Quadrant-Searching: A New Technique to Reduce the Search Space of the Inverse Problem of Eit Using Bem to the Direct Problem

Abstract

The image reconstruction using the EIT (Electrical Impedance Tomography) technique is a nonlinear and ill-posed inverse problem which demands a powerful direct or iterative method. A typical approach for solving the problem is to minimize an error functional using an iterative method. In this case, an initial solution close enough to the global minimum is mandatory to ensure the convergence to the correct minimum in an appropriate time interval. The aim of this paper is to present a new, simple and low cost technique (quadrant-searching) to reduce the search space and consequently to obtain an initial solution of the inverse problem of EIT. This technique calculates the error functional for four different contrast distributions placing a large prospective inclusion in the four quadrants of the domain. Comparing the four values of the error functional it is possible to get conclusions about the internal electric contrast. For this purpose, initially we performed tests to assess the accuracy of the BEM (Boundary Element Method) when applied to the direct problem of the EIT and to verify the behavior of error functional surface in the search space. Finally, numerical tests have been performed to verify the new technique.

Boundary element method and simulated annealing algorithm applied to electrical impedance tomography image reconstruction

“…From Eqs. ( 6) and (7), it is possible to obtain two integral equations, one for the points (ξ, η) inside the domain Ω and another for the points (ξ, η) on the boundary ∂Ω. In the discretized form, these integral equations are…”

“…To deal with it, the researchers have tried to find a good and suitable regularization function or alternative approaches. For example, it is possible to restrain the search-space to speed up the convergence to the actual solution and avoid nonphysical solutions [7].…”

Boundary element method and simulated annealing algorithm applied to electrical impedance tomography image reconstruction

“…To deal with it, the researchers have tried to find a good and suitable regularization function or alternative approaches. For example, it is possible to restrain the search-space to speed up the convergence to the actual solution and avoid nonphysical solutions [7]. A typical way to solve the reconstruction EIT problem is to treat it as an optimization problem.…”