[Mristudio-users] Relationship between acquisition and reconstructed voxel size.

[Susumu Mori]

MRI raw data is so-called time-domain data. This means, within about
10-100ms of time, signals are acquired and recorded. For example, if your
image matrix is 128x128, there are 16,384 data points to acquire. For DTI,
to freeze the motion effect, all 16,384 points are acquired at once (8,192
points if you use a parallel imaging with factor = 2). Actually there are
real and imaginary data points and therefore there are 16,384x2 points. By
the way, because all 16,384 points are acquired at once, the data
acquisition time becomes very long and there is not much signal left by the
time all 16,384 points are read from the signal. Therefore, for DTI, there
is no point to acquire 256x256 (=65,536) points because after about 20,000
point-read, all the remaining points are reading just noise. This is why
all DTI studies have been done using 96x96 or 128x128. Because
field-of-view, which is determined by the brain size, is about 200 - 250
mm, DTI spatial resolution is limited to 2-2.5mm.

Now, when we do interpolation by the scanner, the scanner simply add "0"
and extend the 128 points to 256 points. This is called zerofilling.
After the fourier transform, the time-domain data is converted to the
frequency-domain or image-domain data (the same thing with different
names).

If you have 128x128, after the fourier transformation, you get a
128x128-pixel image.

Now, you have two options, do the interpolation by the scanner (time-domain
interpolation), convert the 128x128 time-domain matrix to 256x256
time-domain matrix and FT it to the 256x256 image-domain matrix.

Alternatively, you can FT first, get a 128x128 image-domain matrix and then
digitally interpolate it to 256x256.

A big question is, are they different? Signal processing people say,
"sinc-interpolation of 128x128 image to 256x256 image is the same as
time-domain zerofilling". However, things are not that easy because
time-domain data has real and imaginary parts. If you have 10 physicists,
I'm sure that you get two camps; one say they are the same and the other
say, time-domain interpolation is better and you can never get the same
quality after the time-domain data are converted to an image.

There is a famous paper by a novel laureate, Dr. Ernst, proving the latter
is the case, but the problem is, ordinary people like us can't understand
the paper.

Anyway, answering your question, you can always interpolate the data into
higher resolution, but many people believe that it is just cosmetic,
especially in the image-domain. We can argue that you are wasting the hard
drive space. I always do twice time-domain zerofilling (128 becomes 256) by
the scanner. In the imaging domain, we further digitally interpolate to
1x1x1mm because that is the voxel size of many atlases.

I don't think there is a large impact on SNR by the interpolation.


On Mon, Aug 12, 2013 at 12:40 PM, Dorian P. <alb.net at gmail.com> wrote:

> Hi all,
>
> Is there any relationship between acquired and reconstructed voxelsize. Is
> there any downside of reconstructing to much smaller voxels, for example
> acquire at 3mm and reconstruct at 2mm or 1mm? Is SNR going to be the same?
>
>
> Thank you.
> Dorian
> TJU
>
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