A new constrained hierarchical reconstruction method for electrical capacitance tomography

In permittivity distribution reconstruction using electrical capacitance tomography (ECT), it is usually required to divide the image area into a finite number of elements. Since finer meshes lead to more accurate results at the detriment of a slower reconstruction time, a good tradeoff is usually sought by researchers. In this paper, a new reconstruction method of the image area in a hierarchical manner is proposed. It consists of localizing gradually the regions of interest which hold the inhomogeneous phases by refining the pixels only around their boundaries. To improve even more the reconstructed images, this paper suggests a new ECT device consisting of a multitude of miniaturized pressure and temperature sensors distributed at different locations of a cross section of a pipeline (in addition to the electrical electrodes surrounding the pipe). Using these sensors, an estimation of the density distribution of the process across a section of the pipeline can be performed using the Bernoulli equation. This density data is then used as a hard constraint for the forward and inverse problem which uses the data acquired from the electrical electrodes. Experimental results on synthetic and real images show that the proposed scheme improves the accuracy and the quality of the reconstructed images while keeping the computation time significantly lower than other traditional methods.

► We developed a reconstruction technique for a new ECT device.
► The image reconstruction process is done in a hierarchical manner.
► We derived an algorithm to solve the ECT inverse problem at each stage of hierarchy.
► We compared the performance of this algorithm over a Gauss–Newton based ECT.
► The spatial resolution and the speed of reconstruction are enhanced.