The path traced in the spatial-frequency domain during data collection as determined by the applied gradients.

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).

Quick Overview

Artifacts either by distorting the k-space trajectory (i.e. due to imperfect shimming) or as a consequence of the reduced bandwidth in the phase encode direction, commonly with EPI sequences.
While a standard spin warp-based sequence has an infinitely large bandwidth in the phase encode direction (about 1 or 2 kH), the bandwidth in EPI is related to the time between the gradient echoes (about a millisecond).
Hence even small frequency offsets can result in significant shifts of the signal in the phase encoding direction. Segmentation can introduce ghosting if there are significant difference in the amplitude and phase of the signal. This can be a particular problem when trying to acquire the segments in rapid succession.

Suitable choices of excitation schemes and/or subsequent correction can help to reduce this artifact. The signal from fat can easily be offset by a large fraction of the FOV, and must be suppressed. The effect of frequency offsets can be reduced by collecting data with more than one excitation, which effectively increases the bandwidth in the phase encoding direction.

(SMASH) Several lines of data are acquired for each phase encoding step, which is also referred to as a k-space trajectory.
SMASH imaging with a four-element array coil is four times faster and can be used to achieve almost real-time imaging. The maximum reduction in acquisition time is determined by the number of array coil elements. Thus, the heart can be scanned with higher temporal resolution and increased spatial resolution.
SMASH and SENSE differ from other techniques in which only one line of k-space data is acquired for each phase encoding gradient step.

See Sensitivity encoding.

The k-space is an extension of the concept of Fourier space that is well known in imaging. In MR imaging the k-space is a temporary memory of the spatial frequency information in two or three dimensions of an object; the k-space is defined by the space covered by the phase and frequency encoding data.
The relation between K-space data and image data is the Fourier Transformation. The data acquisition matrix contains raw image data before the image processing. In 2 dimensional Fourier transformation imaging, a line of data corresponds to the digitized MRI signal at a particular phase encoding level. The position in k-space is directly related to the gradient across the object being imaged. By changing the gradient over time, the k-space data are sampled in a trajectory through Fourier space at each point until it is filled.

See also Spatial Frequency and Raw Data.