Study On ECT Image Reconstruction Algorithm Based On Lp Norm Regularization

Electrical Capacitance Tomography is a process tomography technique that developed in the 1980s for industrial pipeline inspection.ECT technology has the advantages of fast,safe,non-intrusive and non-destructive.It has been applied in many fields,such as voidage measurement,flow pattern identification,concentration distribution measurement of gas-solid two-phase flow,visualization of water migration process in frozen soil and so on.However,in the process of solving inverse problems,the capacitance tomography technology has the problems of undetermined and ill-conditioned,which leads to the incomplete solution and unstable solution process.These two problems always restrict the development of ECT technology.Compressed sensing theory is a sparse decomposition technique for finding underdetermined linear systems.According to the sparsity and compressibility of signals,Accurate reconstruction of sampled signals with a small number of signals.In this paper,compressed sensing theory is applied to the inverse problem of ECT for trying to solve the problem of undetermined of ECT.the following aspects of work and result are mainly carried out in this paper:1.Aiming at the problem that the sensitivity matrix of ECT system as the compressed sensing observation matrix does not satisfy the restricted isometry property,According to the idea of increasing the minimum singular value of the matrix to enhance the independence of the matrix column,the singular value decomposition is used to process the sensitivity matrix,and the average value of the singular value is used to replace the original singular value,thus narrowing the scope of the singular value of the sensitivity matrix.The simulation results show that the proposed matrix transformation algorithm can improve the minimum singular value of the matrix,and the image reconstructed by the optimized observation matrix has high resolution.2.In the lp(0<p<1)norm sparse optimization problem,the sparsity of solution and the quality of image reconstruction depend on the selection of p value.The size of regularization parameter seriously affects the sparsity and smoothness of solution.An adaptive alternating iteration mechanism is proposed,which uses reconstruction error to correct p value and uses regularization function instead of fixed regularization parameter,so that the model can adaptively selected appropriate parametersaccording to input3.In order to solve the problem of more computational challenges and limited by some specific p values in the optimization process of non-convex problems,An improved interpolation function is used to replace ?x?pp and make the improved function approximate?x?pp infinitely by adjusting the parameters.At the same time,the threshold representation theory is introduced.On this basis,A new adaptive threshold iteration algorithm is proposed to solve the new model.