Range-based prior knowledge in the solution of the inverse problem of electrical impedance tomography

The inverse problem in electrical impedance tomography is ill-posed in the sense that a unique solution may not exist, or it might be unstable and extremely sensitive to noise in the boundary measurements. One way to stabilize the solution is to incorporate prior knowledge regarding the conductivity distribution. In this context, a first general prior arises from the physical constraints requiring that the electrical conductivity must be strictly positive over the entire reconstruction domain. In order to enforce the positivity constraint, earlier publications advocated substitution of the conductivity parameter by its logarithm. However, such a change of variable cannot accommodate more specific prior knowledge, as for example the assumption that the electrical conductivity varies within a certain spatial dependent range, which is often the case in practical reconstruction problems. Allowing a more selective prior knowledge is important because it allows to reject estimates that do not comply to our expectations, increasing the reliability of the results. The typical solution to this need is the use of a barrier method, that prevents the estimate from approaching the endpoints of the range too closely. We have compared this approach to two others strategies: the thresholding of the estimate when out of range, and the projection of an out of range estimate back into the appropriate range. From our experiments, the strategy that projects the out of range estimate is the most reliable.

ISBN:978-2-911256-87-5

Jaar van publicatie:2012

Trefwoorden:Electrical Impedance Tomography, inverse problems, least squares methods, constrained optimization