NMR Image Reconstruction in Nonlinearly Varying Magnetic Fields: A Numerical Algorithm

We propose a numerical algorithm for nuclear magnetic resonance (NMR) imaging in low magnetic fields that vary spatially in a nonlinear way. Since we operate at low frequencies ≤3 MHz, moderate electrically conductive materials in large sample volumes can be accessed. Frequency swept spin-echo pulse sequences are employed to control the excitation bandwidth. The resolution and sensitivity of this nonconventional imaging approach is studied. To localize the origin of the NMR signal in the sample volume we do not rely on linear magnetic field gradients as in modern high-field imaging devices, but utilize the generic spatial inhomogeneity of RF and DC fields generated by relatively large surface and volume coils. A numerical forward and inverse modeling example related to applications in the water and oil research is described. The algorithm may be applied to single-sided and borehole imaging systems in the future.