Image distortion correction for MRI in low field permanent magnet systems with strong B(0) inhomogeneity and gradient field nonlinearities

OBJECTIVE: To correct for image distortions produced by standard Fourier reconstruction techniques on low field permanent magnet MRI systems with strong [Formula: see text] inhomogeneity and gradient field nonlinearities. MATERIALS AND METHODS: Conventional image distortion correction algorithms require accurate [Formula: see text] maps which are not possible to acquire directly when the [Formula: see text] inhomogeneities also produce significant image distortions. Here we use a readout gradient time-shift in a TSE sequence to encode the [Formula: see text] field inhomogeneities in the k-space signals. Using a non-shifted and a shifted acquisition as input, [Formula: see text] maps and images were reconstructed in an iterative manner. In each iteration, [Formula: see text] maps were reconstructed from the phase difference using Tikhonov regularization, while images were reconstructed using either conjugate phase reconstruction (CPR) or model-based (MB) image reconstruction, taking the reconstructed field map into account. MB reconstructions were, furthermore, combined with compressed sensing (CS) to show the flexibility of this approach towards undersampling. These methods were compared to the standard fast Fourier transform (FFT) image reconstruction approach in simulations and measurements. Distortions due to gradient nonlinearities were corrected in CPR and MB using simulated gradient maps. RESULTS: Simulation results show that for moderate field inhomogeneities and gradient nonlinearities, [Formula: see text] maps and images reconstructed using iterative CPR result in comparable quality to that for iterative MB reconstructions. However, for stronger inhomogeneities, iterative MB reconstruction outperforms iterative CPR in terms of signal intensity correction. Combining MB with CS, similar image and [Formula: see text] map quality can be obtained without a scan time penalty. These findings were confirmed by experimental results. DISCUSSION: In case of [Formula: see text] inhomogeneities in the order of kHz, iterative MB reconstructions can help to improve both image quality and [Formula: see text] map estimation. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1007/s10334-021-00907-2.