K-space


As we acquire our images, what we are acquiring is many, many waves of varying spatial frequency and directions. As we overlay these on top of one another we form the physical image. These wave signals are stored in stored in K-Space (aka Fourier Space) along a coordinate system.

 

K-space

 

Each column of k-space contains the data obtained during one frequency encoding step. Each row is filled in by repeating the phase-encoding steps. The important things to note are:

  • Any particular point on K-space contributes to the whole image
  • Any image pixel is derived from the whole of K-space
  • K-space is symmetrical

Within K-space the high-frequency signals are within the periphery and the low-frequency signals are within the centre. The x and y-axes determine the orientation of the signal wavelengths.

 

Example of wave signals in K-space

 

A low-pass filter that only includes the centre of K-space produces an image that is very smooth but lacks the edges and details. A high-pass filter that only includes the periphery of K-space produces an image that has very good detail and edges but no low-contrast features.

 

Original input and the K-space map

Input image of K-space

 

High-pass filter

High-pass filter

 

Low-pass filter

Low-pass filter

 

  For more information on k-space these two tutorials are useful


Σ  Summary
  • The wavelength signals acquired are stored in K-space
  • Each column contains data acquired from 1 frequency encoding step
  • Each row contains data acquired from phase-encoding steps
  • Any point in K-space contributes to the whole image
  • Any image pixel is derived from the whole of K-space
  • High-frequency signals (edges) are stored in the periphery
  • Low-frequency signals (contrast) are stored in the centre

 

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Written by radiologists, for radiologists with plenty of easy-to-follow diagrams to explain complicated concepts. An excellent resource for radiology physics revision.

 

FRCR Physics Notes: Beautiful revision notes for the First FRCR Physics exam

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