Tikhonov regularization and prior information in electricalimpedance tomography

The solution of impedance distribution in electrical impedance tomography is a nonlinear inverse problem that requires the use of a regularization method. The generalized Tikhonov regularization methods have been popular in the solution of many inverse problems. The regularization matrices that are usually used with the Tikhonov method are more or less ad hoc and the implicit prior assumptions are, thus, in many cases inappropriate. In this paper, the authors propose an approach to the construction of the regularization matrix that conforms to the prior assumptions on the impedance distribution. The approach is based on the construction of an approximating subspace for the expected impedance distributions. It is shown by simulations that the reconstructions obtained with the proposed method are better than with two other schemes of the same type when the prior is compatible with the true object. On the other hand, when the prior is incompatible with the true object, the method will still give reasonable estimates     

A three‐dimensional finite element model for the control of certain non‐linear bioreactors

This paper deals with the dynamics of non‐linear distributed parameter fixed‐bed bioreactors. The model consists of a pair of non‐linear partial differential (evolution) equations. The true spatially three‐dimensional situation is considered instead of the usual one‐dimensional approximation. This enables one to take into account the effects of flow profiles and the true location of the measurement transducer. The (output) evolution of the corresponding open‐loop control system is simulated. Furthermore, the associated closed‐loop system with respect to the relevant output function is considered. Especially, the asymptotic output tracking is found to be successful by applying the usual process based on the state feedback linearization. Copyright © 2000 John Wiley & Sons, Ltd.     

Sparsity reconstruction in electrical impedance tomography: An experimental evaluation

We investigate the potential of sparsity constraints in the electrical impedance tomography (EIT) inverse problem of inferring the distributed conductivity based on boundary potential measurements. In sparsity reconstruction, inhomogeneities of the conductivity are a priori assumed to be sparse with respect to a certain basis. This prior information is incorporated into a Tikhonov-type functional by including a sparsity-promoting ?¹-penalty term. The functional is minimized with an iterative soft shrinkage-type algorithm. In this paper, the feasibility of the sparsity reconstruction approach is evaluated by experimental data from water tank measurements. The reconstructions are computed both with sparsity constraints and with a more conventional smoothness regularization approach. The results verify that the adoption of ?¹-type constraints can enhance the quality of EIT reconstructions: in most of the test cases the reconstructions with sparsity constraints are both qualitatively and quantitatively more feasible than that with the smoothness constraint.     

Extended X-Ray Absorption Fine Structure Study of Arsenic in HgCdTe

Extended x-ray absorption fine structure (EXAFS) experiments using the As K-edge have been carried out at the European Synchrotron Radiation Facility on two molecular beam epitaxy (MBE) grown arsenic-doped HgCdTe samples. Arsenic (As) is provided by a radio-frequency plasma cell and was incorporated to a level of a few 10¹⁸ at·cm⁻³. Both samples were analyzed as grown and after a high-temperature anneal (410°C/1 h) under saturated mercury pressure. The EXAFS signature of as-grown and annealed samples are strikingly different, indicating a drastic change in the environment of the As atom. In any case, the EXAFS signal originates from at least two different contributions and is found to be dominated by As clusters. The other contribution for as-grown samples comes from tellurium neighbors indicating that As incorporates partially in the (Cd,Hg) site.     

An ultra-weak method for acoustic fluid–solid interaction

We introduce the ultra-weak variational formulation (UWVF) for fluid–solid vibration problems. In particular, we consider the scattering of time-harmonic acoustic pressure waves from solid, elastic objects. The problem is modeled using a coupled system of the Helmholtz and Navier equations. The transmission conditions on the fluid–solid interface are represented in an impedance-type form after which we can employ the well known ultra-weak formulations for the Helmholtz and Navier equations. The UWVF approximation for both equations is computed using a superposition of propagating plane waves. A condition number based criterion is used to define the plane wave basis dimension for each element. As a model problem we investigate the scattering of sound from an infinite elastic cylinder immersed in a fluid. A comparison of the UWVF approximation with the analytical solution shows that the method provides a means for solving wave problems on relatively coarse meshes. However, particular care is needed when the method is used for problems at frequencies near the resonance frequencies of the fluid–solid system.     

Single-trial estimation of multichannel evoked-potential measurements

A method for single-trial estimation of multichannel evoked potentials is presented. The proposed method is based on the regularized least squares scheme. The spatial correlation between the channels is used as additional information in the estimation procedure. Amplitude estimates obtained with the proposed method is compared with the estimates calculated without using the spatial information. The performance of the method is evaluated using simulated and real data of P300 responses measured using auditory stimuli. The multichannel approach is shown to give realistic and comparable information about the amplitude differences of the P300 peak between different channels.     

A Kalman filter approach to track fast impedance changes inelectrical impedance tomography

In electrical impedance tomography (EIT), an estimate for the cross-sectional impedance distribution is obtained from the body by using current and voltage measurements made from the boundary. All well-known reconstruction algorithms use a full set of independent current patterns for each reconstruction. In some applications, the impedance changes may be so fast that information on the time evolution of the impedance distribution is either lost or severely blurred. Here, the authors propose an algorithm for EIT reconstruction that is able to track fast changes in the impedance distribution. The method is based on the formulation of EIT as a state-estimation problem and the recursive estimation of the state with the aid of the Kalman filter. The performance of the proposed method is evaluated with a simulation of human thorax in a situation in which the impedances of the ventricles change rapidly. The authors show that with optimal current patterns and proper parameterization, the proposed approach yields significant enhancement of the temporal resolution over the conventional reconstruction strategy