Post nonlinear blind source separation by geometric linearization

Abstract

We present a novel geometric approach to the popular post nonlinear (PNL) BSS problem. A PNL mixing system includes two stages: a linear mixing followed by a nonlinear transformation. In our method, the process to linearize the nonlinear observed signals, the most critical task in PNL model, is carried out by a geometric transformation. The basic idea is that in a multi-dimensional space, a PNL mixture is represented by a nonlinear surface while a linear mixture is represented by a plane. Thus, by transforming a PNL's representing nonlinear surface to a plane, the PNL mixture can be linearized. The hidden sources are then estimated from linearized signals by a linear BSS algorithm. Experiments show promising performance of our approach.