waveletswaveletswaveletswaveletswaveletswavelets

Matt Jones jonesmat at physiology.wisc.edu
Wed Oct 3 10:49:48 EST 2001


rblue at lccc.edu ("Ronald C. Blue") wrote in message news:<003501c14aa8$03c6b5c0$ce02030a at rblue>...
> Wavelet transform of the EEG reveals differences in low and high gamma
> responses to elementary visual stimuli.
> 
> http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_ui
> ds=11512377&dopt=Abstract
> 
> ---

Hi Ron,

Thanks for posting all these links to papers on the use of wavelets in
analyzing neural data.

I haven't read all the papers, but looked at several of the abstracts.
They all seem to me to be reasonable uses of wavelet transforms
applied to various temporal and spatial data series.

I'm not exactly sure why you posted them all. Perhaps to help educate
us about what wavelets are, and how they can be used, which is a good
thing. Also, perhaps to get us thinking about the connection between
wavelets and brain function.

I would like to point something out, though:
The abstracts and the titles of these papers convey very accurately
the current relation between wavelets and brain function. For example:

"Specified-resolution wavelet analysis....."
"Time-on-task analysis using wavelet networks ...."
"Automated detection of trace......... using discrete wavelet
transform."
"Wavelet analysis of P3a and P3b."
"Wavelet Transform in the analysis of ....."
"Wavelet transform of the EEG reveals ....."

Please note the context of the word "wavelet". It is -always- used in
the context of -using wavelets to analyze brain function-.  This is
appropriate because wavelets are a mathematical tool for dissecting
complicated temporal and spatial data. The wavelets are something the
-researcher- uses to study the brain. None of the papers (I believe
from my brief scans of the abstracts) propose that the -brain- uses
wavelets as part of a computational mechanism.

A somewhat far-fetched, and I hope not too insulting, analogy might be
for me to measure peoples head sizes with a ruler, and thus conclude
that the brain performs its function because it contains a bunch of
little rulers.

I do know scientists that try to model neural processing as a
wavelet-based mechanism. But even these people are very cautious about
claiming that the brain actually uses wavelet algorithms to do
anything itself.

Now, wavelets are an example of a larger class of algorithms that are
good for multiscale, or multiresolution analysis. Some examples would
be special cases of Fourier and Laplace transforms, Wigner-Ville
transforms and Slepian multitaper transforms. It is quite clear that
the brain -does- have machinery for performing multiresolution
analysis of sensory input (e.g., this is why you can recognize a
friend's face regardless of whether they are standing close to you or
far away).

However, it is -not- at all clear which sort of multiresolution
algorithms the brain uses. The most obvious candidate would probably
be a variant of the Fourier transform used by the cochlea. This makes
a certain amount of sense because sine and cosine waves are a sort of
universal waveform. Wavelets are not universal waveforms. They are
very specific kinds of waveforms. Furthermore, for each task that one
wishes to analyze with wavelets, one needs to spend a fair amount of
effort deciding which family of speciifc wavelets is the best one to
use on that particular data set (e.g., Haar vs Coifman vs Daubechies
vs etc.). This is actually a pretty large part of current research
into wavelets themselves. I will bet you that each one of the papers
you cited has chosen a -different- wavelet family to analyze its data.

As far as I know, there is still no evidence that the -brain- performs
wavelet transforms to deal with its own daily information processing
chores.  But if I come across any real data like that, I will
certainly post a link to it here.

Cheers,

Matt




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