k-space

k-space is an abstract concept and refers to a data matrix containing the raw MRI data. This data is subjected to mathematical function or formula called a transform to generate the final image. A discrete Fourier or fast Fourier transform ^1-3 is generally used, though other transforms such as the Hartley ⁴ can also work.

Discussion

A single slice corresponds to a k-space plane acquired in real-time. Each point on the k-space contains specific frequency, phase (x,y coordinates) and signal intensity information (brightness). Inverse FT is applied after k-space acquisition to derive the final image. Each pixel in the resultant image is the weighted sum of all the individual points in the k-space. Hence, disruption of any point in the k-space translates into some form of final image distortion, determined by the frequency- and phase-related data stored in that particular point. In general:

• central regions of the k-space encode contrast information

• peripheral regions of the k-space encode spatial resolution

Relevance

Knowledge of the k-space is essential as it relates to different techniques of image acquisition and explains several MRI artifacts.