Second-Order Underdetermined Blind Source Separation for Sparse Signals

In addressing the challenge of second-order underdetermined blind source separation (UBSS) for sparse signals, an estimation method based on hyperplane normal vectors of the mixing matrix can be employed. This approach involves calculating the normal vectors to hyperplanes formed by scattered data points in the observation space, which correspond to source signal activations. Algorithmically, this can be implemented through clustering techniques (like K-means or hierarchical clustering) applied to the observation data to identify these hyperplanes. Key functions would include computing signal correlations for second-order statistics, identifying sparse components, and extracting normal vectors through eigenvector decomposition of data covariance matrices. This methodology significantly enhances separation accuracy and stability by precisely identifying mixing matrix parameters, thereby improving the recovery of original signal characteristics and information integrity.