Image reconstruction algorithm of electromagnetic tomography based on fractional Kalman filter

Abstract

Aiming at the problem of low quality of image reconstruction of electromagnetic tomography (EMT), in this paper, an image reconstruction algorithm of EMT based on fractional Kalman filter (FKF) is proposed. Firstly, the principle of EMT and the principle of state equation of FKF are expound respectively. FKF is often used in the state estimation of nonlinear systems. There is a nonlinear relationship between the object field distribution and the sensor signal in the EMT. Therefore, according to this feature, FKF is applied to the image reconstruction algorithm of EMT. The image reconstruction process of EMT is regarded as the state estimation process of FKF, the normalized measurement voltage is taken as the observation value, and the sensitivity matrix is taken as the measurement matrix. To establish the nonlinear state estimation equation of the FKF and a priori estimation error covariance equation in the EMT, the gray value of image obtained by LBP is used as the initial value of the state estimation, a prior estimation state vector and a priori estimation error covariance matrix are obtained by prediction update, the Kalman filter gain and the posterior estimation error covariance matrix are obtained by the correction feedback process. After repeated iterations, the final state vector, i.e. reconstructed image of EMT is obtained. Finally, simulation experiments are carried out for seven different flow patterns. The results show that the image error and correlation coefficients of the reconstructed image of this algorithm are better than traditional algorithms such as LBP, Landweber, Kalman filter, and have better anti-noise effect than Kalman filter. Therefore, the image reconstruction algorithm of FKF is a new method and means to study the image reconstruction of EMT.