Blind Identification and Separation of Complex-valued Signals (ePub)

Blind identification consists of estimating a multi-dimensional
system only through the use of its output, and source separation,
the blind estimation of the inverse of the system. Estimation is
generally carried out using different statistics of the
output.

The authors of this book consider the blind identification and
source separation problem in the complex-domain, where the
available statistical properties are richer and include
non-circularity of the sources - underlying components. They
define identifiability conditions and present state-of-the-art
algorithms that are based on algebraic methods as well as iterative
algorithms based on maximum likelihood theory.

Contents

1. Mathematical Preliminaries.

2. Estimation by Joint Diagonalization.

3. Maximum Likelihood ICA.

About the Authors

Eric Moreau is Professor of Electrical Engineering at the
University of Toulon, France. His research interests concern
statistical signal processing, high order statistics and
matrix/tensor decompositions with applications to data analysis,
telecommunications and radar.

Tülay Adali is Professor of Electrical Engineering and
Director of the Machine Learning for Signal Processing Laboratory
at the University of Maryland, Baltimore County, USA. Her research
interests concern statistical and adaptive signal processing, with
an emphasis on nonlinear and complex-valued signal processing, and
applications in biomedical data analysis and communications.
Blind identification consists of estimating a multidimensional
system through the use of only its output. Source separation is
concerned with the blind estimation of the inverse of the system.
The estimation is generally performed by using different statistics
of the outputs.

The authors consider the blind estimation of a multiple
input/multiple output (MIMO) system that mixes a number of
underlying signals of interest called sources. They also
consider the case of direct estimation of the inverse system for
the purpose of source separation. They then describe the estimation
theory associated with the identifiability conditions and dedicated
algebraic algorithms. The algorithms depend critically on
(statistical and/or time frequency) properties of complex sources
that will be precisely described.