The cells of

*k*-space are commonly displayed on rectangular grid with principal axes*kx*and*ky*. The*kx*and*ky*axes of*k*-space correspond to the horizontal (*x*-) and vertical (*y*-) axes of the image. The*k*-axes, however, represent spatial frequencies in the*x*- and*y*-directions rather than positions.__The individual points (__. Each*kx*,*ky*) in*k*-space do**correspond one-to-one with individual pixels (***not**x,y*) in the image*k*-space point contains spatial frequency and phase information about*every*pixel in the final image. Conversely, each pixel in the image maps to*every*point in*k*-space.
Points along the
kx-axis represent frequency components along the x-direction of the image. Conversely, points along the ky-axis reflect frequency components along the y-direction of the image. The k-space image of a square block whose sides are aligned with the x- and y-axes would look like the top image (right). |

If the block were rotated by 45º, the dominant spatial frequencies corresponding to the edges of the block would now be oriented at a 45º angle to the
kx- and ky-axes. The relation between angle of the planar image waves and k-space location is shown below. |

As a final note, the physical size of the object imaged and its frequency expanse in
k-space are inversely related. In other words, small objects (like the small white circle right) have ripples far out into the periphery of k-space, while larger objects have their spectral energies more concentrated at the center. As the object grows larger only a few low spatial frequencies in each direction are required to represent it. At the extreme limit (the object fills the entire field-of-view) only a constant Fourier term is needed. For very large objects the
k-space representation collapses to just a single data point at (kx, ky) = (0,0) whose value reflects the average brightness of the image. |

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**References**

Mezrich R. A perspective on k-space. Radiology 1995; 195: 297-315. [review].

Miller K. MRI image formation (ppt). On-line lecture notes available at users.fmrib.ox.ac.uk/~karla/teaching/image_formation.ppt

"Spatial frequency". Wikipedia, The Free Encyclopedia.

**Related Questions**

*What is k-space?*

*If the points in k-space don't correspond to points in the image, what do they mean?*

*What are 2D- and 3D-Fourier transforms? I don't see how FT works in higher dimensions.*