Content of the meeting ( in room Chartreuse, at 1:30 pm )
– Scientific talk
– Presentation of newcomers (Victor, Alexandre, Saeed and Elsa)
– Drink with the traditional king pie (at about 2:45 pm)
There will be a unique talk, presented by Victor Maurandi, a new post-doc in CHESS/ViBS.
Title: ALGORITHMS FOR NON-UNITARY JOINT DIAGONALIZATION OF TENSORS. APPLICATION TO MIMO SOURCE SEPARATION IN DIGITAL TELECOMMUNICATIONS
This work develops joint diagonalization of matrices and third-order tensors methods for MIMO source separation in the field of digital telecommunications. After a state of the art, the motivations and the objectives are presented. Then the joint diagonalization and the blind source separation issues are defined and a link between both fields is established. Thereafter, five Jacobi-like iterative algorithms based on an LU parameterization are developed. For each of them, we propose to derive the diagonalization matrix by optimizing an inverse criterion. Two ways are investigated: minimizing the criterion in a direct way or assuming that we are close to a diagonalizing the elements from the considered set are almost diagonal. Regarding the parameters derivation, two strategies are implemented: one consists in estimating each parameter independently, the other consists in the independent derivation of couple of well-chosen parameters. Hence, we propose three algorithms for the joint diagonalization of symmetric complex matrices or hermitian ones. The first one relies on searching for the roots of the criterion derivative, the second one relies on a minor eigenvector research and the last one relies on a gradient descent method enhanced by computation of the optimal adaptation step. In the framework of joint diagonalization of symmetric, INDSCAL or non symmetric third-order tensors, we have developed two algorithms. For each of them, the parameters derivation is done by computing the roots of the considered criterion derivative. We also show the link between the joint diagonalization of a third-order tensor set and the canonical polyadic decomposition of a fourth-order tensor. We confront both methods through numerical simulations. The good behavior of the proposed algorithms is illustrated by means of computing simulations. Finally, they are applied to the source separation of digital telecommunication signals. The sets to diagonalize are built using high-order statistics computed from observation signals.