Higher-order image reconstruction with integrated gradient nonlinearity correction using a low-rank encoding operator

Abstract

Conventional MR image reconstruction relies on the assumption of perfectly linear gradient fields. However, the gradient fields contain spatially varying nonlinear components. We present a higher-order image reconstruction method that incorporates a theoretical model of gradient nonlinearity without any external field monitoring device. This approach utilizes the separability of Fourier encoding in Cartesian imaging and employs a low-rank approximation only to the higher-order readout encoding matrix, allowing a memory-efficient implementation suitable for large FOVs. Image distortions due to gradient nonlinearity were successfully mitigated by the proposed method using axial/sagittal/coronal 2D Cartesian datasets acquired on a prototype 0.55T MRI system.