A geometric approach to post nonlinear mixture in blind source separation

In this paper, a novel approach for the post nonlinear mixture blind source separation (PNL BSS) is introduced. The new approach exploits the difference between a linear and nonlinear mixture from their nature of distributions in a multi-dimensional space. The nonlinear mixture is represented by a curved surface while the linear mixture is represented by a plane. A geometric-based algorithm named as geometric post nonlinear independent component analysis (gpnlCA) is developed. This two-stage algorithm geometrically transforms the curved surface of the nonlinear mixture to a plane, i.e., a linear mixture, and then applies a normal linear ICA to extract the unknown signals. Experiments were carried out to illustrate the algorithm performance