Nonuniform Fourier Tansform and Cosensitivity

Nonuniform Fourier tansform:
For MRI, one can only sample in the K-space. If the coordinates of the K-sparce and the Image space are both cardition. Then it is just Fourier transform. If the coordinate of the K-sparse is not cardition but something else. Then the fourier transform is nouniform. The method is firstly do a interpolation in the K-space and then do the Fourier transform.
Cosensitivity:
To enhance the SNR of MRI meaturement and speed up the measurement, the coils are attached to the patient. like

o o o I am coils
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==================
================== I am patient
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====================

So for each Coil can only sample one part of the patient. The reconstruction algorithms should find a way to mix all the sample of the coils to gain a whole sample map of the patient