  Zero echo time (ZTE) sequences have proven a powerful tool for Magnetic
Resonance Imaging (MRI) of ultrashort T2 tissues, but they fail to produce
useful images in the presence of strong field inhomogeneities. Here we present
a method to correct artifacts induced by strong B0 inhomogeneities in
non-Cartesian sequences, based on magnetic field maps obtained from the phase
difference between two fast pointwise acquisitions. These are free of geometric
distortions and can be used for model based image reconstruction with iterative
algebraic techniques. In this paper, we show that distortions and artifacts
coming from inhomogeneites in B0 are largely reverted by our method, as opposed
to standard Conjugate Phase reconstructions. We base this technique on a
Single-Point Double-Shot (SPDS) approach, and we have shown it to work even for
intra-voxel bandwidths (determined by B0 inhomogeneities) comparable to the
encoding bandwidth (determined by the gradient fields). We benchmark the
performance of SPDS for ZTE acquisitions, which can be exploited for e.g.
dental imaging in affordable low-field MRI systems. Furthermore, SPDS can be
used for arbitrary pulse sequences and it may prove useful for extreme magnet
geometries, as in e.g. single-sided MRI.
