Electrical impedance tomography (EIT) reconstruction is a nonlinear and ill-posed problem. Exact reconstruction of an EIT image inverts a high dimensional mathematical model to calculate the conductivity field, which causes significant problems regarding that the computational complexity will reduce the achievable frame rate, which is considered as a major advantage of EIT imaging. The single-step method, state estimation method, and projection method were always used to accelerate reconstruction process. The basic principle of these methods is to reduce computational complexity. However, maintaining high resolution in space together with not much cost is still challenging, especially for complex conductivity distribution. This study proposes an idea to accelerate image reconstruction of EIT based on compressive sensing (CS) theory, namely, CSEIT method. The novel CSEIT method reduces the sampling rate through minimizing redundancy in measurements, so that detailed information of reconstruction is not lost. In order to obtain sparse solution, which is the prior condition of signal recovery required by CS theory, a novel image reconstruction algorithm based on patch-based sparse representation is proposed. By applying the new framework of CSEIT, the data acquisition time, or the sampling rate, is reduced by more than two times, while the accuracy of reconstruction is significantly improved.

Purpose 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. Image reconstruction for EIT is a nonlinear problem. A generalized inverse operator is usually ill-posed and ill-conditioned. Therefore, the solutions for EIT are not unique and highly sensitive to the measurement noise. Design/methodology/approach This paper develops a novel image reconstruction algorithm for EIT based on patch-based sparse representation. The sparsifying dictionary optimization and image reconstruction are performed alternately. Two patch-based sparsity, namely, square-patch sparsity and column-patch sparsity, are discussed and compared with the global sparsity. Findings Both simulation and experimental results indicate that the patch based sparsity method can improve the quality of image reconstruction and tolerate a relatively high level of noise in the measured voltages. Originality/value EIT image is reconstructed based on patch-based sparse representation. Square-patch sparsity and column-patch sparsity are proposed and compared. Sparse dictionary optimization and image reconstruction are performed alternately. The new method tolerates a relatively high level of noise in measured voltages.