  Respiration-induced B$_0$ fluctuation corrupts MRI images by inducing phase
errors in k-space. A few approaches such as navigator have been proposed to
correct for the artifacts at the expense of sequence modification. In this
study, a new deep learning method, which is referred to as DeepResp, is
proposed for reducing the respiration-artifacts in multi-slice gradient echo
(GRE) images. DeepResp is designed to extract the respiration-induced phase
errors from a complex image using deep neural networks. Then, the
network-generated phase errors are applied to the k-space data, creating an
artifact-corrected image. For network training, the computer-simulated images
were generated using artifact-free images and respiration data. When evaluated,
both simulated images and in-vivo images of two different breathing conditions
(deep breathing and natural breathing) show improvements (simulation:
normalized root-mean-square error (NRMSE) from 7.8% to 1.3%; structural
similarity (SSIM) from 0.88 to 0.99; ghost-to-signal-ratio (GSR) from 7.9% to
0.6%; deep breathing: NRMSE from 13.9% to 5.8%; SSIM from 0.86 to 0.95; GSR
20.2% to 5.7%; natural breathing: NRMSE from 5.2% to 4.0%; SSIM from 0.94 to
0.97; GSR 5.7% to 2.8%). Our approach does not require any modification of the
sequence or additional hardware, and may therefore find useful applications.
Furthermore, the deep neural networks extract respiration-induced phase errors,
which is more interpretable and reliable than results of end-to-end trained
networks.
