Hi Garren,

I'm looking into the paper and I believe this was another way to refer to the pseudo-inverse. Say A = U*S*V' is a singular value decomposition of A, then A^(-1) = U*S^(-1)*V'. Perhaps others can confirm.

All the best,

Anderson

On 1 February 2018 at 16:21, Garren Gaut <[log in to unmask]> wrote:

Hi FSL experts,

I'm trying to understand how FSL does prewhitening and am writing MATLAB implementations of some of the prewhitening procedures in the article "Temporal Autocorrelation in Univariate Linear Modeling of FMRI Data". The paper states that for an autocovariance matrix V=KK^T :

"Given an estimate of V, V^{-1} and hence K^{-1} can be obtained by inverting in the spectral domain (some autocorrelation models, e.g., au toregressive, have simple parameterized forms for K^{-1}, and hence inversion in the spectral domain is not necessary)."

Using some of the non-parametric methods for autocorrelation estimation, I've found that I can't invert in the time domain. Do you have a reference for how inverting in the spectral domain is done?

Cheers,

-Garren