Background Robust Artificial-neural-networks for k-space Interpolation (RAKI) is a recently proposed deep-learning-based reconstruction algorithm for parallel imaging. Its main premise is to perform k-space interpolation using convolutional neural networks (CNNs) trained on subject-specific autocalibration signal (ACS) data. Since training is performed individually for each subject, the reconstruction time is longer than approaches that pre-train on databases. In this study, we sought to reduce the computational time of RAKI. Methods RAKI was implemented using CPU multi-processing and process pooling to maximize the utility of GPU resources. We also proposed an alternative CNN architecture that interpolates all output channels jointly for specific skipped k-space lines. This new architecture was compared to the original CNN architecture in RAKI, as well as to GRAPPA in phantom, brain and knee MRI datasets, both qualitatively and quantitatively. Results The optimized GPU implementations were approximately 2-to-5-fold faster than a simple GPU implementation. The new CNN architecture further improved the computational time by 4-to-5-fold compared to the optimized GPU implementation using the original RAKI CNN architecture. It also provided significant improvement over GRAPPA both visually and quantitatively, although it performed slightly worse than the original RAKI CNN architecture. Conclusions The proposed implementations of RAKI bring the computational time towards clinically acceptable ranges. The new CNN architecture yields faster training, albeit at a slight performance loss, which may be acceptable for faster visualization in some settings.

Three-dimensional topological insulators (3D TIs) represent states of quantum matters in which surface states are protected by timereversal symmetry and an inversion occurs between bulk conduction and valence bands. However, the bulk-band inversion, which is intimately tied to the topologically nontrivial nature of 3D Tis, has rarely been investigated by experiments. Besides, 3D massive Dirac fermions with nearly linear band dispersions were seldom observed in TIs. Recently, a van der Waals crystal, ZrTe₅, was theoretically predicted to be a TI. Here, we report an infrared transmission study of a high-mobility [∼33,000 cm²/(V · s)] multilayer ZrTe₅ flake at magnetic fields (B) up to 35 T. Our observation of a linear relationship between the zero-magnetic-field optical absorption and the photon energy, a bandgap of ∼10 meV and a √B dependence of the Landau level (LL) transition energies at low magnetic fields demonstrates 3D massive Dirac fermions with nearly linear band dispersions in this system. More importantly, the reemergence of the intra-LL transitions at magnetic fields higher than 17 T reveals the energy cross between the two zeroth LLs, which reflects the inversion between the bulk conduction and valence bands. Our results not only provide spectroscopic evidence for the TI state in ZrTe₅ but also open up a new avenue for fundamental studies of Dirac fermions in van der Waals materials.