  Here, a separation theorem about Independent Subspace Analysis (ISA), a
generalization of Independent Component Analysis (ICA) is proven. According to
the theorem, ISA estimation can be executed in two steps under certain
conditions. In the first step, 1-dimensional ICA estimation is executed. In the
second step, optimal permutation of the ICA elements is searched for. We
present sufficient conditions for the ISA Separation Theorem. Namely, we shall
show that (i) elliptically symmetric sources, (ii) 2-dimensional sources
invariant to 90 degree rotation, among others, satisfy the conditions of the
theorem.
