FSL uses a linear model to calculate the tensor coefficients from the log of the data - the model is inverted without constraints on the tensor positivity, which means there is a possibility for negative eigenvalues in the presence of noise (think of it as cases where the signal at b=0 is lower than the signal at b>0, which can happen at low SNR or in the presence of motion etc.)
Saad.
On 23 Apr 2010, at 08:19, Burkhard Maedler wrote:
> Thanks Ed (and Jesper),
> but your answer did not satisfy. If the mean <l>=0 that can only happen if all
> eigenvalues are zero (unless you allow negative eigenvalues which is exactly
> my point: Negative eigenvalues should not be permitted no matter what algorithm
> you are going to use to calculate them - they have no physical meaning
> in the diffusion tensor).
>
> If all li=0 than also <l>=0 but now the ratio of numerator and denominator
> in the equation of FA becomes ill-defined sqrt(0/0). Unless you have another
> explanation. Jesper mentioned something about the "true FA" implicating
> that FSL calculates FA-values by statistical means (which by the way is nowhere
> explained or mentioned in the documents).
> I simply find that FA can only approach sqrt(3/2) if one allows negative eigenvalues
> for the calculation of FA and I would consider this an oversight or bug.
> Does FSL use the LaPAck SVD or something different?
>
> If this question was alraedy adressed in the blog - my appologies but I can't
> find it.
> Thanks for your patients,
> Burkhard.
>
--
Saad Jbabdi
University of Oxford, FMRIB Centre
JR Hospital, Headington, OX3 9DU, UK
(+44)1865-222466 (fax 717)
www.fmrib.ox.ac.uk/~saad
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