Modeling MR Image Acquisition

The Fourier transform of MR PSF is given by

y AxAyAz V Ax Ay Az)

where Rect(x; ax, ay, az) = Rect(x; ax) • Rect(y; ay) • Rect(z; az) (Fig. 10.18(b)), and

0 otherwise.

By substituting Eq. (10.62) for T in Eq. (10.64) to obtain 1-D frequency component affecting S(ts), the following is derived

Thus, the Fourier transform of MR image of the sheet structure, F(a>s) is given by

where F-1 represents the inverse Fourier transform. If F-1{S(ms)M(ms)} is a nonnegative function, F(a>s) is given by F(a>s) = S(ms)M(ms) and all the processes can be described as linear filtering processes. Deformation of the original signal due to truncation is clearly understandable in the frequency domain (Fig. 10.18(c)).

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