Electrical impedance tomography (EIT) is a technique for reconstructing the conductivity distribution by injecting currents at the boundary of a subject and measuring the resulting changes in voltage. Many algorithms have been proposed for two-dimensional EIT reconstruction. However, since the human thorax has the characteristic of three-dimensions, EIT is a truly three-dimensional imaging problem. In this paper, we propose a three-dimensional imaging method using tensors for EIT. A tensor EIT model is established by EIT data and the Tucker decomposition is used to obtain the tensor basis. The tensor basis can form a new way to reconstruct image in three-dimensional space. Experiment results revealed that the data structural information of image can be fully used by the tensor method. A comparison of the peak signal to noise ratio (PSNR) shows that the newly proposed method performs better than other methods, i.e. the Dynamic Group Sparse TV algorithm and Tikhonov algorithm. The newly proposed method is closer to the ground truth, thus it can more accurately reflect the state of a lung than two-dimensional EIT. Finally, the EIT experiment is carried out to evaluate the proposed method. The experimental results show that the accuracy of reconstruction based on the new method is efficiently improved.
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