> Good point, I mean that the MRI observations have Rician-distributed
> noise. My question however remains, is this considered in SPM or is it
> assumed that the noise is Gaussian?
There is no single distribution that holds for all MRI data used in
practice. Voxel-based morphometry data, for example, are probability
values bounded between 0 and 1. Other data are ratios of random
variables.
There are two distributional issues to consider in general: marginal
(the distribution of the data seen voxel by voxel) and joint (viewed
multivariately). In the SPM approach, the first affects the marginal
distribution of the parametric map, the second the exactness of the
correction for multiple comparisons.
In general, the marginal distribution may not be the same over the
volume. So it isn't very useful to think of it as just one
distribution. But anyway the parametric map will marginally tend to
normality for large samples, as those commonly found in functional
MRI. So for fMRI/EPI, I would not worry much about distributional
issues arising from the EPI signal. Besides, 'EPI-specific noise' has
a limited influence on the distribution of residuals at the second
level, which is where you carry out inference. Instead, the dominant
source of variance arises from the subject-to-subject variation of the
effect of interest.
The sensitivity of the test to violations of distributional
assumptions depends on the test statistic. Voxelwise corrections
(which use the maximum over the volume as test statistic) are quite
sensitive to marginal violations, and much less to joint
distributional violations. In contrast, cluster-level corrections
(using the maximum cluster size) are very sensitive to violations of
the joint distributional assumption.
There is a simple way to correct for marginal volations: rank the data
voxel by voxel, and carry out a permutation test. The issue of
corrections for joint distributional assumptions is a topic of active
research.
Best wishes,
Roberto Viviani
>
> /Anders
>
> 2010-10-31 10:19, Gael Varoquaux skrev:
>> On Sat, Oct 30, 2010 at 07:45:07PM +0200, Anders Eklund wrote:
>>
>>> An interesting discussion, do you know if SPM uses the fact that the
>>> noise in MRI is Rician distributed and not Gaussian distributed?
>>>
>> Forgive me for asking a naive question, but is the noise in fMRI really
>> Rician-distributed? The MRI-observation noise is Rician-distributed. I
>> believe that this comes directly from the measurement process. However,
>> with EPI, there are much more processes contributing to 'noise' than
>> imaging noise, such as residual movement or vascular and respiratory
>> noise.
>>
>> I am not even sure that the EPI-specific noise (such as
>> field-inhomogeneity fluctuations that can clearly be seen in the
>> ventricles) are Rician-distributed. If someone on the mailing-list who
>> understands the physics behind the EPI noise could enlight me, I'd be
>> much obliged.
>>
>> Gael
>>
>
> --
> --
> -----------------------------------------------------------------------
>
> Anders Eklund
> Phd student
>
> Medical Informatics, Department of Biomedical Engineering
> CMIV, Center for Medical Image Science and Visualization
>
> Tel: +46 73 6003790 mail: [log in to unmask]
> Fax: +46 13 101902 web: http://www.wanderineconsulting.com/
> -----------------------------------------------------------------------
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