Image reconstruction based on L1 regularization and projection methods for electrical impedance tomography.

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 in EIT is a nonlinear and ill-posed inverse problem. The Tikhonov method with L(2) regularization is always used to solve the EIT problem. However, the L(2) method always smoothes the sharp changes or discontinue areas of the reconstruction. Image reconstruction using the L(1) regularization allows addressing this difficulty. In this paper, a sum of absolute values is substituted for the sum of squares used in the L(2) regularization to form the L(1) regularization, the solution is obtained by the barrier method. However, the L(1) method often involves repeatedly solving large-dimensional matrix equations, which are computationally expensive. In this paper, the projection method is combined with the L(1) regularization method to reduce the computational cost. The L(1) problem is mainly solved in the coarse subspace. This paper also discusses the strategies of choosing parameters. Both simulation and experimental results of the L(1) regularization method were compared with the L(2) regularization method, indicating that the L(1) regularization method can improve the quality of image reconstruction and tolerate a relatively high level of noise in the measured voltages. Furthermore, the projected L(1) method can also effectively reduce the computational time without affecting the quality of reconstructed images.