Research On Image Reconstruction Mathematical Theory And Model For Electrical Capacitance Tomography

The electrical capacitance tomography (ECT) is a kind of processtomography (PT) based on capacitance sensing array. The detection process ofthe multiphase flow parameter is more difficult, because the section effect andrelative speed between the multiphases flow etc. So the detection technology ofmultiphase flow parameters becomes an important research direction. Throughthe research of the domestic and international, from the emergence to thedevelopment of process tomography technology, the detection problem ofmultiphase flow parameters have been solved, and the process tomographytechnology has great prospect in the industrial application. The ECT technologybecomes the main research point of the current process tomography technology,because it has a lot of advantages such as low cost, non-invasive, high safetyperformance, simple structure, wide application range, multi-point measurement,fast response and so on. But the development of the ECT is not very maturewhich is unable to achieve the industrial standards, the research and developmentof the ECT is in urgent need of the industrial application now.In this paper, the research object is the12-electrode ECT system. Theproblems of image reconstruction in ECT system based on the Landweberiterative algorithm are explored. So the super-resolution algorithm based on theLandweber iterative algorithm is poposed. The main research contents are asfollowed:1. Based on the research background, points out the important significanceof the ECT in the industrial production and scientific research, expounds thetechnology development in the domestic and international situation, and analysison the prospects of the ECT. 2. This paper describes the components, working principle and the mainfeatures of the ECT, analysis on the process of establishing mathematical modelsand the mathematical model theoretical of image reconstruction.3. This paper introduces the design idea of the finite element method, anddetails analysis on the whole subdivision process of the cross section. Firstly,caculated the subdivision result. Secondly, clear the interpolation function.Thirdly, establish of the finite equations and the corresponding mathematicalmodel.4. Introduces the basic idea and characteristics of the image reconstructionalgorithm of the ECT technology, and then introduce the LBP algorithm, thesteepest descent algorithm, Newton algorithm, Tikhonov regularization algorithmand Landweber algorithm, and the application of these algorithms in imagereconstruction of the ECT.5. According to the ill-posed of the inverse problem and the “soft field”effect in image reconstruction, the super-resolution algorithm based on theLandweber iterative algorithm is poposed, verify the effectiveness of thealgorithm through experiment simulation, and evaluate the quality of the imagereconstruction of the ECT system.