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. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4760253]