Magnetic Resonance Imaging

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Signal Processing Examples

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Example 1:

A single voxel with net magnetization.

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Time and phase domain raw data.

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Fourier transforming first in the frequency encoding direction.

The location in frequency space is: ( n - n_o ) = g x G_f

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Readjusting our perspective.

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Fourier transforming down in the phase encoding direction.

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The frequency and phase of peak correspond to the location of the voxel with spins.

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Example 2:

A single voxel at a new frequency encoding location with net magnetization.

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The raw data.

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Fourier transforming first in the frequency encoding direction.

The location in frequency space is: ( n - n_o ) = g x G_f

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Readjusting our perspective.

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Fourier transforming in the phase encoding direction.

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The frequency and phase of a peak correspond to the location of the voxel with spins.

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Example 3:

A single voxel at a new phase encoding location with net magnetization.

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The raw data.

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Fourier transforming in frequency encoding direction.

The location in frequency space is: ( n - n_o ) = g x G_f.

---

Readjust our perspective.

---

Fourier transforming in phase encoding direction.

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The frequency and phase of a peak correspond to the location of the voxel with spins.

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Example 4:

Two voxels with net magnetization in the imaged plane.

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The raw data.

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Fourier transforming first in the frequency encoding direction.

The location in frequency space is: ( n - n_o ) = g x G_f.

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Readjusting our perspective.

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Fourier transforming in the phase encoding direction.

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The frequency and phase correspond to the location of the voxels with spin.

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The Fourier transformed data is displayed as an image.

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Field of View (FOV)

The widht and/or height of an image in cm.

Recall: With quadrature detection, the sampling rate (f_s) = spectral width.

FOV = f_s / g G_f

To avoid wrap around:
    1. FOV > width of the imaged object, and
    2. FOV must be centered on the object.

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The phase encoding gradient is stepped between a maximum value (G_{f max}) and minimum value (-G_{f max}) in N equal steps.

The relationship between FOV and G_{f max} is:

G_{f max} dt = N / (2 FOV)

N is typically 128 or 256 phase encoding steps.

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Note: The integral, G_{f max} dt, is over the time the phase encoding gradient is turned on. Therefore, the shape of the phase encoding gradient pulse is immaterial, but the area is important.

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Copyright © 2000 J.P. Hornak.
All Rights Reserved.