Biomedical Engineering Reference
In-Depth Information
domains. However, this method can be prohibitive, even for small data sets, because
of its intensive memory usage. Some modifi cations have been attempted to improve
its effi ciency; one example is the TFBSS toolbox (Févotte and Doncarli
2004
).
Reliability of ICA Estimations
One major issue in the application of ICA is that the reliability of the estimated ICs
is not known. In practice, most algorithms may give different results when run mul-
tiple times, as only the local minimum of the objective, the independence measure
to be optimized, is found in each run. One solution is to run the ICA algorithm many
times using different initial values and different bootstrapped data sets (Meinecke
et al.
2002
), which can be implemented using the ICASSO package (Himberg et al.
2004
). If an IC is reliable, the results from multiple runs should yield a cluster that
is close to the ideal component. Based on this concept, we can further evaluate the
quality of each component. The results of the implementation of ICASSO with the
FastICA algorithm on our fear recognition data are shown in Fig.
3.2
.
3.2.2
Time-Frequency Representations
When analyzing neurological signals, TFRs are useful for investigating spectral
contents in addition to studying changes in its time domain features. Two TFRs are
widely used in the analysis of ECoG signals: the spectrogram [the squared magni-
tude of the short-time Fourier transform (STFT)] and the scalogram [the squared
magnitude of the continuous wavelet transform (CWT)].
For the spectrogram, STFT modulates the signal with a window function, com-
monly a Hann window, before performing the Fourier transform to obtain the fre-
quency content in the region of the window. This method is straightforward but has
its own drawbacks of leakage effects and limitation of uniform resolution. Spectral
leakage, which causes false frequency components, could be reduced by imple-
menting the multitaper method, which reduces estimation bias by obtaining multi-
ple independent estimates from the same sample (Thomson
1982
); this can be
implemented using the Chronux library (Bokil et al.
2010
). Furthermore, the
constant-length windows used in STFT result in a uniform partition in the spectro-
gram, which limits the analysis to a single resolution for the complete signal. This
can be problematic, as most of the signals of practical interest have high-frequency
components for short durations and low-frequency components for long durations.
In this aspect, multiresolution TFR, such as the scalogram, is more desirable.
For the scalogram, CWT uses short windows at high frequencies and long win-
dows at low frequencies and is more suitable for the analysis of nonstationary sig-
nals than is the STFT-based spectrogram (Huang et al.
1998
; Mallat
1989
). A brief
overview of a wavelet-based time-scale analysis of biological signals is given in
(Thakor and Sherman
1995
). Scalogram calculation can be implemented using the
Time-Frequency Toolbox developed by CNRS (Auger et al.
1999
).
