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What happens in k-space? This tool allows you to choose changes to be made to a k-space data set. The result of these changes is seen and discussed.

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K-Space Tool: partial Fourier (aka halfscan)

Ever noticed that k-space is quite symmetrical? Scanners can make use of the conjugate symmetry of k-space to reduce scan time. That means they can use the data from the lower part of k-space, to fill the upper part, without actually having to sample the upper part. Theoretically you could sample just one quadrant of k-space and create and fill the rest of k-space from that, but in practice the conjugate symmetry isn't perfect and so this isn't done.

With partial Fourier, just over half of the data is acquired (indicated in red). This is termed "partial Fourier" because a full dataset (all the lines: full Fourier encoding) is not acquired. It may also be referred to as "halfscan" or "half Fourier".¹

In this example, three extra central lines of k-space are acquired, and these help to determine the contrast in the image. Extra lines are acquired at the centre like this because (i) most of the contrast of the image comes from these lines, and (ii) the scanner makes a phase correction using them. There is more noise in the image, though admittedly you can't see it here. The increase in noise comes from the fact that noise is random, but we are copying it from the lower part of k-space along with the signals from there. This means the noise in the upper part of k-space will have addititive effects when combined with the noise from the bottom part of k-space when we create the image.

In real life, you may not be able to set such an extreme partial Fourier. Scanners may set halfscan to a minimum of approximately 60% of k-space, rather than just over 50%, as shown on this page.

Partial Fourier imaging can also mean acquiring partial echoes in the readout direction instead (think of it as missing out the left hand side of k-space rather than the top, sometimes known as asymmetric echo, or partial echo). As before, SNR is reduced, but this may be offset by a reduction in echo time (TE). (The reduction of TE is possible because if we don't acquire the first part of the echo, we don't need the dephasing lobe of the frequency encoding gradient to be on for quite as long, and this saves time.)

¹In some places partial Fourier is referred to as "fractional NEX", which is a bit daft because the number of phase encoding steps (N_y) is reduced, and not the NEX. NEX stands for number of excitations (per phase encoding step), aka NSA, or number of signal averages. NEX = 2, for example, means acquiring k-space twice and making an average, combined k-space. This would increase the signal by a greater amount than the noise increase, because noise is random.

Further reading on this topic:
Books: MRI From Picture to Proton p132, Q&A in MRI p254-255
Online: e-MRI

Choose from the list below alter k-space.

Alter k-space...

• Introduction.
• Apply a low pass filter—see only the contrast of the image.
• Apply a high pass filter—see only the detail of the image.
• Introduce random motion artefacts—cf coughing, swallowing, moving.
• Introduce periodic motion artefacts—cf breathing, pulsatile flow.
• Add random noise.
• Add more random noise.
• Create a large RF spike near centre of k-space.
• Create a small RF spike near centre of k-space.
• Create a large RF spike at the periphery of k-space.
• Create a small RF spike at the periphery of k-space.
• Reduce the scan percentage—miss out the top and bottom of k-space.
• Acquire just over half of k-space—partial Fourier with three extra lines.
• Remove every other k-space line—similar to how SENSE (sensitivity encoding) achieves accelerated data acquisition.

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