Iterative self-consistent parallel imaging reconstruction (SPIRiT) is an effective self-calibrated reconstruction model for parallel magnetic resonance imaging (PMRI). The joint L1 norm of wavelet coefficients and joint total variation (TV) regularization terms are incorporated into the SPIRiT model to improve the reconstruction performance. The simultaneous two-directional low-rankness (STDLR) in k-space data is incorporated into SPIRiT to realize improved reconstruction. Recent methods have exploited the nonlocal self-similarity (NSS) of images by imposing nonlocal low-rankness of similar patches to achieve a superior performance. To fully utilize both the NSS in Magnetic resonance (MR) images and calibration consistency in the k-space domain, we propose a nonlocal low-rank (NLR)-SPIRiT model by incorporating NLR regularization into the SPIRiT model. We apply the weighted nuclear norm (WNN) as a surrogate of the rank and employ the Nash equilibrium (NE) formulation and alternating direction method of multipliers (ADMM) to efficiently solve the NLR-SPIRiT model. The experimental results demonstrate the superior performance of NLR-SPIRiT over the state-of-the-art methods via three objective metrics and visual comparison.

翻译：在K-空间数据中同时采用双向低级别(STDLR)模型来改进重建。最近的方法利用了非本地的图像自异性(NSS)作为等级的代谢,并采用纳什平衡制和相互交替的变异性(ADMM)方法来有效解决NLR-IRSP的高级图像和通过NLR-IRSP的高级图像测试结果。