Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI 48109, USA.
IEEE Trans Med Imaging. 2013 Mar;32(3):556-64. doi: 10.1109/TMI.2012.2229711. Epub 2012 Nov 22.
Several magnetic resonance parallel imaging techniques require explicit estimates of the receive coil sensitivity profiles. These estimates must be accurate over both the object and its surrounding regions to avoid generating artifacts in the reconstructed images. Regularized estimation methods that involve minimizing a cost function containing both a data-fit term and a regularization term provide robust sensitivity estimates. However, these methods can be computationally expensive when dealing with large problems. In this paper, we propose an iterative algorithm based on variable splitting and the augmented Lagrangian method that estimates the coil sensitivity profile by minimizing a quadratic cost function. Our method, ADMM-Circ, reformulates the finite differencing matrix in the regularization term to enable exact alternating minimization steps. We also present a faster variant of this algorithm using intermediate updating of the associated Lagrange multipliers. Numerical experiments with simulated and real data sets indicate that our proposed method converges approximately twice as fast as the preconditioned conjugate gradient method over the entire field-of-view. These concepts may accelerate other quadratic optimization problems.
几种磁共振并行成像技术需要明确估计接收线圈灵敏度分布。这些估计必须在物体及其周围区域都准确，以避免在重建图像中产生伪影。涉及最小化包含数据拟合项和正则化项的代价函数的正则化估计方法提供了稳健的灵敏度估计。然而，当处理大型问题时，这些方法可能计算成本很高。在本文中，我们提出了一种基于变量分裂和增广拉格朗日方法的迭代算法，通过最小化二次代价函数来估计线圈灵敏度分布。我们的方法 ADMM-Circ 通过对正则化项中的有限差分矩阵进行重新表述，使得精确的交替最小化步骤成为可能。我们还提出了该算法的一个更快变体，使用相关拉格朗日乘子的中间更新。使用模拟和真实数据集的数值实验表明，与整个视场相比，我们提出的方法的收敛速度大约快两倍于预处理共轭梯度法。这些概念可能会加速其他二次优化问题。
