Magnetic Resonance Image and k-space

Spatial frequency

Denis Hoa

Fourier transform is able to decompose images. Instead of analyzing a time varying signal, it decomposes a variation of intensity (gray levels) over distance. Time domain becomes space domain (time variable replaced by X-coordinate) and frequency is called spatial frequency.

 

As frequency refers to the (inverse of the) periodicity with which the sound sine wave repeats, the spatial frequency refers to the (inverse of the) periodicity with which the image intensity values change.

Image features that change in intensity over short image distances correspond to high spatial frequencies.
Image features that change in intensity over long image distances correspond to low spatial frequencies.