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Theses

Séparation aveugle de mélanges linéaires convolutifs de sources corrélées

Abstract : In this thesis, we study the problem of the blind separation of over-determined linear convolutive real or complex mixtures of deterministic or random, statistically independent or correlated, stationary, cyclo-stationary or non-stationary and real or complex sources. We have developed approaches that combine the new (non-unitary) joint (block) diagonalization to two novel detectors of particular points to build the matrices set to be joint (block) diagonalized. The main avantages of the proposed approaches are that they are more direct since they do not require a pre-whitening stage any more and that they can be used with correlated signals. Concerning the joint lock-diagonalization algorithms, we have proposed four joint block-diagonalization algoritms. The first algorithm is iterative and based on an algebraic optimization scheme. The three other ones are based on gradient approaches. The first one relies upon a gradient approach, but the matrix gradient is approximated, whereas the two other ones are based on an exact calculus (one is based on the gradient approach, the other is based on the relative gradient approach). The optimal step size versions of these three algorithms is provided to accelerate their convergence. It means that the step size is computed algebraically at each iteration as the rooting of a 3rd-degree polynomial. The main advantage of the proposed algorithms is that they are more general (the real, positive definite or hermitian assumptions about the matrices belonging to the considered set are no more necessary and the found joint block diagonalizer can be either a unitary or a non-unitary matrix). They can also be applied to solve the joint diagonalization problem.
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Submitted on : Tuesday, September 30, 2008 - 4:52:46 PM
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Hicham Ghennioui. Séparation aveugle de mélanges linéaires convolutifs de sources corrélées. Traitement du signal et de l'image [eess.SP]. Université du Sud Toulon Var, 2008. Français. ⟨tel-00325910⟩

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