Electrical impedance tomography reconstruction through simulated annealing with multi-stage partially evaluated objective functions.

The EIT reconstruction problem can be solved as an optimization problem using Simulated Annealing. Different objective functions have already been used: Euclidian distance between the simulated and observed potentials; total least squares error minimization. The objective function was partially evaluated in both methods. In this paper, a new image reconstruction method that combines the best characteristics from both described methods is proposed. The total reconstruction cost is smaller when compared to each method using one objective function alone. A denser reconstruction mesh is used, and a regularization is adopted by adding a new term similar to the first-order Tikhonov functional. The impact of the regularization in the previous two methods is also analyzed.

Image reconstruction using interval simulated annealing in electrical impedance tomography.

Electrical impedance tomography (EIT) is an imaging technique that attempts to reconstruct the impedance distribution inside an object from the impedance between electrodes placed on the object surface. The EIT reconstruction problem can be approached as a nonlinear nonconvex optimization problem in which one tries to maximize the matching between a simulated impedance problem and the observed data. This nonlinear optimization problem is often ill-posed, and not very suited to methods that evaluate derivatives of the objective function. It may be approached by simulated annealing (SA), but at a large computational cost due to the expensive evaluation process of the objective function, which involves a full simulation of the impedance problem at each iteration. A variation of SA is proposed in which the objective function is evaluated only partially, while ensuring boundaries on the behavior of the modified algorithm.

Electrical impedance tomography reconstruction through simulated annealing with total least square error as objective function.

The EIT reconstruction problem can be solved as an optimization problem where the divergence between a simulated impedance domain and the observed one is minimized. This optimization problem can be solved by a combination of Simulated Annealing (SA) for optimization and Finite Element Method (FEM) for simulation of the impedance domain. This combination has usually a very high computational cost, since SA requires an elevated number of objective function evaluations and those, obtained through FEM, are often expansive enough to make the whole process inviable. In here it is presented a new approach for EIT image reconstructions using SA and partial evaluations of objective functions based on overdetermined linear systems. This new reconstruction approach is evaluated with experimental data and compared with previous approaches.