Knopp Tobias, Kunis Stefan, Potts Daniel
Institute of Mathematics, University of Lübeck, 23538 Lübeck, Germany.
Int J Biomed Imaging. 2007;2007:24727. doi: 10.1155/2007/24727.
In magnetic resonance imaging (MRI), methods that use a non-Cartesian grid in k-space are becoming increasingly important. In this paper, we use a recently proposed implicit discretisation scheme which generalises the standard approach based on gridding. While the latter succeeds for sufficiently uniform sampling sets and accurate estimated density compensation weights, the implicit method further improves the reconstruction quality when the sampling scheme or the weights are less regular. Both approaches can be solved efficiently with the nonequispaced FFT. Due to several new techniques for the storage of an involved sparse matrix, our examples include also the reconstruction of a large 3D data set. We present four case studies and report on efficient implementation of the related algorithms.
在磁共振成像（MRI）中，在k空间使用非笛卡尔网格的方法正变得越来越重要。在本文中，我们使用了一种最近提出的隐式离散化方案，该方案推广了基于网格化的标准方法。虽然后者对于足够均匀的采样集和准确估计的密度补偿权重是成功的，但当采样方案或权重不太规则时，隐式方法进一步提高了重建质量。这两种方法都可以用非等距快速傅里叶变换（FFT）有效地求解。由于有几种用于存储相关稀疏矩阵的新技术，我们的示例还包括一个大型三维数据集的重建。我们给出了四个案例研究，并报告了相关算法的高效实现。
