Research On Electrostatic Tomography Algorithm Based On Sparse Representation

Electrostatic Tomography(EST)technology uses the electrostatic sensor to sense the charge in the field and the sensitivity field to invert the distribution of the charged dielectric in the measured field.As a process tomography technology,EST has the characteristics of simple structure,no excitation,and can easily realize real-time rapid imaging and noninvasive measurement.It is a new type of information detection technology with great development potential and research value.At present,electrostatic tomography technology is mainly used in the field of visual inspection of industrial processes such as multiphase flow parameter detection.In order to further analyze electrostatic tomography technology and the problems of poor imaging accuracy and speed caused by the underdetermination of solving equations in the process of image reconstruction,this thesis has carried out the following aspects of work:1.In-depth analysis of the basic principles of EST technology,abstract the positive and inverse problems of the system into mathematical problems,build the imaging model of the EST system,and mathematically describe the positive EST problems through numerical calculation.2.Introduce the characteristics of EST imaging and several typical traditional algorithms widely used in industrial processes,and deduce and briefly evaluate the solution process of each algorithm.3.The sparse representation algorithm is introduced to solve the EST image reconstruction problem,the basic concept of sparse representation is introduced,and the feasibility of related algorithms in EST image reconstruction is verified.Combining the matching pursuit algorithm and backtracking iterative hard threshold algorithm in the model solving process,a backtracking hard threshold iterative algorithm(CMPBIHT)based on compressive sensing matching pursuit is researched.To solve the poor problem,obtain a more sparse and accurate solution vector,further reduce the relative error,increase the correlation between the understanding vector and the real sparse vector,and improve the imaging accuracy and speed.4.Aiming at the phenomenon that ordinary least squares estimation only minimizes the residual sum of squares,the obtained solution vector often performs poorly in prediction and solution.Combined with the sparse representation theory,an Improved Elastic Net(IEN)algorithm with strong convex properties is researched,using the elastic net performs automatic variable selection and continuous shrinking of the objective function,and obtains a set of variables that are most relevant to the observed signal,thereby improving the accuracy of the solution,reducing the artifacts of the reconstructed image,and increasing the edge sharpness in reconstructed image.The accuracy and speed of the reconstructed image are more effectively integrated.5.Aiming at the low resolution of the EST system and the serious ill-posed inverse problem,combine low-rank representation and sparse representation,an Improved Low Rank and Elastic Net(ILREN)algorithm is researched.By implementing low-rank constraints on the data itself and elastic net constraints on noise,both it can maintain the overall structural characteristics of the data,and can fully restrain the noise,thereby improving the image reconstruction accuracy.Simulation and experimental results show that the improved low-rank elastic net algorithm proposed in this thesis can be effectively applied to EST image reconstruction.