Blind Source Separation with Relative Newton Method

We study a relative optimization framework for the quasimaximum likelihood blind source separation and relative Newton method as its particular instance. Convergence of the Newton method is stabilized by the line search and by the modification of the Hessian, which forces its positive definiteness. The structure of the Hessian allows fast approximate inversion. We demonstrate the efficiency of the presented approach on example of sparse sources. The nonlinearity in this case is based on smooth approximation of the absolute value function. Sequential optimization with the gradual reduction of the smoothing parameter leads to the super-efficient separation.