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A new Riemannian geometry for the Compound Gaussian distribution is proposed.In particular, the Fisher information metric is obtained, along withcorresponding geodesics and distance function. This new geometry is applied ona change detection problem on Multivariate Image Times Series: a recursiveapproach based on Riemannian optimization is developed. As shown on simulateddata, it allows to reach optimal performance while being computationally moreefficient.

Riemannian geometry for Compound Gaussian distributions: application to recursive change detection