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Purpose: To rapidly reconstruct undersampled 3D non-Cartesian image-basednavigators (iNAVs) using an unrolled deep learning (DL) model for non-rigidmotion correction in coronary magnetic resonance angiography (CMRA).  Methods: An unrolled network is trained to reconstruct beat-to-beat 3D iNAVsacquired as part of a CMRA sequence. The unrolled model incorporates anon-uniform FFT operator to perform the data consistency operation, and theregularization term is learned by a convolutional neural network (CNN) based onthe proximal gradient descent algorithm. The training set includes 6,000 3DiNAVs acquired from 7 different subjects and 11 scans using a variable-density(VD) cones trajectory. For testing, 3D iNAVs from 4 additional subjects arereconstructed using the unrolled model. To validate reconstruction accuracy,global and localized motion estimates from DL model-based 3D iNAVs are comparedwith those extracted from 3D iNAVs reconstructed with $\textit{l}_{1}$-ESPIRiT.Then, the high-resolution coronary MRA images motion corrected withautofocusing using the $\textit{l}_{1}$-ESPIRiT and DL model-based 3D iNAVs areassessed for differences.  Results: 3D iNAVs reconstructed using the DL model-based approach andconventional $\textit{l}_{1}$-ESPIRiT generate similar global and localizedmotion estimates and provide equivalent coronary image quality. Reconstructionwith the unrolled network completes in a fraction of the time compared to CPUand GPU implementations of $\textit{l}_{1}$-ESPIRiT (20x and 3x speedincreases, respectively).  Conclusion: We have developed a deep neural network architecture toreconstruct undersampled 3D non-Cartesian VD cones iNAVs. Our approachdecreases reconstruction time for 3D iNAVs, while preserving the accuracy ofnon-rigid motion information offered by them for correction.

Reconstruction of Undersampled 3D Non-Cartesian Image-Based Navigators for Coronary MRA Using an Unrolled Deep Learning Model