Tensor approximation and signal processing applications (Q2784649)

The contribution of the paper is twofold. First, it is a small tutorial on the use of tensor (i.e. multi-dimensional array) calculus in signal processing. Second, it describes an improvement of a tensor method to solve a specific blind equalization problem. NEWLINENEWLINENEWLINEThe paper is concerned with blind methods for system identification, where input signals are characterized by statistics but otherwise unknown. It is shown that solving some blind source separation problems amounts to decomposing a cumulant tensor. A standard tensor decomposition method is recalled which is a generalization of the power method and relies on the multi-dimensional singular value decomposition. In the special case of blind equalization problems, for which symmetric tensors arise, it is shown that the standard decomposition method is inefficient and lacks of a clear convergence proof. The authors then describe an enhancement of the tensor power method dealing with symmetric tensors, allowing for a general convergence proof and establishing links with already existing gradient-based super-exponential algorithms.NEWLINENEWLINEFor the entire collection see [Zbl 0972.00034].