2D Fourier Transform



In magnetic resonance imaging (MRI), the k-space or reciprocal space (a mathematical space of spatial frequencies) is obtained as the 2D or 3D Fourier transform of the image measured. It was introduced in 1979 by Likes and in 1983 by Ljunggren and Twieg.

How to use:

  1. Upload an image using the file input
  2. Adjust FFT and render sizes to control detail level
  3. The left canvas shows your original image
  4. The right canvas (k-space) shows frequency components

Reading the k-space visualization:

  • Center: Low frequencies (overall shape and brightness)
  • Edges: High frequencies (fine details and edges)
  • Brightness: Magnitude of each frequency component
  • Pattern: Reveals periodic structures in the image

The overlay slider blends the two views. K-space is crucial in MRI imaging, signal processing, and understanding how images can be compressed.