Blind source extraction in various ill-conditioned cases

The paper discusses blind source extraction in various ill-conditioned cases based on a simple extraction network model. Extractability is first analyzed for the following ill-conditioned cases: the mixing matrix is square but-singular; the number of sensors is smaller than that of sources; the number of sensors is larger than that of sources, but the column rank of the mixing matrix is deficient; the number of sources is unknown and the column rank of the mixing matrix is deficient. A necessary and sufficient condition for extractability is obtained. A cost function and an unsupervised learning algorithm for the extraction network model are developed. Simulation results are also presented to show the validity of the theoretical results and the performance and characteristics of the learning algorithm.