Hatem Hajri

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The Riemannian geometry of the space Pm, of m × m symmetric positive definite matrices, has provided effective tools to the fields of medical imaging, computer vision and radar signal processing. Still, an open challenge remains, which consists of extending these tools to correctly handle the presence of outliers (or abnormal data), arising from excessive(More)
In a previous work, we have defined a Tanaka’s SDE related to Walsh Brownian motion which depends on kernels. It was shown that there are only one Wiener solution and only one flow of mappings solving this equation. In the terminology of Le Jan and Raimond, these are respectively the stronger and the weaker among all solutions. In this paper, we obtain(More)
1. Itô’s formula for Walsh’s Brownian motion Let E = R2; we will use polar co-ordinates (r, α) to denote points in E. We denote by C(E) the space of all continuous functions on E. For f ∈ C(E), we define fα(r) = f (r, α), r > 0, α ∈ [0, 2π [. Throughout this paper we fix μ a probability measure on [0, 2π [, also we define f (r) =  2π 0 f (r, α) μ(dα), r >(More)
This letter introduces a new robust estimation method for the central value of a set of N covariance matrices. This estimator, called Huber's centroid, is described starting from the expression of two well-known methods that are the center of mass and the median. In addition, a computation algorithm based on the gradient descent is proposed. Moreover,(More)
We study a simple stochastic differential equation (SDE) driven by one Brownian motion on a general oriented metric graph whose solutions are stochastic flows of kernels. Under some conditions, we describe the laws of all solutions. This work is a natural continuation of [17, 8, 10] where some particular metric graphs were considered.
Csáki and Vincze have defined in 1961 a discrete transformation T which applies to simple random walks and is measure preserving. In this paper, we are interested in ergodic and asymptotic properties of T . We prove that T is exact: ∩ k=1 σ(T (S)) is trivial for each simple random walk S and give a precise description of the lost information at each step k.(More)
Many signal and image processing applications, including SAR polarimetry and texture analysis, require the classification of complex covariance matrices. The present paper introduces a geometric learning approach on the space of complex covariance matrices based on a new distribution called Riemannian Gaussian distribution. The proposed distribution has two(More)
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