非均匀 FFT 的密度补偿空间域优化。
Optimization in the space domain for density compensation with the nonuniform FFT.
机构信息
Biomedical Informatics and Radiology, University of Colorado Anschutz Medical Campus, Aurora, CO 80045, USA.
Mathematics and Statistics, University of San Francisco, San Francisco, CA, USA.
出版信息
Magn Reson Imaging. 2023 Jul;100:102-111. doi: 10.1016/j.mri.2023.03.003. Epub 2023 Mar 17.
The non-uniform Discrete Fourier Transform algorithm has shown great utility for reconstructing images from non-uniformly spaced Fourier samples in several imaging modalities. Due to the non-uniform spacing, some correction for the variable density of the samples must be made. Common methods for generating density compensation values are either sub-optimal or only consider a finite set of points in the optimization. This manuscript presents an algorithm for generating density compensation values from a set of Fourier samples that takes into account the point spread function over an entire rectangular region in the image domain. We show that the reconstructed images using the density compensation values of this method are of superior quality when compared to other standard methods. Results are shown with a numerical phantom and with magnetic resonance images of the abdomen and the knee.
非均匀离散傅里叶变换算法在从几种成像模式中不均匀间隔的傅里叶采样重建图像方面显示出了巨大的实用性。由于非均匀的间距，必须对采样的可变密度进行一些修正。生成密度补偿值的常用方法要么不是最优的，要么只考虑优化中的有限点集。本文提出了一种从一组傅里叶采样中生成密度补偿值的算法，该算法考虑了图像域中整个矩形区域的点扩展函数。我们表明，与其他标准方法相比，使用该方法的密度补偿值重建的图像质量更高。结果用数值体模和腹部及膝关节的磁共振图像进行了展示。
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