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 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.

An imaginary number is a part of a complex number. Complex numbers are an extension of the real numbers. A complex number has a real and an imaginary part. The imaginary unit (i) is equal to the square root of -1. The complex conjugate is a pair of complex numbers with identical real parts and imaginary parts which differ only in sign (e.g.: 3 + 7i and 3 - 7i).

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.

(PE) The partial echo technique (also called fractional echo) is used to shorten the minimum echo time. By the acquisition of only a part of k-space data this technique benefits (like all partial Fourier techniques) from the complex conjugate symmetry between the k-space halves (this is called Hermitian symmetry).
The dephasing gradient in the frequency direction is reduced, and the duration of the readout gradient and the data acquisition window are shortened. Partial echo gives a better SNR at a given TE when a smaller FOV or thinner slices are selected, allows a longer sampling time, and a larger water fat shift (WFS, see also bandwidth) due to a lower gradient amplitude. The resolution is not affected. This is often used in gradient echo sequences (e.g. FLASH, Contrast Enhanced Magnetic Resonance Angiography) to reduce the echo time and yields a lower gradient moment. The disadvantage of using a partial echo can be a lower SNR, although this may be partly offset by the reduced echo time.
Also called Fractional Echo, Read Conjugate Symmetry, Single Side View.

See also Partial Fourier Technique and acronyms for 'partial echo' from different manufacturers.