  Nyquist ghost artifacts in EPI are originated from phase mismatch between the
even and odd echoes. However, conventional correction methods using reference
scans often produce erroneous results especially in high-field MRI due to the
non-linear and time-varying local magnetic field changes. Recently, it was
shown that the problem of ghost correction can be reformulated as k-space
interpolation problem that can be solved using structured low-rank Hankel
matrix approaches. Another recent work showed that data driven Hankel matrix
decomposition can be reformulated to exhibit similar structures as deep
convolutional neural network. By synergistically combining these findings, we
propose a k-space deep learning approach that immediately corrects the phase
mismatch without a reference scan in both accelerated and non-accelerated EPI
acquisitions. To take advantage of the even and odd-phase directional
redundancy, the k-space data is divided into two channels configured with even
and odd phase encodings. The redundancies between coils are also exploited by
stacking the multi-coil k-space data into additional input channels. Then, our
k-space ghost correction network is trained to learn the interpolation kernel
to estimate the missing virtual k-space data. For the accelerated EPI data, the
same neural network is trained to directly estimate the interpolation kernels
for missing k-space data from both ghost and subsampling. Reconstruction
results using 3T and 7T in-vivo data showed that the proposed method
outperformed the image quality compared to the existing methods, and the
computing time is much faster.The proposed k-space deep learning for EPI ghost
correction is highly robust and fast, and can be combined with acceleration, so
that it can be used as a promising correction tool for high-field MRI without
changing the current acquisition protocol.
