Arto Voutilainen

Non-stationary magnetoencephalography by Bayesian filtering of dipole models

In this paper, we consider the biomagnetic inverse problem of estimating a time-varying source current from magnetic field measurements. It is assumed that the data are severely corrupted by measurement noise. This setting is a model for magnetoencephalography (MEG) when the dynamic nature of the source prevents us from effecting noise reduction by averaging over consecutive measurements. Thus, the potential applications of this approach include the single trial estimation of the brain activity, in particular from the spontaneous MEG data. Our approach is based on non-stationary Bayesian estimation, and we propose the use of particle filters. The source model in this work is either a single dipole or multiple dipole model. Part of the problem consists of the model determination. Numerical simulations are presented.

Estimation of non-stationary region boundaries in EIT—state estimation approach

We propose a novel numerical approach to the non-stationary electrical impedance tomography (EIT) problem in the case of a piecewise constant conductivity distribution. The assumption is that the body Ω consists of disjoint regions with smooth boundaries and known values of the conductivity. In addition, the region boundaries are assumed to be non-stationary in the sense that they may exhibit significant changes during the acquisition of one traditional EIT frame. In the proposed method, the inverse problem is formulated as a state estimation problem. Within the state estimation formulation the shape representation of the region boundaries is considered as a stochastic process. The objective is to estimate a sequence of states for the time-varying region boundaries, given the temporal evolution model of the boundaries, the observation model and the data on ∂Ω. In the proposed method, the state estimates are computed using the extended Kalman filter. The implementation of the method is based on Fourier representation of the region boundaries and on the finite-element method. The performance of the method is evaluated using noisy synthetic data. In addition, the choice of the current injection strategy is discussed and it is found that the use of only a few principal current patterns may lead to substantially better results in non-stationary situations.

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

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 evolution model.

A filtering approach for estimating lake water quality from remote sensing data

Abstract In this paper we consider the estimation of lake water quality constituent distributions from hyperspectral remote sensing data. We present a computational approach that can be used to assimilate information from mathematical evolution models into data processing. The method is based on a reduced order iterated extended Kalman filter, and a convection–diffusion model is used to describe the movement of the water quality constituents. The performance of the technique is evaluated in a simulation study. The results show that the filter approach with an appropriate evolution model yields estimates that have better spatial and temporal resolutions than those obtained with conventional methods. Furthermore, the use of a feasible evolution model may make it possible to obtain information also on the concentrations in the lower parts of the lake.

Optimal current patterns in dynamical electrical impedance tomography imaging

In this paper, the topic of optimal experiment design in electrical impedance tomography (EIT) is studied. More specifically, we consider determination of optimal current patterns in EIT in cases of time-varying targets. The reconstruction problem associated with EIT imaging is known to be an ill-posed inverse problem. Statistical inversion methods have been shown to be advantageous in many cases in EIT. In Kaipio et al (2004 Inverse Problems 20 919–36), we considered the problem of optimal experiment design in statistical framework and we proposed an approach for determining optimal current patterns in cases of imaging of time-invariant targets. The approach was based on the statistical interpretation of the reconstruction problem and optimal current patterns were obtained by minimizing the trace of an approximate posterior covariance matrix. In this paper, we utilize a similar approach to determining optimal current patterns in cases of time-varying targets. The image reconstruction problem of EIT is formulated as a state estimation problem. As in the time-invariant case, the optimality criterion is based on the posterior covariances but instead of considering one specific time instant we minimize the time-averaged mean posterior variance. It is shown in a numerical study that the uncertainties of the estimates obtained with optimized current patterns are smaller than those obtained with conventional current patterns. In addition, the results indicate that in time-varying problems a single optimized current pattern may be sufficient to achieve good accuracy, i.e., multiple optimized current patterns do not provide substantial further information on the target. We also demonstrate that in some cases the increase in the number of current patterns can even decrease the reliability of the estimates. This is one of the reasons for the topic of optimal current patterns being quite important in the case of imaging time-varying targets.

Exposure assessment of particulates of diesel and natural gas fuelled buses in silico.

Lung deposition estimates of particulate emissions of diesel and natural gas (CNG) fuelled vehicles were studied by using in silico methodology. Particulate emissions and particulate number size distributions of two Euro 2 petroleum based diesel buses and one Euro 3 gas bus were measured. One of the petroleum based diesel buses used in the study was equipped with an oxidation catalyst on the vehicle (DI-OC) while the second had a partial-DPF catalyst (DI-pDPF). The third bus used was the gas bus with an oxidation catalyst on the vehicle (CNG-OC). The measurements were done using a transient chassis dynamometer test cycle (Braunschweig cycle) and an Electric Low Pressure Impactor (ELPI) with formed particulates in the size range of 7 nm to 10 microm. The total amounts of the emitted diesel particulates were 88-fold for DI-OC and 57-fold for DI-pDPF compared to the total amount of emitted CNG particulates. Estimates for the deposited particulates were computed with a lung deposition model ICRP 66 using in-house MATLAB scripts. The results were given as particulate numbers and percentages deposited in five different regions of the respiratory system. The percentages of particulates deposited in the respiratory system were 56% for DI-OC, 51% for DI-pDPF and 77% for CNG-OC of all the inhaled particulates. The result shows that under similar conditions the total lung dose of particulates originating from petroleum diesel fuelled engines DI-OC and DI-pDPF was more than 60-fold and 35-fold, respectively, compared to the lung dose of particulates originating from the CNG fuelled engine. The results also indicate that a majority (35-50%) of the inhaled particulates emitted from the tested petroleum diesel and CNG engines penetrate deep into the unciliated regions of the lung where gas-exchange occurs.

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

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.

Estimation of time-varying aerosol size distributions—exploitation of modal aerosol dynamical models

We present a method for improved estimation of size distributions from DMPS measurements in case of a non-steady input aerosol. We assume that the size distribution can be represented using a parametric model and in a simulation study we describe the size distribution as a bi-modal log-normal function. We have previously studied the non-parametric approach for the estimation of time-varying size distributions and in the simulation studies we used the random-walk model to describe the evolution of the size distribution. The use of the parametric approach enables the feasible use of the more realistic evolution models in real-time estimation. The objective is to track the time-evolution of the model parameters using state space approach. Since the problem is non-linear, the extended Kalman filter is employed to determine estimates for the parameters assuming that observation errors are zero-mean Gaussian. The focus is in on-line data processing and two different evolution models are implemented in the computations. The estimates are compared to the estimates obtained with a traditional least-squares approach. The results show that in real-time data processing the accuracy of the estimates can be improved significantly by using more accurate evolution models.

Three-dimensional nonstationary electrical impedance tomography with a single electrode layer

In a tubular vessel equipping a single electrode layer, true three-dimensional electrical impedance tomography imaging is generally not considered possible. In a nonstationary setting, however, the accumulation of information over an epoch can possibly allow for 3D imaging if appropriate evolution models are available. Such an evolution model is the stochastic convection‐diffusion model if the flow field is such that the main flow is along the tube. A single electrode layer sensor would obviously be much cheaper and could be installed in locations in which a multi-layer sensor possibly could not be. In this paper, we assess this possibility both computationally and experimentally. The results show that a single electrode layer system is a potential technique in nonstationary estimation.

Sequential Monte Carlo estimation of aerosol size distributions

The estimation of time-varying aerosol size distributions on the basis of differential mobility particle sizer measurements is a dynamical inverse problem with a non-linear/non-Gaussian state space model. A sequential Monte Carlo approach for determining approximations for the state estimates is proposed. The vapour pressure, which is difficult to measure accurately, is here taken as an unknown state variable instead of assuming an approximate average value. Two simulation studies are carried out and the results are also compared with those obtained by using the extended Kalman filter which employs sequential Gaussian approximations based on the same state space model. The results show that in some cases the extended Kalman filter is a feasible approach while there are also evolution models for which the linear/Gaussian approximation is not sufficient.