Department of Energy and System Engineering, University of Pisa, Pisa, Italy.
Int J Numer Method Biomed Eng. 2013 May;29(5):561-73. doi: 10.1002/cnm.2540. Epub 2013 Feb 14.
Non-Cartesian acquisition strategies are widely used in MRI to dramatically reduce the acquisition time while at the same time preserving the image quality. Among non-Cartesian reconstruction methods, the least squares non-uniform fast Fourier transform (LS_NUFFT) is a gridding method based on a local data interpolation kernel that minimizes the worst-case approximation error. The interpolator is chosen using a pseudoinverse matrix. As the size of the interpolation kernel increases, the inversion problem may become ill-conditioned. Regularization methods can be adopted to solve this issue. In this study, we compared three regularization methods applied to LS_NUFFT. We used truncated singular value decomposition (TSVD), Tikhonov regularization and L₁-regularization. Reconstruction performance was evaluated using the direct summation method as reference on both simulated and experimental data. We also evaluated the processing time required to calculate the interpolator. First, we defined the value of the interpolator size after which regularization is needed. Above this value, TSVD obtained the best reconstruction. However, for large interpolator size, the processing time becomes an important constraint, so an appropriate compromise between processing time and reconstruction quality should be adopted.
非笛卡尔采集策略在 MRI 中被广泛应用，可以在保持图像质量的同时显著缩短采集时间。在非笛卡尔重建方法中，最小二乘非均匀快速傅里叶变换（LS_NUFFT）是一种基于局部数据插值核的网格化方法，它可以最小化最坏情况的逼近误差。插值器是使用伪逆矩阵选择的。随着插值核的增大，反演问题可能会变得病态。可以采用正则化方法来解决这个问题。在这项研究中，我们比较了三种应用于 LS_NUFFT 的正则化方法。我们使用截断奇异值分解（TSVD）、Tikhonov 正则化和 L₁-正则化。使用直接求和法作为参考，对模拟和实验数据进行了重建性能评估。我们还评估了计算插值器所需的处理时间。首先，我们定义了需要正则化的插值器大小的值。在此值之上，TSVD 获得了最佳的重建效果。然而，对于较大的插值器大小，处理时间成为一个重要的限制因素，因此应该在处理时间和重建质量之间做出适当的折衷。
