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

Electrical Capacitance Tomography (ECT) technology is one of the PTtechnologies, which was developed in the late1980s. Electrical CapacitanceTomography (ECT) technology has many advantages such as fast response, lowcost, fast response, non-invasive measurement, good safety performance, etc. It isconsidered that Electrical Capacitance Tomography (ECT) technology hasbecame one of the mainstream in today’s PT technology research anddevelopment.ECT measurement techniques currently still have many pendingresearch and technical difficulties to break through. So carry out relevant theoryand technology research has important significance and application value.Now, ECT hardware design of the system is mainly concentrated inoptimized sensor design and improve data acquisition systemsensor design, forthe sensor design we should make a reasonable allocation of the variousparameters to make the sensitive distribution more uniform; for the dataacquisition systemsensor design we should improve the sensitivity to get therelatively small experimental signal change better. At the same time, because ofECT algorithm have discomfort that means the projection data is limited, theindependent measurements of the capacitance we can get are much less than thenumber of the pixels, so it made the image reconstruction become more difficult.Therefore, we need to explore a reasonable imaging algorithms that is becomeone way to improve the currently ECT technology that under the existingconditions of the hardware.In this paper, we study the capacitance tomography and the mathematicaltheory and focus on solving for electrical capacitance tomography system inverse problem, image reconstruction and evaluate the quality of image reconstructionetc. So the main contents are as follows:First we starting from the composition of electrical capacitance tomographysystem hardware, separately described the various components, and thenintroduce inverse problems of ECT technology by the principle of mathematicaltheory, and starting with the inverse problem model, focuse on the feature of ECTimage reconstruction algorithm. We focused on the LBP algorithm, Tikhonovalgorithm these regular non-iterative algorithms. And Landweber algorithm,Newton algorithm, weighted correction Gauss-Newton algorithm iterativealgorithm these iterative algorithm.Second, based on the ECT image reconstruction characteristics, we get anovel factorized Quasi-Newton image reconstruction algorithm which is given bythe Newton and weighted correction Gauss-Newton, then complete derivation ofthe algorithm, and then through experiments we can verify the effectiveness ofthe algorithm.Last, based on differential evolution algorithm, we can get another algorithmwhich is based population entropy and adaptive differential evolution, and thencomplete derivation of the algorithm, then appled it into ECT imagereconstruction, and then through experiments we can verify the effectiveness ofthe algorithm.