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

Abstract

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 L2 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 L1 regularization allows addressing this difficulty. In this paper, a sum of absolute values is substituted for the sum of squares used in the L2 regularization to form the L1 regularization, the solution is obtained by the barrier method. However, the L1 method often involves repeatedly solving large-dimensional matrix equations, which are computationally expensive. In this paper, the projection method is combined with the L1 regularization method to reduce the computational cost. The L1 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 L2 regularization method, indicating that the L1 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. © 2012 American Institute of Physics.