The partial Fourier technique is a modification of the Fourier transformation imaging method used in MRI in which the symmetry of the raw data in k-space is used to reduce the data acquisition time by acquiring only a part of k-space data.
The symmetry in k-space is a basic property of Fourier transformation and is called Hermitian symmetry. Thus, for the case of a real valued function g, the data on one half of k-space can be used to generate the data on the other half.
Utilization of this symmetry to reduce the acquisition time depends on whether the MRI problem obeys the assumption made above, i.e. that the function being characterized is real.
The function imaged in MRI is the distribution of transverse magnetization Mxy, which is a vector quantity having a magnitude, and a direction in the transverse plane. A convenient mathematical notation is to use a complex number to denote a vector quantity such as the transverse magnetization, by assigning the x'-component of the magnetization to the real part of the number and the y'-component to the imaginary part. (Sometimes, this mathematical convenience is stretched somewhat, and the magnetization is described as having a real component and an imaginary component. Physically, the x' and y' components of Mxy are equally 'real' in the tangible sense.)
Thus, from the known symmetry properties for the Fourier transformation of a real valued function, if the transverse magnetization is entirely in the x'-component (i.e. the y'-component is zero), then an image can be formed from the data for only half of k-space (ignoring the effects of the imaging gradients, e.g. the readout- and phase encoding gradients).
The conditions under which Hermitian symmetry holds and the corrections that must be applied when the assumption is not strictly obeyed must be considered.
There are a variety of factors that can change the phase of the transverse magnetization:
Off resonance (e.g. chemical shift and magnetic field inhomogeneity cause local phase shifts in gradient echo pulse sequences. This is less of a problem in spin echo pulse sequences.
Flow and motion in the presence of gradients also cause phase shifts.
Effects of the radio frequency RF pulses can also cause phase shifts in the image, especially when different coils are used to transmit and receive.
Only, if one can assume that the phase shifts are slowly varying across the object (i.e. not completely independent in each pixel) significant benefits can still be obtained. To avoid problems due to slowly varying phase shifts in the object, more than one half of k-space must be covered. Thus, both sides of k-space are measured in a low spatial frequency range while at higher frequencies they are measured only on one side. The fully sampled low frequency portion is used to characterize (and correct for) the slowly varying phase shifts.
Several reconstruction algorithms are available to achieve this. The size of the fully sampled region is dependent on the spatial frequency content of the phase shifts. The partial Fourier method can be employed to reduce the number of phase encoding values used and therefore to reduce the scan time. This method is sometimes called half-NEX, 3/4-NEX imaging, etc. (NEX/NSA). The scan time reduction comes at the expense of signal to noise ratio (SNR).
Partial k-space coverage is also useable in the readout direction. To accomplish this, the dephasing gradient in the readout direction is reduced, and the duration of the readout gradient and the data acquisition window are shortened.
This is often used in gradient echo imaging to reduce the echo time (TE). The benefit is at the expense in SNR, although this may be partly offset by the reduced echo time. Partial Fourier imaging should not be used when phase information is eligible, as in phase contrast angiography.

See also acronyms for 'partial Fourier techniques' from different manufacturers.

A variation of the (Half Fourier Acquisition Single Shot Turbo Spin Echo) HASTE sequence, whereat half of the image information is acquired after the first excitation pulse, and the half after the second excitation pulse. The acquired data are then interleaved into the raw data matrix. A long time to repetition (TR) is selected to allow the spin system to recover between excitation pulses and the dead time is used for additional slices. The length of the echo train is cut in half. Also more than 2 segments are possible.

Partial averaging is a scan time reduction method that takes advantage of the complex conjugate of the k-space. The number of phase encoding steps of the acquisition matrix are reduced in the phase encoding direction.
Since negative values of phase encoded measurements are identical to corresponding positive values, only a little over half (more than 62.5%) of a scan actually needs to be acquired to replicate an entire scan. This results in a reduction in scan time at the expense of signal to noise ratio. The time reduction can be nearly a factor of two, but full resolution is maintained.
Partial Fourier averaging can be used when scan times are long, the signal to noise ratio is not critical and where full spatial resolution is required. Partial averaging is particularly appropriate for scans with a large field of view and relatively thick slices; and in 3D scans with many slices. In some fast scanning techniques the use of partial averaging enables a shorter TE thus improving contrast.
Partial averaging is also called Fractional NEX, Half Scan, Half Fourier, Phase Conjugate Symmetry, Single Side Encoding.

In single shot techniques (used for EPI, TSE, FSE, RARE, HASTE), the entire raw data set is acquired with a single excitation pulse. The magnetization of a fully relaxed spin system is used. Each of the subsequent echoes is given a different phase encoding. For improved SNR, spatial resolution or FOV, the needed raw data are acquired over a number of sequence repetitions. Each repetition then collects a fraction of the complete raw data set. Only slightly more than a half of the raw data is acquired. The image is obtained through half Fourier reconstruction.
A single shot sequence is useful in cases where movement is to expect e.g. in abdominal Imaging or fetal MRI.

See also Half Fourier Acquisition Single Shot Turbo Spin Echo.

Fractional Nex imaging (GE Healthcare term for imaging with a Nex value less than 1) benefits from the conjugate symmetry of the k-space to reduce the number of phase encoding acquisitions. With fractional Nex imaging (similar to partial Fourier or Half Scan), just over half of the data are acquired and the data from the lower part of k-space are used to fill the upper part, without sampling the upper part. Fractional Nex imaging sequences use a number of excitations values between 0.5 and 1. These values are a bit misleading, because the number of phase encoding steps is reduced, and not the NEX.
Fractional Nex imaging reduces the scan time considerable, by preserving the same contrast between the tissues. The effect by acquiring fewer data points is that the signal to noise ratio decreases.

See also acronyms for 'partial averaging//fractional Nex imaging' from different manufacturers.