基于偏微分方程去躁的磁共振电阻抗成像  

Magnetic Resonance Electrical Impedance Tomography Based on PDE-based Noise Removal

作　　者：李小霞[1] 王泽文[1] 何碧琴[1] 

机构地区：[1]东华理工大学理学院数学系,江西南昌330013

出　　处：《东华理工大学学报（自然科学版）》2012年第1期94-100,共7页Journal of East China University of Technology(Natural Science)

基　　金：国家自然科学基金(10861001);江西省自然科学基金(2009GZS0001;2010GZS0010)

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Bz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Mat-lab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 denoising 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.

关 键 词：不适定问题 磁共振电阻抗成像 椭圆型方程反问题 偏微分方程 图像去噪 

分 类 号：O24[理学—计算数学]