MRI Reconstruction with Learnable High Order Fast Fourier Transform (HOFFT) Kernels

Motivation: Reconstruction in the presence of imperfections currently requires a large number of time-segments (same as number of spatial FFTs). Goal(s): To provide a framework capable of efficiently modeling high order phases. Approach: Similar to NUFFT models, we learn compact convolutional kernels in k-space that are capable of modeling high order phases. These kernels are synergized with spatial weighting functions in order to strengthen the model fit. Results: We show the feasibility of learnable convolutional kernels for linear phase, concomitant field induced phase, and susceptibility induced phase. Further, we show an order of magnitude reduction in the required number of time-segments. Impact: Our method will help reduce the computational burden of high order phase correction in MRI. This opens the door to rapid 3D encoding schemes such as cones, MRF, and time-resolved imaging, potentially turning previously intractable problems to feasible ones.