Mathematics in Independent Component Analysis

286 Chapter 20. Signal Processing 86(3):603-623, 2006
small errors in the independence assumption — and how they can deal with
additional noise.
In the first example of artificially created mixtures, we are able to demonstrate
that a decomposition analysis using the three models was possible, and give
comparisons over larger data sets. Although the recovered sources are all rather
alike, Fig. 5 and Fig. 7, we found that ICA outperformed the other methods
concerning distance to the real solution, which was mainly due to the fact that
the artificial sources — but not in the case of real signals, see below — best
fitted to the ICA model, Tab. 2. However, when considering additional noise
with increasing power, sparse NMF turned out to be more robust than the
ICA model, Fig. 8.
We then applied the BSS methods to real s-EMG data sets, and the three
different models yielded surprisingly similar results, although in theory these
models do not fully overlap. We speculate that this similarity is due to the
fact that — as most probably in all applications — the models do not fully
hold. This allows the various algorithms to only approximate the model solutions,
and hence to arrive at similar solutions, but from different directions.
Furthermore, this indicates that the three models look for different properties
of the sources, and that these properties are fulfilled to varying extent, see
Tab. 3 for numerical details. Comparisons over s-EMG data sets from multiple
subjects again confirmed similar equality of performance, where again
sparse NMF slightly outperformed the other algorithms in the mean (in nice
correspondence with the noise result from above).
Note that the aim of the present work is not the full recovery of a target
MUAPT (source signal) in its original form. In fact, as shown previously [18],
it would be sufficient to increase the amplitude a target MUAPT so that in
average it is above the noise and above the other MUAPTs level. Then, we
are able to cut the interfering signals with a modified dead zone filter and
thus isolating the target MUAPT. And indeed all of the employed sparse BSS
methods fulfill this requirement, which is confirmed by the decrease in the
number of zero-crossings of the separated signals, see Tab. 4.
5 Conclusion
We have compared the effectiveness of various sparse BSS methods for signal
decomposition; namely, ICA, NMF, sparse NMF and SCA, when applied to
s-EMG signals. Surface EMG signals represent an attractive testing signal as
they approximately fulfill all the requirements of these methods and are of
major importance in medical diagnosis and basic neurophysiological research.
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