[Eeglablist] ICA and phase

[Nicholas Rosseinsky]

Georges,

1. When you start with neural data, and then add in artefact, the original
neural signal is "distorted". For example, at time t, the STFT of
neural+artefact data will have a different phase angle, phi-dashed say,
than the STFT of neural data, whose phase is phi say, at t. STFT of EEG
data will give phi-dashed; STFT of EEG-after-ICA-artefact-removal will give
phi (to first order). So the first-order phase "distortion" is not a phase
distortion, it is the *removal of a distortion* introduced by mixing neural
and artefactual signals.

2. I'm not sure about your "weighted linear interpolation" point. If ICA
isolates the artefacts perfectly, what's left is the neural data.

3. The only problem occurs when there is some neural data mixed in with an
ICA "artefact". (Note: this usually only occurs for low channel-number
recordings e.g. 20 electrode-systems.) In this case, one might want to try
to further separate the mainly-artefactual component into
really-artefactual and likely-neural. Here are two papers that describe how
to do this:

Barbati, Giulia, et al. "Optimization of an independent component analysis
approach for artifact identification and removal in magnetoencephalographic
signals." *Clinical Neurophysiology* 115.5 (2004): 1220-1232.

Lindsen, J. P., & Bhattacharya, J. (2010). "Correction of blink artifacts
using independent component analysis and empirical mode decomposition."
*Psychophysiology*, *47*(5), 955-960

4. I read the Montefusco paper to say there is NO phase distortion problem
with ICA, for all practical purposes. First, the simulation set-ups seem
very unfavorable. Next, they do *not* apply either of the methods under (3)
above. Then, (if I read their axes correctly), they identify a "phase
distortion" worst-case that is the equivalent of 1ms time delay at 10Hz,
for which 1ms is 1/100 of a cycle or about 4 degrees (0.06 radian). This is
"not nothing" - but generally we are interested in identifying phase-locked
from non-phase-locked dynamics: adding 4 degree jitter to a randomly
selected subset of trials will *of course* make the
phase-locked/non-phase-locked discrimination harder. If the jitter were
anything from 0 to 180 degrees, then it would be a different matter. (e.g.
at 500Hz, 1 ms *is *a problem ...)

5. There is no way to avoid losing information when removing noise, unless
you have a perfect model of the noise source (or the data). ICA artefact
removal is one of the better choices you can make:

Hoffmann, Sven, and Michael Falkenstein. "The correction of eye blink
artefacts in the EEG: a comparison of two prominent methods." *PLoS One* 3.8
(2008): e3004.

If you use the methods under 3 above, it's as good as it gets, as far as I
know. Any listers with more info, please weigh in.

6. Concerning stationarity, I'm not sure what your point is. Eye-blinks are
non-stationary: they occur at stochastic intervals. The mixing of neural
and artefactual data (point 3 above) will not be predictable, because it
involves ICA decomposition of artefact mixed with different neural dynamics
(ie those occurring at the time of the eye-blink); if each blink was itself
stereotypical, and occurred against the same neural state, then, sure, the
second-order distortion effect (point 3) would be "stationary" (replicable,
predictable). But that's not the situation, and not to be expected.

7. I think it's less of a problem than you think. Try this - PART 1: get
some data; ICA unmix it, removing eyeblinks; run whatever phase-analysis
you are interested in on the non-artefactual, neural, data; PART 2: re-mix
the neural data, *adding in randomly-timed eye-blinks by using artefact
time-series you isolated in Part 1*; then unmix again, discard eye-blinks,
and re-rerun your phase-analyses. This will give a heuristic estimate of
the *magnitude* of eyeblink "phase distortion" problems (i.e. point-3-style
errors)  for whatever analysis you are working on. I'll bet you dinner that
this magnitude turns out to be not-the-largest-source-of-noise in your
overall analysis :)

Hope that helps
Nicholas

PS my bet is based on your data using at least 20 electrodes. Certainly, if
you are using less than one, eye-blinks could be your *joint*-biggest
problem :)






Hope that helps.
Best,
Nicholas
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