Abstract: Electrical capacitance tomography (ECT) has been applied to two-phase flowmeasurement in recent years. Image reconstruction algorithms play an important role in the successful applications of ECT. To solve the ill-posed and nonlinear inverse problem of ECT image reconstruction, a new ECT image reconstruction method based on fast linearized alternating directionmethod ofmultipliers (FLADMM) is proposed in this paper. On the basis of theoretical analysis of compressed sensing (CS), the data acquisition of ECT is regarded as a linear measurement process of permittivity distribution signal of pipe section. A new measurement matrix is designed and L1 regularization method is used to convert ECT inverse problem to a convex relaxation problem which contains prior knowledge. A new fast alternating direction method of multipliers which contained linearized idea is employed to minimize the objective function. Simulation data and experimental results indicate that compared with other methods, the quality and speed of reconstructed images are markedly improved. Also, the dynamic experimental results indicate that the proposed algorithm can fulfill the real-time requirement of ECT systems in the application.

Key words: Electrical capacitance tomography, Image reconstruction, Compressed sensing, Alternating direction method of multipliers, Two-phase flow

摘要： Electrical capacitance tomography (ECT) has been applied to two-phase flowmeasurement in recent years. Image reconstruction algorithms play an important role in the successful applications of ECT. To solve the ill-posed and nonlinear inverse problem of ECT image reconstruction, a new ECT image reconstruction method based on fast linearized alternating directionmethod ofmultipliers (FLADMM) is proposed in this paper. On the basis of theoretical analysis of compressed sensing (CS), the data acquisition of ECT is regarded as a linear measurement process of permittivity distribution signal of pipe section. A new measurement matrix is designed and L1 regularization method is used to convert ECT inverse problem to a convex relaxation problem which contains prior knowledge. A new fast alternating direction method of multipliers which contained linearized idea is employed to minimize the objective function. Simulation data and experimental results indicate that compared with other methods, the quality and speed of reconstructed images are markedly improved. Also, the dynamic experimental results indicate that the proposed algorithm can fulfill the real-time requirement of ECT systems in the application.

关键词: Electrical capacitance tomography, Image reconstruction, Compressed sensing, Alternating direction method of multipliers, Two-phase flow