摘要The structured low-rank model for parallel magnetic resonance(MR)imaging can efficiently reconstruct MR images with limited auto-calibration signals.To improve the reconstruction quality of MR images,we integrate the joint sparsity and sparsifying transform learning(JTL)into the simultaneous auto-calibrating and k-space estimation(SAKE)structured low-rank model,named JTLSAKE.The alternate direction method of multipliers is exploited to solve the resulting optimization problem,and the optimized gradient method is used to improve the convergence speed.In addition,a graphics processing unit is used to accelerate the proposed algorithm.The experimental results on four in vivo human datasets demonstrate that the reconstruction quality of the proposed algorithm is comparable to that of JTL-based low-rank modeling of local k-space neighborhoods with parallel imaging(JTL-PLORAKS),and the proposed algorithm is 46 times faster than the JTL-PLORAKS,requiring only 4 s to reconstruct a 200 × 200 pixels MR image with 8 channels.