Complex-Valued FastICA Estimator with a Weighted Unitary Constraint: A Robust and Equivariant Estimator

Abstract

Independent component analysis (ICA), as a statistical and computational approach, has been successfully applied to digital signal processing. Performance analysis for the ICA approach is perceived as a challenging task to work on. This contribution concerns the complex-valued FastICA algorithm in the range of ICA over the complex number domain. The focus is on the robust and equivariant behavior analysis of the complex-valued FastICA estimator. Although the complex-valued FastICA algorithm as well as its derivatives have been widely used methods for approaching the complex blind signal separation problem, rigorous mathematical treatments of the robust measurement and equivariance for the complex-valued FastICA estimator are still missing. This paper strictly analyzes the robustness against outliers and separation performance depending on the global system. We begin with defining the influence function (IF) of complex-valued FastICA functional and followed by deriving its closed-form expression. Then, we prove that the complex-valued FastICA algorithm based on the optimizing cost function is linear-equivariant, depending only on the source signals.