Frontmatter

Independent component analysis (ICA) is a well-known technique for blind source separation (BSS) based on higher-order statistics. Assuming the sources are independent, the fact that the sources can be uniquely recovered is a consequence of the unicity the canonical polyadic decomposition (CPD), a decomposition of a tensor in rank-one terms. Contrary to matrix decompositions, tensor decompositions can be unique without imposing additional constraints such as orthogonality or nonnegativity. Block component analysis (BCA) is an entirely new technique for BSS and factor analysis which also exploits the unicity of tensor decompositions, but does not make the assumption that the sources should be statistically independent. In this poster, we explain how BCA works and how to compute the associated block term decompositions (BTD). The latter is a generalization of the CPD and multilinear SVD (MLSVD), which are in turn the two most prominent generalizations of the matrix SVD to tensors. Block term decompositions can be formulated as nonlinear optimization problems in which the objective function is not analytic in its complex variables. We generalized several well-known unconstrained optimization methods such as (L-)BFGS, NCG and nonlinear least squares methods such as Levenberg-Marquardt to this class of problems and applied them to compute a certain type of BTD. In the nonlinear least squares methods, we exploited the problem's structure, which resulted in some of the most efficient algorithms for BTDs to date.status: publishe

Séparation aveugle de signaux de type DS-CDMA à l'aide de techniques algébriques

Nous avons établi une nouvelle borne sur le nombre d'utilisateurs dans une cellule beaucoup moins contraignante que la borne actuelle. Nous proposons un algorithme pour résoudre le problème de l'extraction de signaux CDMA qui s'appuie sur la resolution d'un système de matrices à diagonaliser conjointement. Par ailleurs, dans le cas où les symboles d'information appartiennent à une constellation circulaire, nous avons constaté qu'il était possible de combiner la structure des données CDMA avec la propriété du module constant. Nous avons développé deux techniques à cet effet