论文标题
快速nonconvex $ t_2^*$使用ADMM映射
Fast Nonconvex $T_2^*$ Mapping Using ADMM
论文作者
论文摘要
磁共振（MR） - $ T_2^*$映射被广泛用于研究各种临床应用中的出血，钙化和铁沉积，它提供了组织中所需对比的直接而精确的映射。但是，常规3D高分辨率$ T_2^*$映射方法所需的漫长获取时间会给患者带来不适，并引入运动伪像重建图像，从而限制了其更广泛的适用性。在本文中，我们通过使用压缩传感（CS）执行从不足的数据中执行$ T_2^*$映射来解决此问题。我们将重建作为一个非凸问题，可以分解为两个子问题。它们可以通过标准方法分别解决，也可以通过乘数的交替方向方法（ADMM）共同解决。与以前仅在旋转密度$ \ boldsymbol x_0 $和放松率$ \ boldsymbol r_2^*$上应用稀疏正则化的方法相比，我们的公式在多个Echoes上强化了$ t_2^*$加权图像上的额外稀疏先验，以提高生产性能。我们对所提出的算法进行了收敛分析，评估了其在体内数据上的性能，并研究了不同采样方案的效果。实验结果表明，拟议的联合恢复方法通常优于最先进的方法，尤其是在低采样率制度中，这是在实践中执行快速3D $ T_2^*$映射的首选选择。这项工作中采用的框架可以很容易地扩展到MR或其他具有非线性耦合变量的成像方式引起的其他问题。
Magnetic resonance (MR)-$T_2^*$ mapping is widely used to study hemorrhage, calcification and iron deposition in various clinical applications, it provides a direct and precise mapping of desired contrast in the tissue. However, the long acquisition time required by conventional 3D high-resolution $T_2^*$ mapping method causes discomfort to patients and introduces motion artifacts to reconstructed images, which limits its wider applicability. In this paper we address this issue by performing $T_2^*$ mapping from undersampled data using compressive sensing (CS). We formulate the reconstruction as a nonconvex problem that can be decomposed into two subproblems. They can be solved either separately via the standard approach or jointly via the alternating direction method of multipliers (ADMM). Compared to previous CS-based approaches that only apply sparse regularization on the spin density $\boldsymbol X_0$ and the relaxation rate $\boldsymbol R_2^*$, our formulation enforces additional sparse priors on the $T_2^*$-weighted images at multiple echoes to improve the reconstruction performance. We performed convergence analysis of the proposed algorithm, evaluated its performance on in vivo data, and studied the effects of different sampling schemes. Experimental results showed that the proposed joint-recovery approach generally outperforms the state-of-the-art method, especially in the low-sampling rate regime, making it a preferred choice to perform fast 3D $T_2^*$ mapping in practice. The framework adopted in this work can be easily extended to other problems arising from MR or other imaging modalities with non-linearly coupled variables.
