An accelerated version of alternating direction method of multipliers for TV minimization in EIT

Existing total variation (TV) solvers that have been applied in electrical impedance tomography (EIT) smooth the TV function in order to cope with its non-differentiability around the origin, and thus imposes some numerical errors on the solution. Furthermore, these solvers require storage of Hessian, and are thus very impractical for large-scale computations, especially 3D EIT. These shortcomings were addressed by TV solvers that are based on first-order optimization methods. However, the application of these solvers to EIT remains scarce. In this manuscript, we propose an accelerated version of a gradient-based TV solver based on augmented Lagrangian and alternating direction method of multipliers, referred to as TVAL3, and apply it to EIT. The results demonstrate the superiority of the accelerated algorithm over existing TV solvers in EIT with regard to both accuracy and speed.