MRI geometric distortion: a simple approach to correcting the effects of non-linear gradient fields

We present a method to correct intensity variations and voxel shifts caused by non-linear gradient fields in magnetic resonance images. The principal sources of distortion are briefly discussed, as well as the methods of correction currently in use. The implication of the gradient field non-linearities on the signal equations are described in a detailed way for the case of two- and three-dimensional Fourier imaging. A model of these non-linearities, derived from the geometry of the gradient coils, is proposed and then applied in post-processing to correct any images regardless of the acquisition sequence. Initial position errors, as large as 4 mm (i.e., four voxels of 1 x 1 x 1.4 mm3) before correction, are reduced to less than the voxel sizes after correction.