I have a slight twist on the previous question. When you discuss
interpolation in K-space are you referring to the complex data? It would
seem to me that there are potential advantages to sinc interpolating the
K-space data (complex) versus interpolating the magnitude images (real),
although the previously discussed caveats of interpolating still apply. In
the latter information has been discarded. Is the SPM processing that was
discussed below performed on the original complex data or on the post-hoc
FFT of the magnitude data? Comments?
Vince
At 02:49 PM 10/25/99 +0100, Oliver Josephs wrote:
>Dear Dirk,
>
>There is probably little advantage and definite dis-advantages to
>sub-sampling data in this fashion.
>
>Firstly, some interpolation algorithms (e.g. bilinear) are only
>intended to improve the apprearance of displayed images and so do not
>necessarily preserve all of the image information. To prevent this loss
>a band-limited interpolation scheme is necessary (also sometimes known
>as "Fourier", "full sinc" or "ideal" interpolation).
>
>Seondly, the interpolation will increase the amount of data that have
>to be stored and processed (by a factor of 4 in the example you
>mention).
>
>Thirdly, data that have undergone interpolation will exhibit a very
>specific form of spatial autocorrelation. No energy should (generally)
>or will (ideally) be present at the higher spatial frequency points
>introduced by interpolation. In k-space terms ideal interpolation is
>equivalent to (and may actually be implemented by) acquiring only the
>centre of a larger k-space grid (e.g. a 64x64 matix inside a 128x128
>grid).
>
>If no enery is present in the data the same will be true for the
>residuals after a design matrix has been fitted. However, the Gaussian
>random field theory component of SPM presumes a Gaussian residual
>spatial power spectral density. (This can be expressed in terms of
>spatial auto-correlation, which by the Wiener-Khintchine theorem is the
>Fourier transform of the power spectral density). This condition is
>normally (at least approximately) enforced by smoothing the data with a
>Gaussian kernel of 2-3 times the ORIGINAL voxel size. This smoothing
>is, by the convolution theorem, equivalent to multiplying the PSD by a
>Gaussian which has fallen to a low value by the edge of the ACQUIRED
>portion of k-space. Just by padding k-space does not change this and so
>no gain in resolution in an SPM is possible simply by subsampling the
>data.
>
>These points apply equally for any sub-sampling interpolation performed
>off-line including within spatial normalisation by SPM, which, by
>default (I think), sub-samples the output to 2x2x2 mm.
>
>Oliver
>
>
> > From [log in to unmask] Mon Oct 25 10:25:43 1999
> > Date: Mon, 25 Oct 1999 11:32:41 +0200
> > MIME-Version: 1.0
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> > KAA21366
> > Subject: interpolation of raw data
> > From: Dirk-Oliver Granath <[log in to unmask]>
> > To: spm <[log in to unmask]>
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> >
> > Dear SPMers,
> >
> > our MR scanner offers the opportunity to perfom an interpolation after
> > data aquisition with a change of voxelsize. For example a 64*64 matrix,
> > can be transformed into a 128*128 matrix.
> > How would this affect the quality of the data and the spatial
> > pre-processing in SPM.
> > Thank you for any comment.
> >
> > Dirk
> > --
> > -----------------------------------------
> > Dirk-Oliver Granath
> > Universität Bonn
> > Klinik für Psychiatrie
> > und Psychotherapie
> > Sigmund-Freud-Strasse 25
> > 53105 Bonn - Germany
> >
> > E-mail: [log in to unmask]
> > Phone: +49 (228) 287-4695
> > Fax: +49 (228) 287-4697
> > -----------------------------------------
=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
Vince D. Calhoun, MA, MS, PhD Student (UMBC), Research Engineer
WORK: Johns Hopkins Medical Institutions, Psychiatric Neuro-Imaging
600 N. Wolfe St., Meyer 3-166, Baltimore, MD 21287-7362
VOICE: (410) 955-7861, FAX: (410) 614-3676
WWW: http://pni.med.jhu.edu/vcalhoun
=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
"An author [or researcher] should never conceive himself as bringing into
existence beauty or wisdom which did not exist before, but simply and
solely as trying to embody in terms of his own art some reflection of
eternal Beauty and Wisdom...And always, of every idea and of every
method the Christian will ask not, 'Is it mine?' but 'Is it good?", CS Lewis
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