the proposed recursive estimators reach the Intrinsic Cram\'er-Rao bound.The interest of the proposed online CD approach is demonstrated on bothsimulated and real data.

Online Change Detection in SAR Time-Series with Kronecker Product Structured Scaled Gaussian Models