Reconstruction of undersampled 3D non-Cartesian image-based navigators for coronary MRA using an unrolled deep learning model

Purpose To rapidly reconstruct undersampled 3D non-Cartesian image-based navigators (iNAVs) using an unrolled deep learning (DL) model, enabling nonrigid motion correction in coronary magnetic resonance angiography (CMRA). Methods An end-to-end unrolled network is trained to reconstruct beat-to-beat 3D iNAVs acquired during a CMRA sequence. The unrolled model incorporates a nonuniform FFT operator in TensorFlow to perform the data-consistency operation, and the regularization term is learned by a convolutional neural network (CNN) based on the proximal gradient descent algorithm. The training set includes 6,000 3D iNAVs acquired from 7 different subjects and 11 scans using a variable-density (VD) cones trajectory. For testing, 3D iNAVs from 4 additional subjects are reconstructed using the unrolled model. To validate reconstruction accuracy, global and localized motion estimates from DL model-based 3D iNAVs are compared with those extracted from 3D iNAVs reconstructed with l1-ESPIRiT. Then, the high-resolution coronary MRA images motion corrected with autofocusing using the l1-ESPIRiT and DL model-based 3D iNAVs are assessed for differences. Results 3D iNAVs reconstructed using the DL model-based approach and conventional l1-ESPIRiT generate similar global and localized motion estimates and provide equivalent coronary image quality. Reconstruction with the unrolled network completes in a fraction of the time compared to CPU and GPU implementations of l1-ESPIRiT (20x and 3x speed increases, respectively). Conclusions We have developed a deep neural network architecture to reconstruct undersampled 3D non-Cartesian VD cones iNAVs. Our approach decreases reconstruction time for 3D iNAVs, while preserving the accuracy of nonrigid motion information offered by them for correction.