Fast and Calibrationless Low-Rank Parallel Imaging Reconstruction through Unrolled Deep Learning Estimation of Multi-Channel Spatial Support Maps

Low-rank technique has emerged as a powerful calibrationless alternative for parallel magnetic resonance (MR) imaging. Calibrationless low-rank reconstruction, such as low-rank modeling of local k-space neighborhoods (LORAKS), implicitly exploits both coil sensitivity modulations and the finite spatial support constraint of MR images through an iterative low-rank matrix recovery process. Although powerful, this slow iteration process is computationally demanding and reconstruction requires empirical rank optimization, hampering its robust applications for high-resolution volume imaging. This paper proposes a fast and calibrationless low-rank reconstruction of undersampled multi-slice MR brain data, based on the finite spatial support constraint reformulation with a direct deep learning estimation of spatial support maps. The iteration process of low-rank reconstruction is unrolled into a complex-valued network by training on fully-sampled multi-slice axial brain datasets acquired from the same MR coil system. To utilize coil-subject geometric parameters available for datasets, the model minimizes a hybrid loss on two sets of spatial support maps, corresponding to brain data at the original slice locations as actually acquired and nearby locations within the standard reference coordinate. This deep learning framework was integrated with LORAKS reconstruction and was evaluated with publically available gradient-echo T1-weighted brain datasets. It directly produced high-quality multi-channel spatial support maps from undersampled data, enabling rapid reconstruction without iteration. Moreover, it led to effective reductions of artifacts and noise amplification at high acceleration. In summary, our proposed deep learning framework offers a new strategy to advance the existing calibrationless low-rank reconstruction, rendering it computationally efficient, simple, and robust in practice.