Magnetic resonance imaging in nonlinear fields with nonlinear reconstruction

Imaging in the presence of nonlinear static and gradient magnetic fields is outlined. Analytic expressions are provided for the signal obtained using specific magnetic resonance imaging (MRI) sequences with the addition of field nonlinearities. We show that using nonlinear Fourier transform image reconstruction, high-quality images can be obtained for the case when the static magnetic field has large peak-to-peak error, and the gradient field exhibits variations beyond currently acceptable levels over the imaging field-of-view. Our results show that MRI can be performed in nonlinear magnetic fields, provided that a versatile technique is used to reconstruct the images