A Class of Bounded Component Analysis Algorithms for the Separation of Both Independent and Dependent Sources

Bounded Component Analysis (BCA) is a recent approach which enables the separation of both dependent and independent signals from their mixtures. In this approach, under the practical source boundedness assumption, the widely used statistical independence assumption is replaced by a more generic domain separability assumption. This article introduces a geometric framework for the development of Bounded Component Analysis algorithms. Two main geometric objects related to the separator output samples, namely Principal Hyper-Ellipsoid and Bounding Hyper-Rectangle, are introduced. The maximization of the volume ratio of these objects, and its extensions, are introduced as relevant optimization problems for Bounded Component Analysis. The article also provides corresponding iterative algorithms for both real and complex sources. The numerical examples illustrate the potential advantage of the proposed BCA framework in terms of correlated source separation capability as well as performance improvement for short data records.