Algorithms for Blind Source Separation

Recently, I have studied several blind source separation algorithms based on the maximum entropy principle. Blind source separation represents a fundamental challenge in signal processing, addressing the recovery of source signals from mixed observations. The maximum entropy principle serves as a widely-adopted mathematical framework for such separation problems, advocating for the selection of probability distributions that maximize uniformity under maximum uncertainty conditions. Consequently, blind source separation algorithms leveraging this principle demonstrate enhanced capability in preserving signal information while improving separation accuracy. From an implementation perspective, these algorithms typically employ gradient ascent optimization to maximize entropy objectives, often utilizing nonlinear functions like hyperbolic tangent (tanh) as activation functions in the separation model. Key computational steps involve whitening preprocessing through eigenvalue decomposition, followed by iterative weight updates using natural gradient methods to achieve statistical independence between recovered sources.