A novel nonlocal MRI reconstruction algorithm with patch-based low rank regularization

Compressive Sensing Magnetic Resonance Imaging (CSMRI) exploits sparsity of medical images to reconstruct them accurately from undersampled k-space data. In this paper, we propose a novel patch-based nonlocal MRI reconstruction algorithm with low-rank regularization to exploit the structural sparsity of the observed data. In the proposed algorithm, the low-rank regularization is transformed into the nuclear norm minimization problem then the problem is solved by the Singular Value Thresholding (SVT) method with adaptive thresholds estimation and the Alternative Direction Multiplier Method(ADMM). Experimental results show the proposed MRI reconstruction method outperforms many existing algorithms in CSMRI.