Wavelet frames on graphs defined by fMRI functional connectivity

Multiscale representations such as the wavelet transform are useful for many signal processing tasks. Graphs are flexible models to represent complex networks and a spectral graph wavelet transform (SGWT) has recently been developed as a generalization of conventional wavelet designs. Here we extend the SGWT to obtain a Parseval frame, which conserves energy in the transformed domain and makes the reconstruction easy. Moreover, we also show how to deal with negative edge weights. We then apply the modified SGWT to brain functional connectivity data from two different conditions. This shows that the transform that is adapted to the condition, more efficiently captures coherent activity between inter-connected brain regions. The extended SGWT holds promise for the spatial analysis of fMRI data because it captures coherent activity of distinct brain regions that are functionally connected.