Complex valued robust multidimensional SOBI

Complex valued random variables and time series are common in various applications, for example in wireless communications, radar applications and magnetic resonance imaging. These applications often involve the famous blind source separation problem. However, the observations rarely fully follow specific models and robust methods that allow deviations from the model assumptions and endure outliers are required. We propose a new algorithm, robust multidimensional eSAMSOBI, for complex valued blind source separation. The algorithm takes into account possible multidimensional spatial or temporal dependencies, whereas traditional SOBI-like procedures only consider dependencies in a single direction. In applications like functional magnetic resonance imaging, the dependencies are indeed not only one-dimensional. We provide a simulation study with complex valued data to illustrate the better performance of the methods that utilize multidimensional autocovariance in the presence of two-dimensional dependency. Moreover, we also examine the performance of the multidimensional eSAM-SOBI in the presence of outliers.