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 for non-rigid motion correction in coronary magnetic resonance angiography (CMRA). Methods: An unrolled network is trained to reconstruct beat-to-beat 3D iNAVs acquired as part of a CMRA sequence. The unrolled model incorporates a non-uniform FFT operator 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 $\textit{l}_{1}$-ESPIRiT. Then, the high-resolution coronary MRA images motion corrected with autofocusing using the $\textit{l}_{1}$-ESPIRiT and DL model-based 3D iNAVs are assessed for differences. Results: 3D iNAVs reconstructed using the DL model-based approach and conventional $\textit{l}_{1}$-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 $\textit{l}_{1}$-ESPIRiT (20x and 3x speed increases, respectively). Conclusion: 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 non-rigid motion information offered by them for correction.Comment: 34 pages, 5 figures, 1 table, 6 supporting figures, 1 supporting tabl

Data Partition and Migration for High Performance Computation in Distributed Memory Multiprocessors

Data-partition and migration for efficient communication in distributed memory architectures are critical for performance of data parallel algorithms. This research presents a formal methodology for the process of data-distribution and redistribution using tensor products and stride permutations as mathematical tools. The algebraic expressions representing data-partition and migration directly operate on a data vector, and hence can be conveniently embedded into an algorithm. It is also shown that these expressions are useful for a clear understanding and to efficiently interleave problems that involve different data-distributions at different phases. This compatibility made us successfully utilize these expressions in developing and demonstrating matrix transpose and fast Fourier transform algorithms. Usage of these expressions for data interface generated efficient parallel implementation to solve Euler partial differential equation. An endeavor to minimize communication cost using expressions for data-distribution disclosed a routing scheme for Fourier transform evaluation. Results promised that for large parallel machines, this scheme is a solution to today\u27s problems which feature enormous data. Finally, a unique data-distribution technique that effectively uses transpose algorithms for multiplication of two rectangular matrices is derived. Performance of these algorithms are evaluated by carrying out implementations on Intel\u27s i860 based iPSC/860, Touchstone Delta, Gamma, and Paragon supercomputers