W Scott Hoge^{1,2,3} and Jonathan R Polimeni^{2,4,5}

^{1}Radiology, Brigham and Women's Hospital, Boston, MA, United States, ^{2}Athinoula A. Martinos Center for Biomedical Imaging, Massachusetts General Hospital, Charlestown, MA, United States, ^{3}Harvard Medical School, Boston, MA, United States, ^{4}Department of Radiology, Harvard Medical School, Boston, MA, United States, ^{5}Massachusetts Institute of Technology, Cambridge, MA, United States

We examine the relationship between traditional 1D linear phase-error correction methods and Dual-Polarity GRAPPA (DPG) for EPI ghost correction. We first show that conventional ghost correction methods based on 1D linear phase errors can be implemented with convolution kernels in k-space, and then generalized in several steps to replicate a typical DPG kernel. We identify that employing multiple phase-encoded lines is important for ghost correction kernel calibration, while incorporating data from multiple channels is critical. Surprisingly, having a kernel extent along the phase-encoded direction is less critical, demonstrating the utility of DPG kernels with limited extent for ghost correction.

Although the 1x7x31 DPG kernel in Fig. 3(f) provides surprisingly good image quality, we expect DPG kernels need extent along

This work was supported in part by the NIH NIBIB (grants P41-EB015896, R01-EB019437 and R03-EB023489,), by the BRAIN Initiative (NIH NIMH grant R01-MH111419), and by the MGH/HST Athinoula A. Martinos Center for Biomedical Imaging; and was made possible by the resources provided by NIH Shared Instrumentation Grant S10-RR019371.

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Illustration of the relationship between traditional EPI ghost correction methods and convolution-kern\el based ghost correction. Traditional EPI ghost correction, top row, seeks to shift k-space data along *k*_{x} by point-wise multiplication with a phase-ramp function in the {*x*,*k*_{y}} hybrid domain. This can be generalized, bottom row, such that non-linear phase correction functions can be accommodated.

Reconstruction of 7T gradient-echo EPI data using LPC convolution kernels. a: Standard LPC image; b: 1-by-127 kernel image; c: 1-by-7 kernel image. Difference images between the kernel-based and standard LPC reconstructions are shown at 50x-intensity. Note that the 1x127 kernel is almost an exact match to the standard LPC image. Truncating the kernel width as in (c) introduces some error, similar to Gibbs Ringing.

Comparison of images generated from different DPG kernel sizes and calibration data.

Comparison between LPC, DPG with a 2D kernel, and DPG with a 1D kernel reconstructions of data with known 2D phase errors. The top row shows the root-Sum-of-Squares images. The middle row shows a single coil, with significant ghosting in the LPC image highlighted by white arrows. The bottom row shows the RO+ and RO- calibration data, with the phase difference between them shown in the right column. The iso-phase contours run parallel to the black dashed line, with the slope indicating the degree of the 2D phase error.