Trajectory Auto-Corrected Image Reconstruction

Abstract

The goal of this research is to develop image reconstruction techniques to automatically correct for errors in Magnetic Resonance Imaging (MRI) data due to errors in the trajectory used in the data acquisition. A method is presented to perform an iterative image reconstruction correcting for these trajectory errors in non-Cartesian acquisitions, without additional scans or measurements. The Trajectory Auto-Corrected image Reconstruction (TrACR) 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. TrACR was applied to reconstruct images and errors in golden angle radial, center-out radial, and spiral in vivo 7 Tesla brain acquisitions in 5 subjects. Compared to reconstructions using nominal trajectories, TrACR 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. TrACR enables non-Cartesian image reconstructions free from trajectory errors without the need for separate gradient calibrations or trajectory measurements.