A least squares algorithm for global joint decomposition of complex matrix sets

This paper deals with a new approach for the joint decomposition of complex matrix sets. Such problems arise naturally in various signal processing problems, among which the blind source separation one. The suggested algorithm is based on an Alternating Least Square (ALS) optimization procedure. An improved version is also proposed including a global Enhanced Line Search (ELS) in the recursive procedure. In practice, the main interest of our approach is to take advantage of a greater amount of signal information within the same context, since sets of Hermitian and symmetric complex matrices are combined altogether. Simulations are performed to highlight the advantages of this method as compared to other existing algorithms.