A Soft-Constrained Dynamic Iterative Method of Blind Source Separation
Jie Liu, Jack X. Xin, Yingyong Qi · Multiscale Modeling and Simulation · 2009
The blind source separation problem arises when one attempts to recover source signals from their linear mixtures without detailed knowledge of the mixing process. Solutions are nonunique and have degrees of freedom in scaling and permutation. One may impose equality (hard) constraints to fix these scaling parameters; however, small divisor problems may appear. In this paper, an iterative method is introduced based on information maximization and auxiliary equations for the scaling parameters. The method dynamically selects scaling parameters and avoids divisions, and it is called the soft-constrained method. Global boundedness of the algorithm is proved. The convergence of solutions in the large time and small step size regimes is analyzed. An upscaled, dynamically averaged equation for the separating matrix is derived. The stable and accurate separation performance is illustrated by examples of instantaneous random mixtures of two and eight sound signals.