LORAKS: Low-Rank Modeling of Local k -Space Neighborhoods

This work presents a novel framework for constrained image reconstruction based on Low-Rank Modeling of Local k -Space Neighborhoods (LORAKS). We first demonstrate that k -space data for low-dimensional images can be mapped into high-dimensional matrices, such that the resulting matrices possess low-rank structure when the original images have limited support and/or slowly-varying phase. Subsequently, we propose a flexible approach to exploiting this low-rank structure that enables image reconstruction from undersampled data. The approach is analogous to a single-channel calibrationless generalization of GRAPPA, and is demonstrated to outperform sparsity-guided reconstructions of undersampled data in certain contexts.

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