Simultaneous Shape and Permittivity Reconstruction in ECT With Sparse Representation: Two-Phase Distribution Imaging

Abstract

Electrical capacitance tomography (ECT) is a technique to visualize the permittivity distribution inside a domain from the interelectrode mutual capacitances on the domain boundary. The potential applications of ECT in nondestructive testing (NDT) depend on accurate and stable image reconstruction. To improve image quality, this article presents a reconstruction framework with the sparse representation of phase boundaries in two-phase distributions. By adopting a sparsity-promoting basis, i.e., radial basis functions, the reconstruction problem is transformed into searching for the optimal phase boundaries and real-permittivity values of inclusions by formulating an optimization problem accordingly. This can reduce the number of unknowns significantly and has a strong ability to accommodate to the topology changes of inclusion geometries, which can improve the reconstruction accuracy and robustness. Both simulation and phantom experiments are performed to investigate the reconstruction performance, especially regarding the antinoise ability and robustness against choices of model parameters. Compared with typical conventional methods, our method can not only provide significantly improved image quality but also accurately estimate the real-permittivity values of inclusions. This would enable ECT to be applied in challenging NDT applications.