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
>
