ICASSP '98. Multidimensional independent component analysis.

In this ICASSP '98 paper, I suggest extending the idea independent component analysis (ICA) to a more general idea of multidimensional independent component analysis (MICA). This idea comes to mind very naturally when processing ECG recordings from a pregnant woman. The source separation task consists in separating the maternal signal and the fetal signal: a straightforward application of a source separation algorithm reveals that the maternal ECG signal and/or the fetal ECG signal behave as multidimensional components. This fact is probably known since the work of Widrow (LMS-based signal subtraction for extracting the fetal ECG). In the context of ICA/source separation, it is well documented in the 1995 paper Fetal electrocardiogram extraction by source subspace separation by De Lathauwer et al. which also points out the relevance of the notion of subspace associated to each component.

This page points to some Matlab code allowing to reproduce the experiment on a restricted data set as reported in the paper and to make another, even more convincing experiment, on the whole data set.

If you do not want to run the code for this last experiment and are only interested in checking the results of the MICA analysis on the whole data set, take a look at this figure (postscript file) which is in the same spirit as the figure of the ICASSP paper.

To run the experiments using Matlab, you need the following files:

• The data set. We do not feel untitled to distribute the ECG data set ourselves because it comes from the DAISY database (Database for the Identification of Systems). You can get to the home page of DAISY and find your way to the files referenced [96-012] (Cutaneous potential recordings of a pregnant woman) or access these files directly: you need the data set itself and you should check this brief description of it, which includes credits and references.

• The JADE algorithm for ICA. You can use this implementation for real signals (version 1.5). Ideally, any implementation could be used but because the demo program is rudimentary (it does not associate automatically the various parts of a multidimensional component), it has to rely on the particular ordering of the sources signals as returned by JADE 1.5. Therefore a correct demo is not guaranteed if an other implementation of JADE is used.

• Demo front end programs. We make available two demo programs.
  • The first one allows you to reproduce the experiment which appeared in the ICASSP'98 paper. In the ICASSP paper, due to space limitations, the analysis is restricted to processing the ouputs of 3 ECG sensors out of 8.

  • The second front end program yields even cleaner results. We perform a MICA analysis using the whole set of 8 sensors. In this case, it is found that the maternal component should be alloted a dimension of 4, that the fetal component should be alloted a dimension of 2 and that two extra dimensions are essentially inhabited by noise. Check it out!