Re: Reverse FFT ?

["Jonas" <jonas_2(at)hotmail.com>]

Hi

Oki, if you have the real and imaginary part of the image, just put them in
a 2d complex vector and do a 2D FFT (forward or reverse?) on that vector.
The result is your 2D k-space (maybe you would like to shift the resulting
data so that the lowest "frequency", ie the k-space center, is centered in
the image instead of positioned in the corners). Note that the kspace _is_ a
complex space, so you should not do the FFT on the real and imaginary part
separately, instead you should combine them to a complex vector and then do
the FFT... something like this (assuming that your real and imaginary images
are stored in two 2d vectors called real_part and imag_part):

;combine the real and imaginary part to a complex image
complex_image = complex(real_part, imag_part)

;perform fft
k_space = FFT(complex_image, /inverse)

;shift the image data to get centre of kspace in the centre of the image
;assuming the size of the image is [xsize,ysize]
k_space = SHIFT(k_space, xsize/2, ysize/2)


So, how do you visualise the complex valued kspace in the best way? Well the
most common way to take a look at the k-space is to take a look at the
magnitude of it:

tvscl, abs(k_space)

Since the difference between the highest signal value, ie the center of
kspace, and the surrounding values are so large, maybe you instead would
like to look at the logarithm of the kspace:

tvscl, alog(abs(k_space)


hope this helps a bit....

regards
/Jonas


--
====================================
Jonas Svensson, MSc
Medical Physicist, MRI
Department of Radiation Physics
Malmö University Hospital
SE-205 02 Malmö, SWEDEN
+46 40 331021 (phone), +46 40 963185 (FAX)




Richard Tyc <richt@sbrc.umanitoba.ca> skrev i
diskussionsgruppsmeddelandet:8mrobi$ne3$1@canopus.cc.umanitoba.ca...
> Thanks Jonas,
>
> I do retain the phase and magnitude image (from which I can find the Real
> and Imaginary Data).
>
> So, from Craig's reply, I should be able to find "k" space by doing a
> reverse FFT on the Real/Imaginary image date right ?
> Would the real part of this reverse FFT solution be true k space ? ie.
> setting the second term to a negative number
> Also, would I have to do  a 1D FFT Row by Row on my data or can it be done
> as a 2D FFT.
>
>
> Rich
>
> Jonas <jonas_2@hotmail.com> wrote in message
> 8mrhpq$hkk$1@news.lth.se">news:8mrhpq$hkk$1@news.lth.se...
> > Hi Rich
> >
> > If the image data you have is not complex, then it is not possible to
> > retrieve the correct k-space data by doing an FFT. A reconstructed MR
> image
> > is always in complex form (to be represented by a mgnitude and a phase
> > angle, or by a real and an imaginary number), but the image shown on the
> > screen is the magnitude of each complex number. If you only have the
> > magnitude data, you have "thrown away" some important information, and
> will
> > not be able to get a correct k-space. k-space is by definition filled
with
> > complex data.
> >
> > Furthermore, if I remember my MR physics correct, you are supposed to do
a
> > forward transform when going from image space to k-space, but I am not
> > sure...
> >
> >
> > However, if you just want to have a look at a "general k-space", you
might
> > take a look at the magnitude of a FFT of a magnitude image... don't
forget
> > to shift the transformed data so that the lowest frequency is centered
in
> > the image....
> >
> > regards
> > Jonas
> >
> >
> > --
> > ====================================
> > Jonas Svensson, MSc
> > Medical Physicist, MRI
> > Department of Radiation Physics
> > Malmö University Hospital
> > SE-205 02 Malmö, SWEDEN
> > +46 40 331021 (phone), +46 40 963185 (FAX)
> >
> >
>
>
>