(MY) Dimension in the stationary (laboratory) frame of reference in the plane orthogonal to the direction of the static magnetic field (B0 and H0), z, and orthogonal to x, the other dimension in this plane. This is commonly defined to be in the direction of the phase encoding gradient.

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.

The process of locating a MR signal by altering the phase of spins in one dimension with a pulsed magnetic field gradient along that dimension prior to the acquisition of the signal.
If a gradient field is briefly switched on and then off again at the beginning of the pulse sequence right after the radio frequency pulse, the magnetization of the external voxels will either precess faster or slower relative to those of the central voxels.
During readout of the signal, the phase of the xy-magnetization vector in different columns will thus systematically differ. When the x- or y- component of the signal is plotted as a function of the phase encoding step number n and thus of time n TR, it varies sinusoidally, fast at the left and right edges and slow at the center of the image. Voxels at the image edges along the phase encoding direction are thus characterized by a higher 'frequency' of rotation of their magnetization vectors than those towards the center.
As each signal component has experienced a different phase encoding gradient pulse, its exact spatial reconstruction can be specifically and precisely located by the Fourier transformation analysis. Spatial resolution is directly related to the number of phase encoding levels (gradients) used. The phase encoding direction can be chosen, e.g. whenever oblique MR images are acquired or when exchanging frequency and phase encoding directions to control wrap around artifacts.

The temporal order in which the phase encoding gradient pulses are applied. The order can be sequential, centric, reverse centric, random, etc.

The schematic figures of a pulse sequence timing diagram illustrate the steps of basic hardware activity that are incorporated into a pulse sequence. Time during sequence execution is indicated along the horizontal axes. Each line belongs to a different hardware component. One line is needed for the radio frequency transmitter and also one for each gradient (G_s = slice selection gradient x, G_f = phase encoding gradient y, G_f = frequency encoding gradient z, also called readout gradient).
In picture 1, a timing diagram for a 2D pulse sequence is shown.
Slice selection and signal detection are repeated in duration, relative timing and amplitude, each time the sequence is repeated. A single phase encoding component is present each time the sequence is executed.
Additional lines are added for ADC (Analog to Digital Converter) and sampling. A gradient pulse is shown as a deviation above or below the horizontal line. Simultaneous component activities such as the RF pulse and slice selection gradient are indicated as a non-zero deviation from both lines at the same horizontal position. Simple deviations from zero show constant amplitude gradient pulse. Gradient amplitudes that change during the measurement, e.g. phase encoding are represented as hatched regions.

The second picture shows a timing diagram for a 3D pulse sequence.
Volume excitation and signal detection are repeated in duration, relative timing and amplitude, each time the sequence is repeated. Two phase encoding components are present, one in the phase encoding direction and the other in slice selection direction (irrespectively incremented in amplitude) in each time the sequence is executed. A description of the comparison of hardware activity between different pulse sequences.