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.

Quadrature detection is used in magnetic resonance imaging as well as in Doppler ultrasound and is also called quadrature demodulation or phase quadrature technique.
With this phase sensitive demodulation technique the complex demodulated signal is separated into two components. One is called the real channel; the second part is called the imaginary channel and is located 90° away from the real channel. The signals from both channels are combined to produce a single set of quadrature detected real and imaginary spectra. In MRI, the parts of the demodulated MR signal are further processed by Fourier transformation analysis. All information on the MR signal components e.g. amplitude, phase, and frequency is given by this quadrature detection combined with Fourier analysis.

The cardiac anatomy is complex, and cardiac structures have different appearances depending on the imaging plane. The most useful imaging planes are those parallel and perpendicular to the cardiac axes. The short axis (SA), vertical long cardiac axis (VLA - 2 chamber view - 2C) and horizontal long axis (HLA - 4 chamber view - 4C) are the standard views in cardiovascular imaging. The orientation of a heart is described relative to an imaginary line drawn from the base of the heart (valve plane) to the apex.
Obtaining cine images in these double-oblique planes requires the use of multiple localizing MRI sequences and knowledge of the cardiac anatomy. The long axis image plane is determined by the line that runs from the apex of the heart to a midpoint at the base of the heart, often taken to be midway between the mitral valve leaflets. The short axis is planned perpendicular to the long axis view.

An operation on a complex number, which negates the sign of the imaginary component of a complex vector. The two vectors then form a complex-conjugate pair.

The complex numbers extend the real numbers by including the imaginary unit i (satisfying i2 = - 1). The term 'complex' when used as an adjective means that the field of complex numbers is as the underlying number field considered. In MRI, complex data are used for example in the Fourier transforms.