Spatial encoding in MR techniques is achieved by sampling the signal as a function of time in the presence of a magnetic field gradient. The gradients are assumed to generate a linear magnetic field gradient, and typical image reconstruction relies upon this approximation. However, high-speed gradients in the current generation of MRI scanners often sacrifice linearity for improvements in speed. Such nonlinearity results in distorted images. The problem is presented in terms of first principles, and a correction method based on a gradient field spherical harmonic expansion is proposed. In our case, the amount of distortion measured within a typical field of view (FOV) required for head imaging is sufficiently large that without the use of some distortion correction technique, the images would be of limited use for stereotaxy or longitudinal studies, where precise volumetric information is required.
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