Reconstruction of MRI data encoded by multiple nonbijective curvilinear magnetic fields

Parallel imaging technique using localized gradients (PatLoc) uses the combination of surface gradient coils generating nonbijective curvilinear magnetic fields for spatial encoding. PatLoc imaging using one pair of multipolar spatial encoding magnetic fields (SEMs) has two major caveats: (1) The direct inversion of the encoding matrix requires exact determination of multiple locations which are ambiguously encoded by the SEMs. (2) Reconstructed images have a prominent loss of spatial resolution at the center of field-of-view using a symmetric coil array for signal detection. This study shows that a PatLoc system actually has a higher degree of freedom in spatial encoding to mitigate the two challenges mentioned above. Specifically, a PatLoc system can generate not only multipolar but also linear SEMs, which can be used to reduce the loss of spatial resolution at the field-of-view center. Here, we present an efficient and generalized image reconstruction method for PatLoc imaging using multiple SEMs without explicitly identifying the locations where SEM encoding is not unique. Reconstructions using simulations and empirical experimental data are compared with those using conventional linear gradients to demonstrate that the general combination of SEMs can improve image reconstructions.