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Communication Dans Un Congrès Année : 2020

Riemannian geometry and Cramér-Rao bound for blind separation of Gaussian sources

Résumé

We consider the optimal performance of blind separation of Gaussian sources. In practice, this estimation problem is solved by a two-step procedure: estimation of a set of co-variance matrices from the observed data and approximate joint diagonalization of this set to find the unmixing matrix. Rather than studying the theoretical performance of a specific method, we are interested in the optimal attainable performance of any estimator. To do so, we consider the so-called intrinsic Cramér-Rao bound, which exploits the geometry of the parameters of the model. Unlike previous works developing a Cramér-Rao bound in this context, our solution does not require any additional hypotheses. To obtain our bound, we define and study a new Riemannian manifold holding the parameters of interest. An original estimation error measure is defined with the help of our Riemannian distance function. The corresponding Fisher information matrix is then obtained from the Fisher information metric and orthonormal bases on the tangent spaces of the manifold. Finally, our theoretical results are validated on simulated data.
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Dates et versions

hal-02571093 , version 1 (12-05-2020)

Identifiants

Citer

Florent Bouchard, Arnaud Breloy, Alexandre Renaux, Guillaume Ginolhac. Riemannian geometry and Cramér-Rao bound for blind separation of Gaussian sources. ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), May 2020, Barcelona, Spain. ⟨10.1109/icassp40776.2020.9052996⟩. ⟨hal-02571093⟩
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