What is K-space?

K-space is a domain where a spatial domain arrangement of a time domain signal is the frequency domain representation of a spatial domain object.

If you are kind of confused by that but you understand what spatial, time and frequency domain mean, it's understandable. In MRI, changing magnetic fields and radio frequency pulses cause the atoms in your body to emit electromagnetic signals that are detected by the scanner. If you take the received signal from the MRI (which is a normal time domain signal where you get a value for each time point in the recording) and you arranged it in a data space according to a certain trajectory (i.e. put the value at each time point in a specific location), you actually get the Fourier transform of the image of the object you are imaging (which is obviously spatial domain because we live in real space). This is how the math works out but what I really like is the symmetry in which you can boil it down to in that sentence above, which keeps it confusing enough to pass as some kind of ancient philosophical proverb.

About Peter Yu I am a research and development professional with expertise in the areas of image processing, remote sensing and computer vision. I received BASc and MASc degrees in Systems Design Engineering at the University of Waterloo. My working experience covers industries ranging from district energy to medical imaging to cinematic visual effects. I like to dabble in 3D artwork, I enjoy cycling recreationally and I am interested in sustainable technology. More about me...

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