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The image acquisition strategy and/or the image reconstruction methods will likely need refinement if the homogeneity specifications of the magnet are relaxed to achieve a more desirable POC footprint. Mullins and Garwood review the signal dropout and distortion consequences of inhomogeneities of >10 kHz in conventional sequences and some acquisition approaches [124]. In conventional gradient echo acquisition sequences, simple image reconstructions require that all gradient pulses (slice-select, phase-encoding, and readout) use a gradient strength that dominates the local gradients from the inhomogeneous magnet. Thus, strong gradient fields are desirable for reducing geometric distortions, but at odds with the constraints of portable or POC use where power and cooling infrastructure might be limited. For 3D spin echo sequences, only the readout gradient must dominate since a spin echo can be arranged to refocus the spurious gradients but not the phase-encoding field.

The distortions induced in the image’s coordinate system are described by the Jacobian matrix formed from the partial spatial derivatives of the B₀ field. If the magnet’s B₀ field map is known, the Jacobian is fully known and, in principle, can be used to correct the distortions. But no spatial encoding occurs in locations where the magnet’s static gradient is equal and opposite to the applied gradient, and the correction problem is singular. Because of this, it can be desirable to acquire the image twice, for example once with a positive readout gradient and once with the readout gradient current reversed to ensure that all locations are spatially encoded for at least one acquisition. A general approach is to use a “model-based reconstruction” where the “forward model” describes how measured data are produced given any object input to the model. Conversely, given a set of measured data, an inversion of the forward model (generally by some form of iterative search) finds the object giving the “best fit” to the data, possibly subject to some constraints or prior knowledge [125–128].

Acquisition approaches to the magnet inhomogeneity problem include relying on multiple spin echo sequences, which have a long history of use in the oil well-logging industry where NMR is performed in very inhomogeneous fields [129]. This approach was used with phase encoding and the fixed “readout” gradient inherent to an inhomogeneous magnet to image in single-sided devices [49,130] and in a Halbach cylinder with a built-in readout gradient [20,22]. Other approaches include quadratic phase-encoding approaches [131,132] and missing point steady-state free precession (MS-SSFP) methods [133].