Image reconstruction algorithm based on 1-norm for electrical resistance tomography

Image reconstruction for Electrical Resistance Tomography (ERT) is an inverse problem, which is both nonlinear and ill-posed. In this paper, the l₁-regularized least-squares program (LSP) is presented to improve the results of the reconstructed images due to the sparse feature of the ERT measurement data. The idea is to transform the reconstructed problem into a convex quadratic problem with linear inequality constraints and the solution is obtained by interior-point methods. The simulation results of this LSP were compared with the l₂ regularization method, indicating that the new method can avoid the over-smoothing of the reconstructed image based on l₁ regularization method and improve the quality of reconstruction images.