动态电阻抗成像中Tikhonov正则化参数的选择  

The Selection of Tikhonov Regularization Parameter in Dynamic Electrical Impedance Imaging

作　　者：彭源[1] 莫玉龙[1] 

机构地区：[1]上海大学通信与信息工程学院,上海200072

出　　处：《生物医学工程学杂志》2003年第4期571-573,共3页Journal of Biomedical Engineering

基　　金：国家自然科学基金资助项目 (60 0 75 0 0 9)

摘　　要：动态电阻抗成像是一个非线性逆问题 ,在通过有限元法离散化为线性问题求解时 ,由于系数矩阵的病态性 ,需要正则化处理才能得到稳定解。 Tikhonov方法因为易于实现而应用广泛 ,但在用 Tikhonov方法正则化时涉及到正则化参数的选择 ,它对重构图像的质量影响很大 ,至今还没有通用的方法确定。本研究在大量试验的基础上 ,提出一种新的选择正则化参数的方法 ,充分利用了重构图像的误差的范数与正则化解的范数的乘积的变化规律 。Dynamic electrical impedance imaging is a non linear inverse problem which is always discretized by finite element method and solved by linear model. Since the coefficient matrix of the linear model is ill conditioned, the regularization method is used to get stable solution. However Tikhonov regularization is easy to realize, the selection of the regularization parameter is bothering. In this paper, according to the results of a great number of experiments, a new method for determining the regularization parameter is presented which uses the characteristic of the product of the norm of the error and the regularization solution. The reconstructed image using the regularization parameter selected by the proposed method has good spatial resolution.

关 键 词：动态电阻抗成像 Tikhonov正则化参数 选择 正则化 图像重构 

分 类 号：R310[医药卫生—基础医学]