We develop a new geometric approach for high resolution Doppler processing based on the
Riemannian geometry of Toeplitz covariance matrices and the notion of Riemannian p …

Abstract Information Geometry has been introduced by Rao, and axiomatized by Chentsov,
to define a distance between statistical distributions that is invariant to non-singular …

Abstract Main issue of High Resolution Doppler Imagery is related to robust statistical
estimation of Toeplitz Hermitian positive definite covariance matrices of sensor data time …

This paper is a short summary of our recent work on the medians and means of probability
measures in Riemannian manifolds. Firstly, the existence and uniqueness results of local …

When performing statistics on elements of sets that possess a particular geometric structure,
it is desirable to respect this structure. For instance in a Lie group, it would be judicious to …

In this paper, we define the geometric median for a probability measure on a Riemannian
manifold, give its characterization and a natural condition to ensure its uniqueness. In order …

Consider a probability measure μ supported by a regular geodesic ball in a manifold. For
any p≥ 1 we define a stochastic algorithm which converges almost surely to the p-mean ep …

The asymptotic concentration of the Fr {\'e} chet mean of IID random variables on a Rieman-
nian manifold was established with a central limit theorem by Bhattacharya\& Patrangenaru …

We develop the theory of discrete-time gradient flows for convex functions on Alexandrov
spaces with arbitrary upper or lower curvature bounds. We employ different resolvent maps …

We develop a new geometric approach for radar target detection which is based on the
notion of Riemannian median and the information geometry of covariance matrices. First of …