Low-rank matrix completion with phase constraints have been applied to the single-channel magnetic resonance imaging (MRI) reconstruction. In this paper, the reconstruction of sparse parallel imaging with smooth phase in each coil is formulated as the completion of a low-rank data matrix, which is modeled by the k-space neighborhoods and symmetric property of samples. The proposed algorithm is compared with a calibrationless parallel MRI reconstruction method based on both simulation data and real data. The experiment results show the proposed method has better performance in terms of MRI imaging enhancement, scanning time reduction, and denoising capability.
