Qu Peng, Zhong Kai, Zhang Bida, Wang Jianmin, Shen Gary X
Department of Electrical and Electronic Engineering, the University of Hong Kong, Pokfulam.
Magn Reson Med. 2005 Oct;54(4):1040-5. doi: 10.1002/mrm.20648.
In non-Cartesian SENSE reconstruction based on the conjugate gradient (CG) iteration method, the iteration very often exhibits a "semi-convergence" behavior, which can be characterized as initial convergence toward the exact solution and later divergence. This phenomenon causes difficulties in automatic implementation of this reconstruction strategy. In this study, the convergence behavior of the iterative SENSE reconstruction is analyzed based on the mathematical principle of the CG method. It is revealed that the semi-convergence behavior is caused by the ill-conditioning of the underlying generalized encoding matrix (GEM) and the intrinsic regularization effect of CG iteration. From the perspective of regularization, each iteration vector is a regularized solution and the number of iterations plays the role of the regularization parameter. Therefore, the iteration count controls the compromise between the SNR and the residual aliasing artifact. Based on this theory, suggestions with respect to the stopping rule for well-behaved reconstructions are provided. Simulated radial imaging and in vivo spiral imaging are performed to demonstrate the theoretical analysis on the semi-convergence phenomenon and the stopping criterion. The dependence of convergence behavior on the undersampling rate and the noise level in samples is also qualitatively investigated.
在基于共轭梯度（CG）迭代法的非笛卡尔敏感性编码（SENSE）重建中，迭代常常呈现出“半收敛”行为，其特征是开始时向精确解收敛，随后发散。这种现象给该重建策略的自动实现带来了困难。在本研究中，基于CG方法的数学原理分析了迭代SENSE重建的收敛行为。结果表明，半收敛行为是由基础广义编码矩阵（GEM）的病态性和CG迭代的内在正则化效应引起的。从正则化的角度来看，每个迭代向量都是一个正则化解，迭代次数起着正则化参数的作用。因此，迭代次数控制着信噪比（SNR）和残余混叠伪影之间的平衡。基于该理论，给出了关于良好重建停止规则的建议。进行了模拟径向成像和体内螺旋成像，以证明对半收敛现象和停止准则的理论分析。还定性研究了收敛行为对欠采样率和样本噪声水平的依赖性。
