Research On Image Reconstruction Algorithm For Electrical Capacitance Tomography System Based On Homotopy Continuation Regularization

Electrical capacitance tomography is a non-invasive,low-cost and high security CT technology,which has been widely used in the fields of medicine,petrochemical,metallurgy,energy and other multiphase flow detection.The capacitance value of the measured object is obtained by the capacitance sensor equipment,and the medium distribution in the cross section of the object is obtained according to the specific mathematical model and the appropriate ect image reconstruction algorithm.Therefore,the key to the success of ECT is to choose the appropriate image reconstruction algorithm.Aiming at the "soft field" effect and ill posed problem of ECT Image reconstruction,this paper proposes an ECT Image Reconstruction Algorithm Based on homotopy continuation regularization.From the simulation results,the algorithm has the advantages of high imaging quality and fast imaging speed,which provides a new idea for ECT image reconstruction.At the same time,in order to make the image reconstructed by homotopy continuation regularization algorithm more suitable for the actual production environment,it is also necessary to compensate the gray level of the edge region of the reconstructed image to improve the accuracy and stability of the reconstructed image.The main contents of this paper can be summarized as follows.(1)The basic composition and technical principles of the ECT system are introduced in detail,and the definitions of the positive and negative problems of ECT technology are explained.At the same time,the ill-posedness of the ECT image reconstruction problem is analyzed based on the mathematical model of the ECT inverse problem.Finally,the basic principles and formula derivation process of a variety of classic ECT image reconstruction algorithms are introduced,and the classic algorithm and the algorithm proposed in this article are simulated together,and the experimental results of the image reconstruction algorithm are compared and analyzed.(2)Aiming at the "soft field" effect and ill-conditioned problems in ECT image reconstruction,this paper proposes an ECT image reconstruction algorithm based on homotopy continuation regularization.This paper expounds the basic principles of the homotopy continuation regularization algorithm,and derives the mathematical model that uses this algorithm to solve the ECT image reconstruction problem,and then uses the Morozov criterion in the posterior strategy to select the regularization parameters,and finally the homotopy extension The convergence analysis of the extension regularization algorithm is carried out.The experimental results show that the image reconstructed by the homotopy continuation regularization algorithm is very close to the original image in terms of visual and intuitive effects.Compared with other ECT image reconstruction algorithms,it has higher accuracy and faster iteration speed,which improves ECT.Stability of image reconstruction.(3)Aiming at the ill-posed problem of ECT technology,the theory of ECT image reconstruction problem to solve the asymptotic optimal order is further analyzed,which proves the necessity of edge compensation for ECT reconstructed image.By expounding the basic theories of genetic algorithm and artificial fish school algorithm,this paper proposes an edge compensation algorithm based on genetic artificial fish school.At the same time,the geometric convex hull method is used to determine the boundary area of the ECT reconstructed image.In order to increase the accuracy and stability of the homotopic continuation regularized image reconstruction,the genetic artificial fish swarm algorithm is used to perform edge compensation on the homotopy continuation regularized image reconstruction result.The experimental results show that the image quality of ECT reconstruction after edge compensation of genetic artificial fish school algorithm is far better than that of other ECT image reconstruction algorithms.Moreover,in the homotopic continuation regularization reconstructed images of low-level laminar flow,mid-level laminar flow,and small-radius core flow,the imaging effect after edge compensation is better than that without compensation.Not only that,the visual effect of the reconstructed image of the genetic artificial fish school algorithm is also closer to the original image than other reconstruction algorithms.