Image reconstruction based on 11 regularization for electrical impedance tomography (EIT)

Electrical impedance tomography (EIT) aims to estimate the electrical properties at the interior of an object from current-voltage measurements on its boundary. The image reconstruction for EIT is an inverse problem, which is both nonlinear and ill-posed. Little noise in the measured data can cause large errors in the estimated conductivity. Image reconstruction using the l₁ regularization allows addressing this difficulty, in comparison to traditional reconstruction using the l₂ regularization or Tikhonov method. In this paper, a sum of absolute values are substituted for the sum of squares used in the Tikhonov regularization to form the l₁ regularization, the solution is obtained by the barrier method. The selection of parameters is also discussed. Both simulation and experimental results of the l₁ regularization method were compared with the l₂ regularization method, indicating that the l₁ regularization method can improve the quality of image reconstruction and tolerance a relatively high level of noise in the measured voltages.