基于互易原理磁感应成像中灵敏度矩阵的计算

Calculation of sensitivity matrix in magnetic induction tomography based on reciprocity principle

磁感应成像(MIT)是一种利用线圈传感器重建所测物体内部电导率分布的成像方法。MIT中的灵敏度矩阵为所测感应电压对物体电导率变化的函数,是反演成像的关键。基于有限元方法和互易原理,提出一种有效计算MIT灵敏度矩阵的方法,在所建立测量模型基础上,运用该方法进行了实验与分析。实验结果表明,该方法可以快速求解MIT中的灵敏度矩阵,应用在高斯一步牛顿算法中可以实现图像重建,为MIT逆问题提供了更有效的解决方案。

Magnetic induction tomography is an imaging method,which employs coil sensor to reconstruct the internal conductivity distribution of target object.The sensitivity matrix of MIT,which is the corresponding function of the measured induced voltage with the conductivity changes,is the key issue of inversion imaging.Based on the finite element method and reciprocity principle,an effective method of calculating the sensitivity matrix of MIT is proposed;and experiment and analysis are carried out using the proposed method based on the measurement model.Experiment results show that the proposed method can solve the sensitivity matrix of MIT,and can also realize image reconstruction when it is applied to Gauss-Newton one-step algorithm,which provides a more effective solution for the inverse problem of MIT.