Geometric Concept-Driven Blind Source Separation: Comparative Analysis of Analytical and Optimization Methods for Determining Separation Angles

This paper introduces a novel approach to Blind Source Separation (BSS) for instantaneous linear mixtures, leveraging geometric principles to recover statistically independent source signals. The separation process begins by decorrelating mixed signals to obtain whitened signals, followed by an algorithm that optimally determines rotation angles. We compare three methods: genetic optimization for identifying optimal rotation angles, and two proposed analytical approaches—kurtosis maximization and cross-cumulant minimization. Our comparative analysis demonstrates that effective separation can be achieved by processing each pair of whitened signals independently. Further, a single statistical independence criterion, whether based on kurtosis or cross-cumulants, is sufficient to determine accurate separation angles, resulting in precise and computationally efficient separation, especially compared to genetic optimization.