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Image reconstruction methods based on structured low-rank matrix completion have drawn growing interest in magnetic resonance imaging. In this work, we propose a locally structured low-rank image reconstruction method which imposes low-rank constraints on submatrices of the Hankel structured k-space data matrix. Simulation experiments based on numerical phantoms and experimental data demonstrated that the proposed method achieves robust and significant improvements over the conventional, global structured low-rank methods across a variety of structured matrix constructions, sampling patterns and noise levels, at the cost of slower convergence speed only.

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