基于偏微分方程去躁的磁共振电阻抗成像

摘要

介绍了医学成像技术中磁共振电阻抗成像(MREIT)的数学模型和调和Bz算法.为克服调和Bz算法的不适定性,提出了一种偏微分方程去躁方法对Bε的躁声数据进行去噪.结合截断奇异值分解(TSVD)正则化方法,给出了基于Mat1ab偏微分方程工具箱的磁共振电阻抗成像的数值算法.用两个数值模拟算例验证了算法的有效性.%In this study, the reconstruction algorithm of magnetic resonance electrical impedance tomography is studied. First, we introduce the mathematical model of magnetic resonance electrical impedance tomography and the harmonic Bz algorithm. In order to overcome the ill-posedness of the harmonic Bz algorithm, a PDE-based de-noising technique is proposed to process the noise data of Bz. Then, combining with the truncate singular value decomposition regularization method, an algorithm of magnetic resonance electrical impedance tomography based on the Matlab PDE-tool is developed. Finally, two numerical examples are presented to verify the efficiency of the algorithm.