Blind signal separation into groups of dependent signals using joint block diagonalization

Multidimensional or group independent component analysis describes the task of transforming a multivariate observed sensor signal such that groups of the transformed signal components are mutually independent - however dependencies within the groups are still allowed. This generalization of independent component analysis (ICA) allows for weakening the sometimes too strict assumption of independence in ICA. It has potential applications in various fields such as ECG, fMRI analysis or convolutive ICA. Recently we could calculate the indeterminacies of group ICA, which finally enables us, also theoretically, to apply group ICA to solve blind source separation (BSS) problems. In this paper we introduce and discuss various algorithms for separating signals into groups of dependent signals. The algorithms are based on joint block diagonalization of sets of matrices generated using several signal structures.