Image Reconstruction for Electrical Capacitance Tomography Based on Sparse Representation

Abstract

Image reconstruction for electrical capacitance tomography (ECT) is a nonlinear problem. A generalized inverse operator is usually ill-posed (unbounded) and ill-conditioned (with a large norm). Therefore, the solutions for ECT are not unique and highly sensitive to the measurement noise. To improve the image quality, a new image reconstruction algorithm for ECT based on sparse representation is proposed. An unconventional basis, i.e., an extended sensitivity matrix consisting of some normalized capacitance vectors corresponding to the base permittivity elements is designed as an expansion frame. The permittivity distributions to be reconstructed can have a natural sparse representation based on the new basis and can be represented as a linear combination of the base elements. Another sparsity regularization method-the standard Landweber iteration with a threshold is also conducted for comparison. The proposed algorithm has been evaluated by both simulation (with and without noise) and experimental results for different permittivity distributions.