基于奇异值分解方法的磁感应磁声断层重建算法  

Magneto-acoustic tomography with magnetic induction reconstruction algorithm based on singular value decomposition method

作　　者：马任[1] 杨铭 张顺起[1] 周晓青 殷涛 刘志朋[1] MA Ren;YANG Ming;ZHANG Shunqi;ZHOU Xiaoqing;YIN Tao;LIU Zhipeng(Institute of Biomedical Engineering,Chinese Academy of Medical Sciences & Peking Union Medical College,Tianjin 300192,China)

机构地区：[1]北京协和医学院中国医学科学院生物医学工程研究所

出　　处：《生物医学工程研究》2019年第2期129-133,共5页Journal Of Biomedical Engineering Research

基　　金：国家自然科学基金资助项目(61701545,81772004,81772003);天津市自然科学基金重点资助项目(17JCZDJC32400);中国医学科学院医学与健康科技创新工程协同创新团队资助项目(2017-I2M-3-020)

摘　　要：为了提高磁感应磁声成像的成像分辨率,克服低信噪比的磁声信号对磁感应磁声成像重建效果的影响,本研究基于实验系统参数及磁声声源产生传播接收过程,建立了一个磁感应磁声实验系统矩阵,采用截断奇异值分解(TSVD)方法求解了该系统矩阵的特征值及逆矩阵,并将该系统矩阵应用到磁感应磁声成像的正逆问题算法中。为了验证该算法的普适性,建立了一个具有不同形状的电阻抗分布仿体模型,使用Matlab计算数值,得到了三种不同条件下的重建结果。仿真结果证明:该算法在信噪比较高的情况下重建的电导率分布与原始电导率分布基本一致,且能够在信噪比较低的情况下较好的重建电导率分布。该研究为进一步实验研究和实验重建的精确性提供了研究基础。In order to improve the imaging resolution of magneto-acoustic tomography with magnetic induction(MAT-MI)and overcome the influence of the magneto-acoustic signal with low signal-to-noise ratio(SNR)on the reconstruction effect of magnetic induction magnetic acoustic imaging,a matrix of MAT-MI system matrix was established based on the parameters of the experimental system and the generation,propagation process of the magneto-acoustic source.By using the truncated singular value decomposition(TSVD)methods,the singular values decomposition and inverse matrix of the system matrix were computed,the matrix of the system was applied to the forward and inverse problem of MAT-MI.In order to verify the universality of the algorithm,a conductivity distribution phantom model which had different shapes was established,and the reconstruction results under three different conditions were obtained by using Matlab for numerical simulation.The simulation results showed that the conductivity distribution of the proposed algorithm was basically the same as that of the original conductivity distribution under the condition of high signal-to-noise ratio,and the conductivity distribution can be reconstructed well under the condition of low SNR.This study provides a basis for further experimental research and the accuracy of experimental reconstruction.

关 键 词：磁感应磁声成像 系统矩阵 特征值 逆问题 重建算法 

分 类 号：R318[医药卫生—生物医学工程]