Second-order tensor-based convolutive ICA: Deconvolution versus tensorization

Independent component analysis (ICA) research has been driven by various applications in biomedical signal separation, telecommunications, speech analysis, and more. One particular class of algorithms for instantaneous ICA uses tensors, which have useful properties. In an attempt to port these properties to convolutive methods, we zoom in on an existing method that uses second-order statistics. By pointing out links in the literature, we show that this method is in fact a typical tensor-based method, even though this was not recognized by the authors at the time. The existing method mentioned above can be interpreted as a tensorization step followed by a deconvolution step. However, as sometimes done in literature, one may consider using the opposite approach; starting with a deconvolution step and then tensorizing the remaining instantaneous mixture. Because subspace-based deconvolution can be slow, we propose a fast variant which uses only partial information. We then use this variant to compare the approach starting with tensorization and the one starting with deconvolution.