Modeling MR Image Acquisition

The 1-D point spread function (PSF) of MR images [39] is given by

where Nx is the number of samples in the frequency domain, and Ax represents the sampling interval in the spatial domain. Eq. (10.45) is well approximated

The 3-D PSF is given by m (x; Ax, Ay,Az) = m (x; Ax) ■ m (y; Ay) ■ m (z; Az), (10.48)

where Ax, Ay, and Az are sampling intervals along the x-axis, y-axis, and z-axis, respectively.

In actual MR imaging, the magnitude operator is applied to the complex number obtained at each voxel by FFT reconstruction, whose effects are not negligible [41]. Thus, the MR image of the sheet structure with orientation and thickness t is given by f (x) = |s(x; t, re4) * m(x; Ax, Ay, Az)l (10.49)

where * denotes the convolution operation.

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