OBJECTIVE: To provide a navigator-based run-time motion and first-order field correction for three-dimensional human brain imaging with high precision, minimal calibration and acquisition, and fast processing.
METHODS: A complex-valued linear perturbation model with feedback control is extended to estimate and correct for gradient shim fields using orbital navigators (2.3 ms). Two approaches for sensitizing the model to gradient fields are presented, one based on finite differences with three additional navigators, and another projection-based approximation requiring no additional navigators. A mechanism for noise decorrelation of the matrix and the data is proposed and evaluated to reduce unwanted parameter biases.
RESULTS: The rigid motion and first-order field control achieves robust motion and gradient shim corrections improving image quality in a series of phantom and in vivo experiments with varying field conditions. In phantom scans, magnet drifts, forced gradient field perturbations and field distortions from shifts of a second bottle phantom are successfully corrected. Field estimates of the magnet drifts are in good agreement with concurrent field probe measurements. For in vivo scans, the proposed method mitigates field variations from torso motions while being robust to head motion. In vivo gradient field precisions were 30   nT / m $$ 30\\;\\mathrm{nT}/\\mathrm{m} $$ along with single-digit micrometer and millidegree rigid precisions.
CONCLUSIONS: The navigator-based method achieves accurate, high-precision run-time motion and field corrections with low sequence impact and calibration requirements.

OBJECTIVE: Navigator-based correction of rigid-body motion reconciling high precision with minimal acquisition, minimal calibration and simple, fast processing.
METHODS: A short orbital navigator (2.3 ms) is inserted in a three-dimensional (3D) gradient echo sequence for human head imaging. Head rotation and translation are determined by linear regression based on a complex-valued model built either from three reference navigators or in a reference-less fashion, from the first actual navigator. Optionally, the model is expanded by global phase and field offset. Run-time scan correction on this basis establishes servo control that maintains validity of the linear picture by keeping its expansion point stable in the head frame of reference. The technique is assessed in a phantom and demonstrated by motion-corrected imaging in vivo.
RESULTS: The proposed approach is found to establish stable motion control both with and without reference acquisition. In a phantom, it is shown to accurately detect motion mimicked by rotation of scan geometry as well as change in global B0 . It is demonstrated to converge to accurate motion estimates after perturbation well beyond the linear signal range. In vivo, servo navigation achieved motion detection with precision in the single-digit range of micrometers and millidegrees. Involuntary and intentional motion in the range of several millimeters were successfully corrected, achieving excellent image quality.
CONCLUSIONS: The combination of linear regression and feedback control enables prospective motion correction for head imaging with high precision and accuracy, short navigator readouts, fast run-time computation, and minimal demand for reference data.