A re-derivation of the nc-FastICA optimization algorithm using generalized linear transform

Source abstract

Independent Component Analysis (ICA) is a cornerstone technique in blind source separation, with significant applications in signal processing fields such as telecommunications and radar systems. For complex-valued signals, the FastICA algorithm has two prominent variants: c-FastICA, which assumes signal circularity, and nc-FastICA, which accommodates non-circular signals. This paper presents a re-derivation of the nc-FastICA algorithm using a generalized linear transform, also termed a linear-conjugate-linear transform, enhanced by Wirtinger calculus and augmented vector representations. We provide a comprehensive theoretical framework, including detailed mathematical derivations and proofs, and demonstrate how this formulation naturally degenerates to c-FastICA under circularity assumptions. This unification enhances the theoretical understanding and practical applicability of complex-valued ICA.