# Spherical wavelet for EEG?

Spherical wavelet consists in decomposing EEG data on a spherical wavelet base.

This means that the EEG signal at each latency will be a linear combination of a set of spatial wavelet basis.

Once every time point has been decomposed on this base, the smallest coefficient accross all time points may be removed. Then ICA may be run on this basis. Removing some wavelet coefficient may alter the linearity in the data (which is not good for ICA since ICA assumes linearity) but it will also denoise the data.

The ultimate denoising before running ICA would be to use 3-D spherical wavelet which have properties in both the spatial and the frequency domain then run a complex ICA algorithm. These 3-D wavelets coul be choosen using Matching pursuit (first select the wavelet with the highest coefficient, then removing it from the data, and iterate). If the wavelets are not orthogonal (redundant) it is usually necessary to remove from the data the orthogonal projection of the selected wavelet on the previously removed wavelets.

What is the potential advantages of using wavelets

- Denoising EEG data prior to running ICA
- Adapted to EEG since EEG activation are usually smothly distributed on the scalp and also also oscilatory in the frequency domain.
- Better and less noisy ICA decompositions (or worse ICA decompositions)
- Better classifications (using wavelet coefficients as features).

These free toolboxes might be useful to estimate spherical wavelets:

- Matlab Surface wavelet toolbox http://www.ceremade.dauphine.fr/~peyre/matlab/wavelets-meshes/content.html
- Minimum norm estimation toolbox http://www.nmr.mgh.harvard.edu

I am interested in this topic so please leave feedback on this page or any link towards Pubmed references and Matlab functions. You may also send me an email at arno@ucsd.edu.