K-space

K-space is the spatial frequency domain in which MRI data are acquired before image reconstruction. The term borrows from the wavevector notation of solid-state physics: each point in k-space represents a spatial frequency component of the object being imaged, with the center encoding low spatial frequencies (contrast and coarse structure) and the periphery encoding high spatial frequencies (fine detail and edges). The trajectory through k-space is determined by the gradient waveforms applied during acquisition, and the image is recovered by inverse Fourier transformation. What makes k-space conceptually powerful is that it separates the physics of encoding from the mathematics of reconstruction: the scanner samples frequencies, and the algorithm synthesizes space. The same concept appears in synthetic aperture radar, optical diffraction, and crystallography — any domain where spatial information is gathered in the Fourier domain rather than the image domain.