介质导电率成像数值反演的正则化方法

AN INVERSE PROBLEM FOR CONDUCTIVITY IMAGING WITH REGULARIZATION

磁共振技术(MREIT)是一种新的医学成像技术,它利用介质内部的部分磁场信息来重建介质内部的导电率.本文对调和B_z反演算法,提出了利用样条插值函数来处理误差输入数据的正则化方法,并给出了正则化方法的误差估计.在此基础上,我们还考虑了调和B_z算法对多个导电率异常的算法实现,检验了该方法对误差输入数据借助于正则化方法可能达到的空间分辨率.本文的工作为调和B_z算法利用实测的误差数据提供了一条可行的途径.

Magnetic Resonance Electrical Impedance Tomography（MREIT） is a new medical imaging technique. The basic idea of MREIT is to reconstruct the medium conductivity using the internal magnetic flux information. This paper considers the numerical realization of the well-developed harmonic-Bz algorithm for noisy input data. By constructing the minimizer of the Tikhonov functional in terms of the spline function, we propose a stable realization of harmonic-Bz algorithm. The error estimates are provided. Finally, numerical examples are given to show the validity of the proposed method. Our work provides a feasible way to the realization of harmonic-Bz algorithm for the noisy input data. Also our numerical work gives the applicable scope of harmonic-Bz algorithm.