Trajectory Auto-Corrected Image Reconstruction

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To estimate k-space trajectory errors in non-Cartesian acquisitions and reconstruct distortion-free images, without trajectory measurements or gradient calibrations.

Theory and Methods:

The Trajectory Auto-Corrected image Reconstruction method jointly estimates k-space trajectory errors and images, based on SENSE and SPIRiT parallel imaging reconstruction. The underlying idea is that parallel imaging and oversampling in the center of k-space provides data redundancy that can be exploited to simultaneously reconstruct images and correct trajectory errors. Trajectory errors are represented as weighted sums of trajectory-dependent error basis functions, the coefficients of which are estimated using gradient-based optimization.


Trajectory Auto-Corrected image Reconstruction was applied to reconstruct images and errors in golden angle radial, center-out radial, and spiral in vivo 7 Tesla brain acquisitions in five subjects. Compared to reconstructions using nominal trajectories, Trajectory auto-corrected image reconstructions contained considerably less blurring and streaking and were of similar quality to images reconstructed using measured k-space trajectories in the center-out radial and spiral cases. Reconstruction cost function reductions and improvements in normalized image gradient squared were also similar to those for images reconstructed using measured trajectories.


Trajectory Auto-Corrected image Reconstruction enables non-Cartesian image reconstructions free from trajectory errors without the need for separate gradient calibrations or trajectory measurements. Magn Reson Med 76:757–768, 2016. © 2015 Wiley Periodicals, Inc.

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