A comparison between new L1 minimization algorithms in Electrical Impedance Tomography using the Pareto Curve

Electrical Impedance Tomography (EIT) calculates the internal conductivity distribution within a body using electrical contact measurements. Conventional EIT reconstruction methods solve a linear model by minimizing the least squares error, i.e., the Euclidian or L2-norm, with regularization. Recently, total variation and L1 regularization have become more popular in medical image reconstruction. Here, we introduce new method for evaluating and finding the regularization parameters by using the L1-curve (Pareto Frontier curve). This method traces the optimal trade-off between the least-squares fit of residual and the L1-norm of the solution. In this paper, we compare this algorithm with two L1-norm regularization methods. The results show that this method can help us to have more control on filtering and sparsity of the solution. It also shows that visualizing the L1-curve (Pareto Curve) in order to understand the trade-offs between the norms of the residual and the solution can be helpful in situation where we do not have a very good estimation about the level of the noise.