Tong R, Cox R W
Biophysics Research Institute, Medical College of Wisconsin, Milwaukee 53226-0509, USA.
Magn Reson Med. 1999 Feb;41(2):253-6. doi: 10.1002/(sici)1522-2594(199902)41:2<253::aid-mrm7>3.0.co;2-1.
A quick and accurate way to rotate and shift nuclear magnetic resonance (NMR) images using the two-dimensional chirp-z transform is presented. When the desired image grid is rotated and shifted from the original grid due to patient motion, the chirp-z transform can reconstruct NMR images directly onto the ultimate grid instead of reconstructing onto the original grid and then applying interpolation to get the final real-space image in the conventional way. The rotation angle and shift distances are embedded in the parameters of the chirp-z transform. The chirp-z transform implements discrete sinc interpolation to get values at grid points that are not exactly on the original grid when applying the inverse Fourier transform. Therefore, the chirp-z transform is more accurate than methods such as linear or bicubic interpolation and is more efficient than direct implementation of sinc interpolation because the sinc interpolation is implemented at the same time as reconstruction from k-space.
提出了一种使用二维线性调频Z变换来旋转和移位核磁共振（NMR）图像的快速且准确的方法。当由于患者运动导致所需图像网格相对于原始网格发生旋转和移位时，线性调频Z变换可以直接将NMR图像重建到最终网格上，而不是像传统方法那样先重建到原始网格上，然后再进行插值以获得最终的实空间图像。旋转角度和移位距离被嵌入到线性调频Z变换的参数中。在应用逆傅里叶变换时，线性调频Z变换通过实现离散辛克插值来获取不完全位于原始网格上的网格点处的值。因此，线性调频Z变换比线性或双三次插值等方法更准确，并且比直接实现辛克插值更高效，因为辛克插值是在从k空间进行重建的同时实现的。
