Research On EMT Image Reconstruction Algorithm Based On Fractional Kalman Filter

Electromagnetic Tomography(EMT)is a type of electrical tomography technology that was just developed in the early 1990 s.EMT has the advantages of wide range of use,strong operability,simple structure,non-invasiveness,and low cost.Therefore,EMT has a wide range of applications and good development prospects in industrial applications such as biomedicine and non-destructive testing.However,there are still nonlinear problems in the existing applications of EMT technology,resulting in low quality and low accuracy of EMT image reconstruction results.To response these problems,Read a lot of Chinese and English related theoretical literature of the basic principles of EMT and the theory of Fractional Kalman filter,Combining the idea of fractional Kalman filtering with the mathematical model for solving the EMT inverse problem,an EMT image reconstruction algorithm based on fractional Kalman filtering is proposed.The main contents of this paper are as follows:1.Firstly,the research background of EMT in this paper are analyzed,the research status of EMT system is analyzed by referring to a lot of literatures,and the popular and widely used EMT image reconstruction algorithm is introduced in detail.The characteristics of several classical image reconstruction algorithms are classified and summarized according to these characteristics.2.The working principle and main functions of each structural unit in the EMT system are introduced.The theoretical basis of EMT are studied,firstly,the mathematical model of EMT electromagnetic measurement is deduced according to Radon transform theory and Maxwell equation,and then the solutions of forward and inverse problems are analyzed.Finally,the measured voltage value is solved according to the mathematical model of electromagnetic measurement,and the relevant theory about the sensitivity field of the EMT system is expounded.3.Due to the nonlinear relationship between the object field distribution and the sensor signal in the solution of the inverse problem of EMT,the traditional image reconstruction algorithm approximates the image reconstruction process to a linear relationship,which is an important factor affecting the quality of image reconstruction.By studying the basic principle of fractional differential theory and Kalman filter,and according to the characteristic that fractional Kalman filter can realize the state estimation of nonlinear system,the idea of combining EMT technology with fractional Kalman filter is proposed.Fractional Kalman filtering can regard the EMT image reconstruction process as a state estimation process,and the measured voltage value of the EMT system is used as the measurement input signal.Then give the nonlinear state estimation equations and measurement equations.4.Aiming at the low quality problem of EMT,an algorithm based on fractional Kalman filter is design,and the mathematical model of prediction update and correction feedback of EMT is designed,the image gray value of LBP is used as the initial value of state estimation,The prior estimation state gray level vector and prior estimation error covariance matrix are obtained by the prediction update,and then the fractional Kalman filter gain is obtained through the correction feedback process,and the posterior estimation error covariance matrix is obtained after the prior estimation error covariance matrix is known.Variance matrix,the optimization feedback changes the gain of the fractional Kalman filter during the correction feedback process,and the estimated value of the EMT image state is finally output after multiple iterations.5.COMSOL software is used to model the EMT construct seven different flow patterns.The fractional Kalman filter algorithm is used to compare the image reconstruction results of the traditional Kalman filter algorithm,and other algorithms.The image reconstruction results and evaluation indicators show that the algorithm in this paper has higher imaging accuracy than other algorithms.Experiments show that the results are better than the traditional Kalman filter algorithm in the case of noise interference and the construction of flow patterns for different materials.Therefore,it also confirms that the EMT image reconstruction algorithm based on fractional Kalman filter effectiveness and stability.