FastICA: The Most Classic Fixed-Point Algorithm in Blind Source Separation

In the field of signal processing, blind source separation represents a significant research topic. Among the most classical algorithms is FastICA, which is grounded in the theoretical framework of independent component analysis. This algorithm enables the recovery of source signals without prior knowledge of either the source signals or the mixing matrix through computational methods. The FastICA algorithm is particularly user-friendly for beginners due to its simplicity and ease of implementation. Key implementation steps typically involve signal whitening (using eigenvalue decomposition), optimization of non-Gaussianity through contrast functions (e.g., kurtosis or negentropy), and fixed-point iteration using the Newton-Raphson method for rapid convergence. Beyond FastICA, other blind source separation algorithms such as JADE (Joint Approximate Diagonalization of Eigenmatrices) and SOBI (Second-Order Blind Identification) offer alternative approaches, each with distinct advantages and limitations. JADE utilizes higher-order statistics through joint diagonalization of cumulant matrices, while SOBI leverages time-delayed correlations for separation. The choice of algorithm depends on specific application requirements, including signal characteristics and computational constraints. In practical applications, blind source separation algorithms find extensive use across signal processing, image processing, and speech processing domains, demonstrating broad prospects for real-world implementations such as EEG signal decomposition, image feature extraction, and speech signal enhancement.