Independent Component Analysis Using Maximum Negentropy Method

The MATLAB implementation of maximum negentropy-based Independent Component Analysis (ICA) has been widely applied in signal processing domains. This method's primary advantage lies in its ability to separate mixed signals into distinct independent components, making it suitable for various applications such as image processing and speech recognition. In our implementation, we employed orthogonalization processing to ensure simultaneous separation of all independent components under ideal noise-free conditions. The algorithm utilizes numerical optimization techniques to maximize negentropy, typically implemented using Newton-type iterations or fixed-point algorithms. Key computational steps include estimating the score function and handling the Hessian matrix for efficient convergence. Additionally, we incorporated standard preprocessing techniques including whitening (via eigenvalue decomposition of the covariance matrix) and centering (mean removal) to enhance the accuracy and reliability of separation results. The whitening process involves linear transformation using the inverse square root of the covariance matrix, while centering adjusts signals to zero mean. These preprocessing steps improve numerical stability and accelerate convergence during the optimization phase. The core implementation features functions for gradient computation, orthogonal constraint enforcement using symmetric decorrelation, and convergence monitoring through negentropy measurement changes between iterations.