Dynamic decomposition of spatiotemporal neural signals
Fig 9
Spherical harmonics and covariance functions.
Visualization of the spherical harmonics morphed onto the cortex and the resulting spatial correlation structure. A) Example of spherical harmonics on the brain cortex for frequency numbers from 0 to 2. For each frequency number l there are 2l+1 harmonics with “phase” number m ranging from −l to l. As clear from the picture, the spatial frequency increases as a function of the frequency number. In all our analyses we truncated the harmonic expansion after the 11th frequency number. B,C) Prior correlation structure induced by Eq (24). Panel B shows the prior correlations on the cortical surface from a cortical point identified by a red dot. Panel C shows the same function on the spherical hull. The spatial correlations are determined by the frequency discount function f(l); here we used the same smoothing parameters as all analyses in the paper: k = 2 and υ = 3.