Blind Identification and Separation of Complex-valued Signals

Blind identification consists of estimating a multi-dimensionalsystem only through the use of its output, and source separation,the blind estimation of the inverse of the system. Estimation isgenerally carried out using different statistics of theoutput.The authors of this book consider the blind identification andsource separation problem in the complex-domain, where theavailable statistical properties are richer and includenon-circularity of the sources - underlying components. Theydefine identifiability conditions and present state-of-the-artalgorithms that are based on algebraic methods as well as iterativealgorithms based on maximum likelihood theory.Contents1. Mathematical Preliminaries.2. Estimation by Joint Diagonalization.3. Maximum Likelihood ICA.About the AuthorsEric Moreau is Professor of Electrical Engineering at theUniversity of Toulon, France. His research interests concernstatistical signal processing, high order statistics andmatrix/tensor decompositions with applications to data analysis,telecommunications and radar.Tülay Adali is Professor of Electrical Engineering andDirector of the Machine Learning for Signal Processing Laboratoryat the University of Maryland, Baltimore County, USA. Her researchinterests concern statistical and adaptive signal processing, withan emphasis on nonlinear and complex-valued signal processing, andapplications in biomedical data analysis and communications.Blind identification consists of estimating a multidimensionalsystem through the use of only its output. Source separation isconcerned with the blind estimation of the inverse of the system.The estimation is generally performed by using different statisticsof the outputs.The authors consider the blind estimation of a multipleinput/multiple output (MIMO) system that mixes a number ofunderlying signals of interest called sources. They alsoconsider the case of direct estimation of the inverse system forthe purpose of source separation. They then describe the estimationtheory associated with the identifiability conditions and dedicatedalgebraic algorithms. The algorithms depend critically on(statistical and/or time frequency) properties of complex sourcesthat will be precisely described.