Generalised multi-scale image reconstruction algorithm for electrical capacitance tomography

Successful applications of electrical capacitance tomography (ECT) depend mainly on the precision and speed of the image reconstruction algorithms. In this paper, based on the wavelet multi-scale analysis method, a generalised multi-scale model of considering the inaccuracy of the capacitance data and reconstruction model is proposed, in which the original inverse problem is decomposed into a sequence of inverse problems based on the scale variables and then solved successively from the largest scale to the smallest scale until the solution of the original inverse problem is found. A generalised multi-scale objective functional, which has been developed using the least trimmed squares (LTS) estimation and theM-estimation, is proposed. This objective functional unifies the regularised LTS estimation, the regularised M-estimations, the regularised least squares (LS) estimation, the regularised combinational estimation of the LTS estimation and the M-estimations, the regularised combinational estimation of the LS estimation and the M-estimations into a concise formulation. An efficient solver, which integrates the beneficial advantages of the homotopy algorithm, the harmony search (HS) algorithm that has been developed using the multi-harmony techniques based on the cooperation of solutions, and the particle collision (PC) algorithm, is designed for searching a possible global optimal solution. The proposed algorithm is tested by six typical reconstruction objects using a 12-electrode square sensor. Numerical results show the efficiency and superiority of the proposed algorithm in solving ECT image reconstruction problem. In the cases considered in this paper, good results that show great improvement in the spatial resolution and accuracy are observed. The spatial resolution of the reconstructed images by the proposed algorithm is enhanced and the artefacts in the reconstructed images can be eliminated effectively. Meanwhile, the reconstructed results derived from the noise-contaminated capacitance data indicate that the proposed algorithm is successful in dealing with the inaccurate property in the capacitance data.