(PEAKS) This function offers consistent arterial enhancement for contrast enhanced MRA studies, augmenting the k-space with filling flexibility.

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 strategy for incrementing the position of the k-space trajectory of an echo planar imaging (EPI) pulse sequence.
Echo planar imaging (EPI) uses a constant gradient amplitude in one direction. This, combined with an oscillating gradient system in the frequency encoding direction, produces a zigzag trajectory in k-space. In the blipped phase encoding variant of EPI, the k-space position in the phase encoded direction is incremented by gradient 'blips' of the appropriate area. These, when timed to occur during the reversals of the read-out gradient, produce a rectilinear path in k-space.
The artifacts in an EPI image can arise from both hardware and sample imperfections. These are most easily understandable from examination of the k-space trajectory involved, which is either a zigzag form (when using a constant phase encoding gradient) or a rastered zigzag (when the phase encoding is performed with small gradients at the end of each scan line, so-called 'blipped' EPI).

(FSE) In the pulse sequence timing diagram, a fast spin echo sequence with an echo train length of 3 is illustrated. This sequence is characterized by a series of rapidly applied 180° rephasing pulses and multiple echoes, changing the phase encoding gradient for each echo.
The echo time TE may vary from echo to echo in the echo train. The echoes in the center of the K-space (in the case of linear k-space acquisition) mainly produce the type of image contrast, whereas the periphery of K-space determines the spatial resolution. For example, in the middle of K-space the late echoes of T2 weighted images are encoded. T1 or PD contrast is produced from the early echoes.
The benefit of this technique is that the scan duration with, e.g. a turbo spin echo turbo factor / echo train length of 9, is one ninth of the time. In T1 weighted and proton density weighted sequences, there is a limit to how large the ETL can be (e.g. a usual ETL for T1 weighted images is between 3 and 7). The use of large echo train lengths with short TE results in blurring and loss of contrast. For this reason, T2 weighted imaging profits most from this technique.
In T2 weighted FSE images, both water and fat are hyperintense. This is because the succession of 180° RF pulses reduces the spin spin interactions in fat and increases its T2 decay time. Fast spin echo (FSE) sequences have replaced conventional T2 weighted spin echo sequences for most clinical applications. Fast spin echo allows reduced acquisition times and enables T2 weighted breath hold imaging, e.g. for applications in the upper abdomen.
In case of the acquisition of 2 echoes this type of a sequence is named double fast spin echo / dual echo sequence, the first echo is usually density and the second echo is T2 weighted image. Fast spin echo images are more T2 weighted, which makes it difficult to obtain true proton density weighted images. For dual echo imaging with density weighting, the TR should be kept between 2000 - 2400 msec with a short ETL (e.g., 4).
Other terms for this technique are:
Turbo Spin Echo
Rapid Imaging Spin Echo,
Rapid Spin Echo,
Rapid Acquisition Spin Echo,
Rapid Acquisition with Refocused Echoes

The symmetry in k-space is a fundamental property of Fourier transformations. For a two-dimensional example, let g(x,y) be a complex function, i.e. the value of g at any (x,y) is a complex number. If nothing is known about the function g, data throughout all of k-space is needed to fully characterize it.
If the function g is 'real', meaning that at every (x,y) the imaginary component of g(x,y) is zero, then you only need half as much data to characterize g. The result is redundancy between the data on one half of k-space and the other. Specifically, if G(kx,ky) is the Fourier transformation of g(x,y), and g(x,y) is real, then G(kx,ky)=G*(- kx,- ky), where * indicates a complex conjugate. The data in mirrored positions in k-space, i.e. (kx,ky) versus (- kx,- ky), are conjugates of each other.

See Imaginary Numbers and Complex Conjugate.