kspace

K-space, short for frequency space, is the domain used to represent the spatial frequency content of an image. In two dimensions, it is typically a two-dimensional grid with coordinates kx and ky. The image is obtained by applying an inverse Fourier transform to the data collected in k-space. Low spatial frequencies near the center encode overall image contrast, while high-frequency components toward the edges contribute to fine detail and sharpness.

In magnetic resonance imaging, k-space data are acquired by applying magnetic field gradients that encode spatial information into the phase and frequency of the detected signal. The frequency-encoding gradient maps to kx and the phase-encoding gradient maps to ky. Data can be collected on a Cartesian grid or along non-Cartesian trajectories such as radial or spiral paths. The sampling pattern, density, and extent determine image resolution, signal-to-noise ratio, and potential artifacts.

Reconstruction converts k-space samples into an image by performing an inverse Fourier transform. Non-Cartesian acquisitions require gridding or iterative reconstruction techniques to interpolate data onto a regular grid before transforming. Undersampling k-space speeds up scans but can cause aliasing artifacts. Techniques such as parallel imaging and compressed sensing are used to accelerate acquisition while reducing quality loss, by exploiting redundancy in the data.

Beyond MRI, k-space is a general term in signal processing referring to the Fourier domain of spatial signals. It is used in related fields such as nuclear magnetic resonance spectroscopy and optics to analyze and reconstruct spatial information.