Study On Image Reconstruction Algorithms For Electrical Capacitance Tomography System

Electrical Capacitance Tomography(ECT)is a low consumption of resources,fast,safe,inexpensive process tomography(Process Tomography,PT),Using the different dielectric constant characteristics of different substances,the fluid condition of the cross section of the pipe is obtained by detecting the node constant distribution corresponding to the different substances in the pipeline.In recent years,ECT has been widely used in gas-liquid two-phase flow porosity measurement and flow identification,fluidized bed gas-solid two-phase flow concentration distribution visualization,pneumatic conveying and other fields.In order to more comprehensively learn to master the ECT image reconstruction algorithm,mainly done the following aspects of the work:Firstly,the basic principle of ECT technique,the mathematical model of the forward and inverse problem and the principle of the reconstruction algorithm are analyzed,and the ECT positive problem is solved by finite difference method.Secondly,depth study of the existing existence of several traditional image reconstruction algorithm,the imaging concepts of several typical algorithms are introduced.The algorithm is deduced and validated.The advantages and disadvantages of the algorithm are compared with the image evaluation parameters.Thirdly,in order to solve the problem of image detail loss caused by excessive smoothing of Tiknonov regularization in image reconstruction process of capacitive tomography system,An image reconstruction model with norm l2,p(0<p?1)both on the data fidelity term and regularization term was introduced,the fractional matrix norm l2,P(0<p?1),which combines the smoothness of Euclid norm l2 and the sparsity of norm lp(0<p ? 1),has better joint sparsity and stronger reliability than matrix norm l2,1.Fourthly,To deal with the ill-posed problem of sensitivity matrix in ECT image reconstruction and the singular value decomposition which consumes most of the computation time,the partial singular value decomposition algorithm is improved,The algorithm provides a new implicit start rule when compute singular values and singular vectors which are larger than a certain threshold value,and provides a directly callable function without additionally predicting the dimension of the optimal base vector group of sensitivity matrix.Finally,a set of improved pretreatment and optimization scheme of Jacobi singular value decomposition algorithm is presented.Fifthly,aiming at the numerical instability caused by the singular value decomposition algorithm and the over-smooth caused by the Tiknonov regularization in the image reconstruction of electrical capacitance tomography(ECT)system,a more generalized regularization algorithm is proposed.Firstly,the penalty phase of the regularized objective function is modified by the positive definite matrix so that it can reconstruct the image with non smooth information,In the process of solving the objective function,the diagonal weight matrix is introduced,and the data items based on l2-norm are improved.