  Independent component analysis (ICA) aims at decomposing an observed random
vector into statistically independent variables. Deflation-based
implementations, such as the popular one-unit FastICA algorithm and its
variants, extract the independent components one after another. A novel method
for deflationary ICA, referred to as RobustICA, is put forward in this paper.
This simple technique consists of performing exact line search optimization of
the kurtosis contrast function. The step size leading to the global maximum of
the contrast along the search direction is found among the roots of a
fourth-degree polynomial. This polynomial rooting can be performed
algebraically, and thus at low cost, at each iteration. Among other practical
benefits, RobustICA can avoid prewhitening and deals with real- and
complex-valued mixtures of possibly noncircular sources alike. The absence of
prewhitening improves asymptotic performance. The algorithm is robust to local
extrema and shows a very high convergence speed in terms of the computational
cost required to reach a given source extraction quality, particularly for
short data records. These features are demonstrated by a comparative numerical
analysis on synthetic data. RobustICA's capabilities in processing real-world
data involving noncircular complex strongly super-Gaussian sources are
illustrated by the biomedical problem of atrial activity (AA) extraction in
atrial fibrillation (AF) electrocardiograms (ECGs), where it outperforms an
alternative ICA-based technique.
