A comparison between compressed sensing algorithms in Electrical Impedance Tomography

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. Compressed sensing provides unique advantages in Magnetic Resonance Imaging (MRI) [1] when the images are transformed to a sparse basis. EIT images are generally sparser than MRI images due to their lower spatial resolution. This leads us to investigate ability of compressed sensing algorithms currently applied to MRI in EIT without transformation to a new basis. In particular, we examine four new iterative algorithms for L1 and L0 minimization with applications to compressed sensing and compare these with current EIT inverse L1-norm regularization methods. The four compressed sensing methods are as follows: (1) an interior point method for solving L1-regularized least squares problems (L1-LS); (2) total variation using a Lagrangian multiplier method (TVAL3); (3) a two-step iterative shrinkage / thresholding method (TWIST) for solving the L0-regularized least squares problem; (4) The Least Absolute Shrinkage and Selection Operator (LASSO) with tracing the Pareto curve, which estimates the least squares parameters subject to a L1-norm constraint. In our investigation, using 1600 elements, we found all four CS algorithms provided an improvement over the best conventional EIT reconstruction method, Total Variation, in three important areas: robustness to noise, increased computational speed of at least 40x and a visually apparent improvement in spatial resolution. Out of the four CS algorithms we found TWIST was the fastest with at least a 100x speed increase.