基于Kaczmarz算法的磁粒子成像快速重建算法研究

Fast reconstruction algorithm of magnetic particle imaging based on Kaczmarz algorithm

目的:为了解决磁粒子断层成像中系统矩阵方法成像时间长、计算复杂的问题,提出一种基于Kaczmarz算法的磁粒子成像快速重建算法。方法:首先,分析经典Kaczmarz算法及其变体算法的收敛速度,并计算在任意矩阵下的迭代次数和计算时间;其次,比较欧氏距离和余弦距离对系统数据的区分能力,并运用基于余弦距离的K-means算法来增强块Kaczmarz算法的运算能力,缩短系统矩阵重建时间并最终实现磁粒子成像快速重建。最后,通过计算机仿真实验验证提出的算法的有效性。结果:提出的算法大幅缩短了重建时间,提高了重建图像的空间分辨力和质量。结论:提出的算法可以实现磁粒子成像的快速重建,并且在处理含有噪声的数据时具备较强的重建能力。

Objective To propose a Kaczmarz algorithm-based fast reconstruction method of magnetic particle imaging to solve the problems of magnetic particle tomography in prolonged imaging time and computational complexity.Methods Firstly,the convergence speeds of the classical Kaczmarz algorithm and its variant algorithms were analyzed,and the number of iterations and computational time under arbitrary matrices were calculated.Secondly,the abilities of Euclidean distance and cosine distance in differentiating system data were compared,and the cosine distance-based K-means algorithm was employed to enhance the computational capability of block Kaczmarz algorithm,shorten the system matrix reconstruction time,and ultimately fast reconstruction of magnetic particle imaging was realized.The effectiveness of the proposed algorithm was verified through computer simulation.Results The proposed algorithm reduced greatly the reconstruction time and improved the spatial resolution and quality of the reconstructed images.Conclusion The proposed algorithm enables fast reconstruction of magnetic particle imaging and behaves well in reconstruction of data containing noise.