A Kurtosis-based Algorithm for Blind Sources Separation Using the Cayley Transformation And Its Application to Multi-channel Electrogastrograms

This paper presents a new kurtosis-based algorithm for blind separation of convolutively mixed source signals. The algorithm whitens the signals not only spatially but also temporally beforehand. A separator is built for the whitened signals and it exists in the set of para-unitary matrices. Since the set forms a curved manifold, it is hard to treat its elements. In order to avoid the difficulty, this paper introduces the Cayley transformation for the para-unitary matrices. The transformed matrix is referred to as para-skew-Hermitian matrix and the set of such matrices forms a linear space. In the set of all para-skew-Hermitian matrices, the kurtosis-based algorithm obtains a desired separator. This paper also shows the algorithm's application to electrogastrogram datum which are observed by 4 electrodes on subjects' abdomen around their stomachs. An electrogastrogram contains signals from a stomach and other organs. This paper obtains independent components by the algorithm and then extracts the signal corresponding to the stomach from the data.