磁共振螺旋采样的一种基于Trivial尺度因子的NUFFT重建算法

在解决磁共振成像的非笛卡尔采样,比如螺旋轨迹采样的重建问题中,最小二乘意义上的NUFFT算法是其中重要的方法之一。该NUFFT算法,在最小二乘意义上能够针对每一个数据点生成一个卷积核矩阵,因而计算精度高;但是,尺度因子作为构成核矩阵的参数之一,它的选择目前尚没有定论。本文在该算法的基础上,采用Trivial尺度因子,并将之应用在螺旋采样的磁共振重建上。实验结果表明本文的方法比目前采用Cosine尺度因子的NUFFT算法,重建误差更小,速度更快。

A NUFFT Algorithm Based on the Trivial Scaling Factor for the Spiral Magnetic Resonance Reconstruction

For magnetic resonance imaging with non-Cartesian sampling,such as spiral trajectories,one of the most important approaches is the NUFFT algorithm in the Least Square sense.A convolutional kernel matrix can be generated in the Least Square sense for the every point in this NUFFT algorithm at a high precision of the computation.At this point,however,the selection of the scaling factor,one of the parameters composing the kernel matrix,is not determined at present yet.In this article,the method based on the algorithm with the trivial factor,is applied for the reconstruction for the spiral magnetic resonance.Numerical results show that this method in the article provides the lower approximation errors and the faster speed than the method with cosine factor presently.