Self-calibrated trajectory estimation and signal correction method for robust radial imaging using GRAPPA operator gridding

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In radial imaging, projections may become “miscentered” due to gradient errors such as delays and eddy currents. These errors may result in image artifacts and can disrupt the reliability of direct current (DC) navigation. The proposed parallel imaging–based technique retrospectively estimates trajectory error from miscentered radial data without extra acquisitions, hardware, or sequence modification.

Theory and Methods:

After phase correction, self-calibrated GRAPPA operator gridding (GROG) weights are iteratively applied to shift-miscentered projections toward the center of k-space. A search algorithm identifies the shift that aligns the peak k-space signals by maximizing the sum-of-squares DC signal estimate of each projection. The algorithm returns a trajectory estimate and a corrected radial k-space signal.


Data from a spherical phantom, the head, and the heart demonstrate that image reconstruction with the estimated trajectory restores image quality and reduces artifacts such as streaks and signal voids. The DC signal level is increased and variability is reduced.


Retrospective phase correction and iterative application of GROG can be used to successfully estimate the trajectory error in two-dimensional radial acquisitions for improved image reconstruction without requiring extra data acquisition or sequence modification. Magn Reson Med 75:883–896, 2016. © 2015 Wiley Periodicals, Inc.

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