There are several applications where conjugate mirroring of the k-space is important. In may case, I want to increase SNR. So, flipping the dimensions and conjugate the complex values is easy if the center of the k-space is known exactly. In my example my k-space K has the dimensions:
z,y,x = 160x160x144
where z is the read-out dimension. For y and x I know from the meta-data that the center is at 80 and 72. Hence, I flip the dimensions and shift them by 1 px. For the read-out dimension z, the theoretical center is at 79.5 which is perfect as I only would have to flip the dimensions without shifting. However, if I combine K with the mirrored K'
K+K'
I get phase-shift artifacts. I had a look on the read-out dimension at 80/72 and it seems that the center is shifted by 0.5 or 1 px i.e. the center is between 78 and 79 px. Hence, if I flip the dimensions and do an interpolated shift by -0.5, -1, -1.5 or -2 px, then K+K' does not have any artifacts for -1.5. Furthermore, as one would expect, it has better SNR and contrast.
Finally my question:
How can I estimate where the exact k-space center in the read-out direction is located?
Thank's for any hints
Christoph
The center of k-space in the read-out dimension is where the integral of the read-out gradient is zero. Normal sequences are programed to make that happen at the center of the read-out line. But sometimes it is intentionally shifted and sometimes it is shifted due to errors in the gradient wave-form. If you have access to the pulse sequence source code, you can find where the center is intended to be, but practically speaking the k-space point with the largest magnitude is the center of k-space. When the gradient integral is something other than zero, the signal is de-phased, so the magnitude is lower. Normally people try to program sequences so k-space is centered on a pixel rather than in-between pixels, but eddy-currents or other gradient wave-form errors may shift the actual position.
As an aside, if the sequence is sensitive to motion (for example a diffusion sequence) then rotational motion can cause the center of k-space to move.
1. In practical, the center of k-space which is intended to be is not exactly the center. So you'd better locate it by the maximum amplitude.
2. k-space is centered on a pixel when the read-out dimension is even (easy to do fft).
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