Department of Mathematics, University of Florida, Gainesville, FL 32611, USA.
IEEE Trans Med Imaging. 2011 May;30(5):1055-63. doi: 10.1109/TMI.2010.2073717. Epub 2010 Sep 7.
In this paper, we present a fast numerical algorithm for solving total variation and l(1) (TVL1) based image reconstruction with application in partially parallel magnetic resonance imaging. Our algorithm uses variable splitting method to reduce computational cost. Moreover, the Barzilai-Borwein step size selection method is adopted in our algorithm for much faster convergence. Experimental results on clinical partially parallel imaging data demonstrate that the proposed algorithm requires much fewer iterations and/or less computational cost than recently developed operator splitting and Bregman operator splitting methods, which can deal with a general sensing matrix in reconstruction framework, to get similar or even better quality of reconstructed images.
本文提出了一种快速数值算法，用于求解基于全变分和 l(1)范数（TVL1）的图像重建问题，并将其应用于部分并行磁共振成像中。我们的算法使用变量分裂方法来降低计算成本。此外，我们的算法采用了 Barzilai-Borwein 步长选择方法，以实现更快的收敛速度。在临床部分并行成像数据上的实验结果表明，与最近开发的算子分裂和 Bregman 算子分裂方法相比，所提出的算法需要更少的迭代次数和/或更低的计算成本，这些方法可以在重建框架中处理一般的传感矩阵，从而获得相似甚至更好的重建图像质量。
