Elias' Article

Decomposing tensors with structured matrix factors reduces to rank-1 approximations.
Pierre Comon, Mikael Sørensen, and Elias P. Tsigaridas.
In 35th Int. Conf. on Acoustics, Speech, and Signal Processing (ICASSP), pp. 3858–3861, Dallas, USA, March 2010.

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Abstract:

Tensor decompositions are now known to permit to estimate in a deterministic way the parameters in a multi-linear model. Applications have been already pointed out in antenna array processing and digital communications, among others, and are extremely attractive provided some diversity at the receiver is available. Non iterative algorithms are proposed in this paper to compute the required tensor decomposition into a sum of rank-1 terms when some factor matrices enjoy some structure, such as block-Hankel, triangular, band, etc. The only condition is that the number of parameters characterizing the structure of a matrix should be significantly smaller than the number of its entries.

@InProceedings{cst-icassp-2010,
  author =       {Pierre Comon and Mikael S{\o}rensen and
                  Elias~P. Tsigaridas},
  title =        {Decomposing tensors with structured matrix factors
                  reduces to rank-1 approximations},
  booktitle =    {35th Int. Conf. on Acoustics, Speech, and Signal
                  Processing (ICASSP)},
  pages =        "3858--3861",
  month =        "March",
  year =         2010,
  address =      {Dallas, USA},
  abstract =     "Tensor decompositions are now known to permit to
                  estimate in a deterministic way the parameters in a
                  multi-linear model. Applications have been already
                  pointed out in antenna array processing and digital
                  communications, among others, and are extremely
                  attractive provided some diversity at the receiver
                  is available. Non iterative algorithms are proposed
                  in this paper to compute the required tensor
                  decomposition into a sum of rank-1 terms when some
                  factor matrices enjoy some structure, such as
                  block-Hankel, triangular, band, etc.  The only
                  condition is that the number of parameters
                  characterizing the structure of a matrix should be
                  significantly smaller than the number of its
                  entries.",
}

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