Smith M R, Nichols S T
Department of Electrical Engineering, University of Calgary, Alberta, Canada.
Magn Reson Med. 1988 Jun;7(2):156-71. doi: 10.1002/mrm.1910070204.
This paper discusses the two-dimensional implementation of a number of modified fast Fourier transform (FFT) algorithms that efficiently interpolate (zoom) magnetic resonance (MR) images. If the original image was sampled at a rate satisfying the Nyquist criterion, these algorithms would effectively increase the sampling rate, permitting image details to be more easily discerned. The Skinner interpolating fast Fourier transform (SIFFT) avoids many of the computationally unnecessary complex multiplications that occur when interpolating using the normal fast Fourier transform algorithm. The novel interpolating fast Fourier transform (NIFFT) offers further savings when a subimage is required. Theoretical and experimental timings that compare the use of the normal FFT, SIFFT, and NIFFT algorithms for interpolation are given using magnetic resonance image reconstruction examples. Time savings of a factor of 2 to 4 are possible in typical experimental situations. Time savings of factors of 5 to 20 are possible when zooming images using two-dimensional band selectable digital filtering (2D-BSDF) in combination with decimation and the SIFFT algorithm. In 2D-BSDF, the original MRI data set is reduced in size to retain only those frequency components corresponding to a desired subimage, thereby decreasing the computational load associated with further processing. A significant reduction in computation time is achieved when modeling is combined with 2D-BSDF and SIFFT as fewer points require modeling.
本文讨论了多种改进的快速傅里叶变换（FFT）算法的二维实现，这些算法可有效地对磁共振（MR）图像进行插值（缩放）。如果原始图像是以满足奈奎斯特准则的速率进行采样的，那么这些算法将有效地提高采样率，使图像细节更容易辨别。斯金纳插值快速傅里叶变换（SIFFT）避免了在使用常规快速傅里叶变换算法进行插值时出现的许多计算上不必要的复数乘法。当需要子图像时，新型插值快速傅里叶变换（NIFFT）能进一步节省计算量。利用磁共振图像重建示例给出了比较使用常规FFT、SIFFT和NIFFT算法进行插值的理论和实验计时结果。在典型的实验情况下，可能节省2至4倍的时间。当使用二维带选数字滤波（2D - BSDF）结合抽取和SIFFT算法对图像进行缩放时，可能节省5至20倍的时间。在2D - BSDF中，原始MRI数据集的大小会减小，只保留与所需子图像对应的那些频率分量，从而减少与后续处理相关的计算负荷。当建模与2D - BSDF和SIFFT相结合时，由于需要建模的点更少，计算时间会显著减少。
