中文摘要：

提出了一种高效的磁共振成像重建算法,将磁共振成像重建看作标准的线性求逆问题,基于变量分离技术重新建立线性求逆问题的目标函数,用交替最小化方法处理新目标函数的优化问题。新目标函数的优化包含两个交替的过程：一个凸的光滑函数的优化和一个凸的非光滑函数的优化。为处理非光滑函数的优化问题,引入投影算法对其求解。实验结果表明了该磁共振成像重建算法的有效性,与同类算法性比,重建的磁共振图像的均方误差（MSE）最小,重建的速度最快。

英文摘要：

An efficient magnetic resonance imaging reconstruction（MRI） algorithm is proposed,which the MRI is treated as a standard linear inverse problem（LIP）.The objective function of the LIP is redefined using variable splitting technology,and then the redefined objective function is optimized by alternating minimization method.The optimization of the new objective function is composed of two alternate procedures： the optimization of a convex smooth function and the optimization of a convex non-smooth function.For solving the non-smooth function optimization,projection method is introduced.The experimental results demonstrate the effectiveness of the proposed MRI reconstruction algorithm and the comparisons show that the optimal MSE values are obtained.Moreover,compared with current state-of-the-art algorithms,the proposed algorithm is faster.