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Purpose: To introduce two novel learning-based motion artifact removalnetworks (LEARN) for the estimation of quantitative motion- and$B0$-inhomogeneity-corrected $R_2^\ast$ maps from motion-corruptedmulti-Gradient-Recalled Echo (mGRE) MRI data.  Methods: We train two convolutional neural networks (CNNs) to correct motionartifacts for high-quality estimation of quantitative$B0$-inhomogeneity-corrected $R_2^\ast$ maps from mGRE sequences. The firstCNN, LEARN-IMG, performs motion correction on complex mGRE images, to enablethe subsequent computation of high-quality motion-free quantitative $R_2^\ast$(and any other mGRE-enabled) maps using the standard voxel-wise analysis ormachine-learning-based analysis. The second CNN, LEARN-BIO, is trained todirectly generate motion- and $B0$-inhomogeneity-corrected quantitative$R_2^\ast$ maps from motion-corrupted magnitude-only mGRE images by takingadvantage of the biophysical model describing the mGRE signal decay. We showthat both CNNs trained on synthetic MR images are capable of suppressing motionartifacts while preserving details in the predicted quantitative $R_2^\ast$maps. Significant reduction of motion artifacts on experimental in vivomotion-corrupted data has also been achieved by using our trained models.  Conclusion: Both LEARN-IMG and LEARN-BIO can enable the computation ofhigh-quality motion- and $B0$-inhomogeneity-corrected $R_2^\ast$ maps.LEARN-IMG performs motion correction on mGRE images and relies on thesubsequent analysis for the estimation of $R_2^\ast$ maps, while LEARN-BIOdirectly performs motion- and $B0$-inhomogeneity-corrected $R_2^\ast$estimation. Both LEARN-IMG and LEARN-BIO jointly process all the availablegradient echoes, which enables them to exploit spatial patterns available inthe data. The high computational speed of LEARN-BIO is an advantage that canlead to a broader clinical application.

Learning-based Motion Artifact Removal Networks (LEARN) for Quantitative $R_2^\ast$ Mapping