Study On Mathematical Characteristics Of Inverse Problem And Image Reconstruction Algorithm For Electrical Capacitance Tomography

Capacitance tomography (ECT, Electrical Capacitance Tomography) is atomographic tomography. Capacitance Tomography mainly by measuring around theelectrode capacitance values between objects inside the object to achieve the spatialdistribution of the dielectric constant is calculated. ECT has a simple structure，non-intrusive, wide application, good security and fast response and so on.Currently, ECT technology at home and abroad have been widely used, mainly forthe detection of multiphase flow within the pipeline industry.Mass accuracy andspeed, and image reconstruction inverse problem solving is the key to the successfulapplication of ECT technology. Therefore, to carry out related research has importanttheoretical and technical significance and application value.In this paper, ECT inverse problems of mathematical features and imagereconstruction algorithm for the study, and solve for the electrical capacitancetomography system involved inverse problems， conduct research imagereconstruction, image reconstruction algorithm design and evaluation of the qualityand other issues, research the main content as follows:First, the combination of background, the significance of the study subjectswere correlation analysis，and research status ECT technology and future trends arereviewed.Foundation Secondly, to electrical capacitance tomography system，workingprinciple and the principle of the pros and cons of problem solving and mathematicalanalysis of the characteristics in the Matlab environment, for several typical imagereconstruction algorithm simulation studies to determine the different algorithmstime image reconstruction accuracy and image reconstruction, to provide a theoretical basis for the follow-up study of image reconstruction algorithms.Again, the establishment of a three-dimensional model using COMSOL ECT tocomplete a typical farm field sensitivity analysis using Landweber algorithm,conjugate gradient algorithm and truncated singular value true imaging algorithmsimulation experiments to verify the validity of the model.Finally, by building a model of capacitance tomography based onregularization.using relative error, image correlation coefficient, singular valuespectrum and the sensitivity matrix methods to evaluate quality ofreconstruction image. and by using conjugate gradient method, the truncatedsingular value algorithm and Landweber algorithm to compare the imagingeffect,verify the effectiveness of the imaging model based on regularization.