The experiment protocol of generating MRI signal is very simple: place an object in an uniform, main magnetic filed and then exite it with a oscilating magnetic filed (also called RF pulse) at the resonance frequency.

    However, the received signal is a "sum" signal from all the pixels. Therefore, in order to differenciate local signals from different parts of a given object, spatial encoding is very necessay.

  Fourier transform is the essential imaging equation in MR imaging. Combining the Fourier transform and spatial encoding, we can get the imaging equation in MRI, which is very important for us to understand the essential of many mechanisms.

  This note starts from the siglal localization, and then we can get a different express of spacial encoding, whick is call k-space. The relationship between normal spatial encoding and k-space is also described. Based on the Fourier transform equation, we add the concept of k-space to it and get the imaging equation of MRI. At last, we analyse two kinds of k-space filling strategy using imaging equation.

 This script is a note of "Priciples of Manetic Resonance Imaging: A signal Processing Perspective" by Zhi-pei Liang and Paul C. Lauterbur. If you want to get the original article, your can purchase one copy for Amzon.

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