A permittivity imaging method in the polar coordinates: Electrical capacitance tomography based on the electromagnetic momentum

Electrical capacitance tomography (ECT) is widely used in petroleum, chemical, and other industrial detection. The ECT equations are nonlinear, and their corresponding inverse problems are ill-posed, so the imaging resolution is low. The ECT technique detects scalar data. The permittivity imaging method based on the electromagnetic momentum reciprocity theorem detects vector data, which carries more information than scalar data. To improve the ability of the imaging system to recognise permittivity boundaries, we propose a permittivity imaging method in the polar coordinate system, which is centred on electrical capacitance tomography based on the electromagnetic momentum (ECT-EMM). ECT-EMM principle with the electrodes-moving scheme and the object-moving scheme is proposed. We reconstruct the permittivity gradient from the capacitance gradient. We adopt the object-moving scheme and use the Tikhonov regularisation algorithm to reconstruct the permittivity through the permittivity gradient. The image reconstruction results and image evaluation metrics show that the proposed method clearly recognises the object boundaries compared to ECT. The proposed method performs better when using threshold filtering.