Dynamic imaging method using the low n-rank tensor for electrical capacitance tomography

• A multiple measurement vectors model is proposed for ECT image reconstruction.
• A series of dynamic images is cast as a third-order tensor.
• An objective functional is proposed to model ECT reconstruction problem.
• An iteration scheme is developed for solving the proposed objective functional.
• The feasibility of the proposed reconstruction method is numerically validated.

Imaging objects in electrical capacitance tomography (ECT) measurement are often in a dynamic evolution process, and exploiting the spatial–temporal properties of the dynamic reconstruction objects is crucial for the improvement of the reconstruction quality. Based on the multiple measurement vectors, in this paper a robust dynamic reconstruction model that incorporates the ECT measurement information and the dynamic evolution information of a dynamic object, in which a series of dynamic images is cast as a third-order tensor that the first two dimensions are space and the third is time, is proposed. Under the considerations of the two-dimensional spatial structure property of a difference image and the spatial–temporal property of a third-order image tensor, a new objective functional that fuses the ECT measurement information, the dynamic evolution information, the temporal constraint, the spatial constraint, the low rank constraint of a difference image and the low n-rank constraint of a third-order tensor is proposed, where the images are reconstructed by a batching pattern. The split Bregman iteration (SBI) algorithm is developed for solving the proposed objective functional. Numerical simulations are implemented to demonstrate the advantages of the proposed algorithm on improving the reconstruction quality and the robustness.