Dimensionality reduction-based dynamic reconstruction algorithm for electrical capacitance tomography

Abstract

The image reconstruction task in electrical capacitance tomography (ECT) is an ill-posed problem, in which image reconstruction methods play a vital role in real applications. In this paper, a multiple measurement vector-based dimensionality reduction dynamic reconstruction model that simultaneously utilizes the ECT measurement information and the dynamic evolution information of a dynamic object is proposed. A robust sparse orthogonal projective non-negative matrix factorization (RSOPNMF) method is proposed for extracting the basis vectors from a set of snapshots, and the split Bregman iteration (SBI) algorithm is used to solve the RSOPNMF model. The original unknown variables are projected onto the subspaces spanned by a set of the basis vectors extracted by the RSOPNMF method from a set of snapshots to obtain a low-dimensional model, where the images are indirectly reconstructed by solving the corresponding low-dimensional coefficient vector, and thus the dimensionality of the unknown variables is reduced and the computational cost are decreased. Based on the multiple measurement vectors and the dimensionality reduction model, an objective functional that incorporates the ECT measurement information, the dynamic evolution information of a dynamic object, the spatial constraint and the temporal constraint is proposed, in which the unknown variables are solved in a batching pattern. An iterative scheme that integrates the beneficial advantages of the SBI method and the forward–backward splitting algorithm is developed for solving the proposed objective functional. Numerical simulation results validate the feasibility of the proposed algorithm.