Pipe J G, Menon P
Department of Radiology, Wayne State University, Detroit, Michigan, USA.
Magn Reson Med. 1999 Jan;41(1):179-86. doi: 10.1002/(sici)1522-2594(199901)41:1<179::aid-mrm25>3.0.co;2-v.
Data collection of MRI which is sampled nonuniformly in k-space is often interpolated onto a Cartesian grid for fast reconstruction. The collected data must be properly weighted before interpolation, for accurate reconstruction. We propose a criterion for choosing the weighting function necessary to compensate for nonuniform sampling density. A numerical iterative method to find a weighting function that meets that criterion is also given. This method uses only the coordinates of the sampled data; unlike previous methods, it does not require knowledge of the trajectories and can easily handle trajectories that "cross" in k-space. Moreover, the method can handle sampling patterns that are undersampled in some regions of k-space and does not require a post-gridding density correction. Weighting functions for various data collection strategies are shown. Synthesized and collected in vivo data also illustrate aspects of this method.
在k空间中进行非均匀采样的磁共振成像（MRI）数据采集，通常会被插值到笛卡尔网格上以实现快速重建。为了进行准确的重建，在插值之前必须对采集到的数据进行适当加权。我们提出了一种用于选择补偿非均匀采样密度所需加权函数的准则。还给出了一种数值迭代方法，用于找到满足该准则的加权函数。该方法仅使用采样数据的坐标；与先前的方法不同，它不需要了解轨迹，并且可以轻松处理在k空间中“交叉”的轨迹。此外，该方法可以处理在k空间某些区域欠采样的采样模式，并且不需要进行网格化后密度校正。展示了各种数据采集策略的加权函数。合成的和采集的体内数据也说明了该方法的各个方面。
