k-space in magnetic resonance imaging

When k-space is full (at the end of the scan) the data are mathematically processed to produce a final image.

Typically, k-space has the same number of rows and columns as the final image and is filled with raw data during the scan, usually one line per TR (Repetition Time).

An MR image is a complex-valued map of the spatial distribution of the transverse magnetization Mxy in the sample at a specific time point after an excitation.

Conventional qualitative interpretation of Fourier Analysis asserts that low spatial frequencies (near the center of k-space) contain the signal to noise and contrast information of the image, whereas high spatial frequencies (outer peripheral regions of k-space) contain the information determining the image resolution.

A nice symmetry property exists in k-space if the image magnetization Mxy is prepared to be proportional simply to a contrast-weighted proton density and thus is a real quantity.

However, these techniques are approximate due to phase errors in the MRI data which can rarely be completely controlled (due to imperfect static field shim, effects of spatially selective excitation, signal detection coil properties, motion etc.)

or nonzero phase due to just physical reasons (such as the different chemical shift of fat and water in gradient echo techniques).

MRI k-space is related to NMR time-domain[4] in all aspects, both being used for raw data storage.

As a result of this difference, the NMR FID signal and the MRI spin-echo signal take different mathematical forms: and where Due to the presence of the gradient G, the spatial information r (not the spatial frequency information k) is encoded onto the frequency