Skip to Main content Skip to Navigation
Journal articles

Blind Identification of Under-Determined Mixtures based on the Characteristic Function

Abstract : Linear Mixtures of independent random variables (the so-called sources) are sometimes referred to as Under-Determined Mixtures (UDM) when the number of sources exceeds the dimension of the observation space. The algorithms proposed are able to identify algebraically a UDM using the second characteristic function (c.f.) of the observations, without any need of sparsity assumption on sources. In fact, by taking high-order derivatives of the multivariate c.f. core equation, the Blind Identification problem is shown to reduce to a tensor decomposition. With only two sensors, the first algorithm only needs a SVD. With a larger number of sensors, the second algorithm executes an Alternating Least Squares (ALS) algorithm. The joint use of statistics of different orders is possible, and a LS solution can be computed. Identifiability conditions are stated in each of the two cases. Computer simulations eventually demonstrate performances in the absence of sparsity, and emphasize the interest in using jointly derivatives of different orders.
Complete list of metadata

Cited literature [25 references]  Display  Hide  Download
Contributor : Pierre Comon <>
Submitted on : Wednesday, March 12, 2008 - 7:21:04 PM
Last modification on : Wednesday, October 14, 2020 - 1:56:08 PM
Long-term archiving on: : Friday, May 21, 2010 - 12:23:32 AM


Files produced by the author(s)


  • HAL Id : hal-00263668, version 1



Pierre Comon, Myriam Rajih. Blind Identification of Under-Determined Mixtures based on the Characteristic Function. Signal Processing, Elsevier, 2006, 86 (9), pp.3334-3338. ⟨hal-00263668⟩



Record views


Files downloads