Showing papers by "Jari P. Kaipio published in 2009"

Compensation of errors due to discretization, domain truncation and unknown contact impedances in electrical impedance tomography

Abstract: Inverse problems can be characterized as problems that tolerate measurement and modelling errors poorly. Typical sources of modelling errors include (pure) approximation errors related to numerical discretization, unknown geometry and boundary data, and possibly sensor locations. With electrical impedance tomography (EIT), the unknown contact impedances are an additional error source. Recently, a Bayesian approach to the treatment of approximation and modelling errors for inverse problems has been proposed. This approach has been shown to be applicable to a variety of modelling and approximation errors, at least with simulations. Recently, it was shown that recovery from significant model reduction and moderate mismodelling of geometry in EIT was also possible with laboratory EIT data. In this paper, we show that the errors due to the unknown contact impedances can also be compensated for by employing the approximation error approach. Furthermore, the recovery from simultaneous contact impedance, domain truncation and discretization-related errors is also feasible.

Approximation errors and model reduction in three-dimensional diffuse optical tomography

Abstract: Model reduction is often required in diffuse optical tomography (DOT), typically because of limited available computation time or computer memory. In practice, this means that one is bound to use coarse mesh and truncated computation domain in the model for the forward problem. We apply the (Bayesian) approximation error model for the compensation of modeling errors caused by domain truncation and a coarse computation mesh in DOT. The approach is tested with a three-dimensional example using experimental data. The results show that when the approximation error model is employed, it is possible to use mesh densities and computation domains that would be unacceptable with a conventional measurement error model.

Dynamical inversion of geophysical ERT data: state estimation in the vadose zone

Abstract: The imaging of the evolution of conductive fluids in porous media with electrical resistance tomography (ERT) can be considered as a dynamic inverse problem, in which the time-dependent electrical conductivity distribution in the target region is inferred from voltage measurements at electrodes placed in boreholes or on the ground surface. A petrophysical relationship is then used to relate the electrical conductivity to water saturation. We consider a state estimation approach that combines the complete electrode model for simulating ERT measurements and a hydrological evolution model for unsaturated flow. To demonstrate the approach, we consider synthetic measurements from a simulated experiment in which water is injected from a point source into an initially dry soil. The purpose is to carry out a feasible study. In the studied simple cases, the proposed method provides improved estimates of the water saturation distribution compared to the traditional reconstruction approach, which does not employ an ...

State estimation in process tomography—reconstruction of velocity fields using EIT

Abstract: In this paper, we consider imaging of moving fluids with electrical impedance tomography (EIT). In EIT, the conductivity distribution is reconstructed on the basis of electrical boundary measurements. In the case of time-varying targets—such as moving fluids in process industry—it is advantageous to formulate the reconstruction problem as a state-estimation problem, because the state-estimation approach allows incorporation of target evolution models in the reconstruction. The reconstruction algorithms consist of recursions in which the state predictions given by the evolution model are updated with the information provided by measurements. When monitoring single-phase flow, the evolution of the substance concentration can be described with the convection–diffusion model. The convection–diffusion model includes the fluid velocity field. In our previous studies, we have assumed that the velocity field is known. In this paper, we extend the approach to cases of unknown velocity fields. The velocity field is reconstructed simultaneously with the conductivity distribution by using an extended Kalman filter. The numerical results indicate that estimating the velocity field from EIT measurements is possible—at least to some extent.

Model reduction and pollution source identification from remote sensing data

Abstract: We consider a source identification problem related to determination of contaminant source parameters in lake environments using remote sensing measurements. We carry out a numerical example case study in which we employ the statistical inversion approach for the determination of the source parameters. In the simulation study a pipeline breaks on the bottom of a lake and only low-resolution remote sensing measurements are available. We also describe how model uncertainties and especially errors that are related to model reduction are taken into account in the overall statistical model of the system. The results indicate that the estimates may be heavily misleading if the statistics of the model errors are not taken into account.