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Décompositions conjointes de matrices complexes : application à la séparation de sources

Abstract : This thesis deals with the study of joint diagonalization of complex matrices methods for source separation, wether in the field of numerical telecommunications and radioastronomy. After having introduced the motivations that drove this study, we present a brief state-of-the-art in the field. The joint diagonalization and source separation problems are reminded, and a link between these two themes is established. Thereafter, several iterative algorithms are developed. First, methods using a gradient-like update of the separation matrix are introduced. They are based on wise approximations of the considered criterion. In order to improve the convergence speed, a method using a computation of an optimal step size is presented, and variations around this computation, based on the previously introduced approximations are done. Two other approaches are then introduced. The first one analytically determines the separation matrix, by algebraically computing the terms composing the update matrix pairwise from a linear equation system. The second one recursively estimates the mixing matrix, based on an alternating least squares method. In order to enhance the convergence speed, a seek of an enhanced line search algorithm is proposed. These methods are then validated on a classical joint diagonalization problem. Aterwards, these algorithms are applied to the source separation of numerical communication signals, while using second or higher order statistics. Comparisons are also made with well-known methods. The second application relates to elimination of rterrestrial interferences from the estimation of the associated space in order to observe at best cosmic sources from LOFAR station data.
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Submitted on : Thursday, March 7, 2013 - 5:37:52 PM
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  • HAL Id : tel-00798019, version 1


Tual Trainini. Décompositions conjointes de matrices complexes : application à la séparation de sources. Autre. Université de Toulon, 2012. Français. ⟨NNT : 2012TOUL0010⟩. ⟨tel-00798019⟩



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