Showing papers by "Jari P. Kaipio published in 2001"
TL;DR: A MATLAB package is written which can be used for two-dimensional mesh generation, solving the forward problem and reconstructing and displaying the reconstructed images (resistivity or admittivity).
Abstract: The EIDORS (electrical impedance and diffuse optical reconstruction software) project aims to produce a software system for reconstructing images from electrical or diffuse optical data. MATLAB is a software that is used in the EIDORS project for rapid prototyping, graphical user interface construction and image display. We have written a MATLAB package (http://venda.uku.fi/ vauhkon/) which can be used for two-dimensional mesh generation, solving the forward problem and reconstructing and displaying the reconstructed images (resistivity or admittivity). In this paper we briefly describe the mathematical theory on which the codes are based on and also give some examples of the capabilities of the package.
249 citations
TL;DR: In this paper, the state estimation problem is solved with the fixed-lag Kalman smoother algorithm, which can be stated in different ways based on the available temporal information and can be used to obtain the tomographic reconstructions of rapidly varying objects in process tomography.
Abstract: In this paper we consider the reconstruction of rapidly varying objects in process tomography. The evolution of the physical parameters can often be approximated with stochastic convection-diffusion and fluid dynamics models. We use the state estimation approach to obtain the tomographic reconstructions and show how these flow models can be exploited with the actual observation models that by themselves induce ill-posed problems. The state estimation problem can be stated in different ways based on the available temporal information. We concentrate on such cases in which continuous monitoring is essential but a small delay for the reconstructions is allowable. The state estimation problem is solved with the fixed-lag Kalman smoother algorithm. As the boundary observations we use the voltage data of electrical impedance tomography. We also give a numerical illustration of the approach in a case in which we track a bolus that moves rapidly through a pipeline.
111 citations
TL;DR: This paper considers appropriate safety constraints and discusses how to find the optimal current patterns with those constraints.
Abstract: There are a number of constraints which limit the current and voltages which can be applied on a multiple drive electrical imaging system. One obvious constraint is to limit the maximum ohmic power dissipated in the body. Current patterns optimizing distinguishability with respect to this constraint are singular functions of the difference of transconductance matrices with respect to the power norm (the optimal currents of Isaacson). If one constrains the total current (L1 norm) the optimal patterns are pair drives. On the other hand if one constrains the maximum current on each drive electrode (an L(infinity) norm), the optimal patterns have each drive channel set to the maximum source or sink current value. In this paper we consider appropriate safety constraints and discuss how to find the optimal current patterns with those constraints.
85 citations
TL;DR: In this paper, a non-stationary electrical impedance tomography (EIT) problem in the case of a piecewise constant conductivity distribution is formulated as a state estimation problem and the shape representation of the region boundaries is considered as a stochastic process.
Abstract: 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.
54 citations
TL;DR: In this paper, the state estimation problem is solved with the fixed-lag Kalman smoother algorithm that is a feasible approach for continuous observation with an insignificant delay in the reconstructions.
Abstract: In this paper we consider process tomography in the case of time-varying objects. Especially, we concentrate on the case in which the indirect observations from the system are obtained via electrical impedance tomographic (EIT) measurements and in which the time-evolution of the target can be described by a stochastic convection-diffusion model. We use the state estimation approach to obtain the tomographic reconstructions. The state estimation problem is solved with the fixed-lag Kalman smoother algorithm that is a feasible approach for continuous observation with an insignificant delay in the reconstructions. In particular we focus on the covariance structures associated with state space model. The covariance structures determine the temporal and spatial regularization properties of the algorithm. It is shown that the adoption of nontrivial covariance structures in the evolution model yields good estimates for the time-varying object in such a situation in which stationary reconstructions are completely...
39 citations
TL;DR: In this paper, the authors consider the determination of the particle size distribution function from Poisson distributed observations arising in aerosol size distribution measurements with the differential mobility particle sizer (DMPS).
Abstract: We consider the determination of the particle size distribution function from Poisson distributed observations arising in aerosol size distribution measurements with the differential mobility particle sizer (DMPS). The DMPS measurement data consists of counts of aerosol particles classified into different size ranges and the goal is to compute an estimate for the particle size distribution function on the basis of this data. This leads to an ill-posed inverse problem. The approach we take in this paper is to consider this inverse problem by treating both the observations and the unknown parameters as random variables. We construct a realistic posterior model for the aerosol size distribution function by using the Bayes' theorem. In the construction of this model we assume that the measurements obey Poisson statistics and that the solution is a smooth non-negative function. We discuss the computation of two point estimates from the posterior density. These are the maximum a posteriori estimate, which is co...
34 citations
TL;DR: In this paper, a priori known internal structures inside the vessels which could be used as internal electrodes in tomographical imaging were modeled and used as additional electrodes in two-dimensional electrical process tomography.
Abstract: Classical electrical impedance tomography is an imaging modality in which the internal impedivity distribution is reconstructed from the known injected currents and voltages measured on the surface of the object. However, in many industrial cases there are a priori known internal structures inside the vessels which could be used as internal electrodes in tomographical imaging. In this paper we consider modelling of certain types of internal structures and using them as internal electrodes in two-dimensional electrical process tomography. We also propose an inversion approach in which directional smoothness of the resistivity distribution can be taken into account. Simulations and laboratory experiments show that, by utilizing internal structural information and using these internal structures as additional electrodes, we can achieve significant improvements in image reconstruction. Improvements are shown for the cases in which the electrodes are placed at the centre of the object and are surrounded by a resistive layer.
32 citations
TL;DR: In this paper, a fixed-lag smoother was used to solve the dynamic EIT reconstruction problem, and the data storage difficulties that are associated with the previously used fixed-interval smoother can be avoided using the fixedlag smoother.
Abstract: In electrical impedance tomography (EIT), an approximation for the internal resistivity distribution is computed based on the knowledge of the injected currents and measured voltages on the surface of the body. The conventional approach is to inject several different current patterns and use the associated data for the reconstruction of a single distribution. This is an ill-posed inverse problem. In some applications the resistivity changes may be so fast that the target changes between the injection of the current patterns and thus the data do not correspond to the same target distribution. In these cases traditional reconstruction methods yield severely blurred resistivity estimates. We have earlier proposed to formulate the EIT problem as an augmented system theoretical state estimation problem. The reconstruction problem can then be solved with Kalman filter and Kalman smoother algorithms. In this paper, we use the so-called fixed-lag smoother to solve the dynamic EIT reconstruction problem. We show that data storage difficulties that are associated with the previously used fixed-interval smoother can be avoided using the fixed-lag smoother. The proposed methods are compared with simulated measurements and real data. Copyright © 2001 John Wiley & Sons, Ltd.
27 citations
TL;DR: In this article, the effects of internal conductive structures on the reconstructed images in two-dimensional cases are considered and possible improvements in the reconstructions by taking into account the locations and resistivities of these structures are studied.
Abstract: In process tomography the aim is to obtain information typically from the interior of the process vessels based on the measurements made on the surface of the vessel. Electrical impedance tomography (EIT) is an imaging modality in which the internal resistivity distribution is reconstructed based on the known injected currents and measured voltages on the surface. Since the reconstructed image represents the resistivity distribution of the interior, certain internal structures such as highly conductive mixing paddles in a stirred vessel may entail difficulties in the image reconstruction. This is because EIT is a diffuse, nonlinear imaging modality which makes it difficult to reconstruct high contrasts in the internal resistivity distribution. In this paper the effects of internal conductive structures on the reconstructed images in two-dimensional cases are considered and possible improvements in the reconstructions by taking into account the locations and resistivities of these structures are studied. I...
27 citations
TL;DR: It is shown that the estimation scheme is relatively tolerant to modeling errors in the flow field, and relatively reliable estimates can be obtained, for example, in a case in which a laminar flow model is used in turbulent flow conditions.
Abstract: In this paper we consider the reconstruction of rapidly varying objects in process tomography. The evolution of the physical parameters is approximated with stochastic convection diffusion and fluid dynamics models. The actual time-varying reconstruction is carried out as a state estimation problem. As the boundary observations we use the voltage data of electrical impedance tomography. We have previously shown that state estimation works well in process tomography in the cases in which the fluid dynamics of the system are modeled correctly. In the real case, however, the velocity field cannot usually be determined accurately. This may be caused, for example, by complex nature of the flow, the turbulence, discretization, etc. In adopting the first proposed approach, it is essential to know how much the inaccuracies in the fluid dynamical model affect the state estimates in process tomography. In this paper we consider the tolerance of the approach with respect to these inaccuracies. We show that the estimation scheme is relatively tolerant to modeling errors in the flow field. Thus relatively reliable estimates can be obtained, for example, in a case in which a laminar flow model is used in turbulent flow conditions. However, the degradation that is due to incorrect flow fields is not insignificant and it is also conjectured that it could be possible that an extension of the proposed method could be used to estimate some flow field parameters.
22 citations
TL;DR: In this article, the problem of estimating time-varying aerosol size distributions from DMPS measurements is formulated as a discrete-time state estimation problem and the reconstruction approach is based on the use of the Kalman filter and fixed-interval smoother algorithms.
TL;DR: In this paper, a boundary element-based method which utilizes data also from internal electrodes in the image reconstruction is proposed, assuming that the internal geometry is known a priori and only the conductivities of the predetermined regions are estimated.
Abstract: Traditionally in electrical impedance tomography an approximation for the internal resistivity distribution is computed based on the knowledge of the injected currents and measured voltages on the surface of the object. However, in certain applications it is also possible to use internal current sources and voltage measurements. In this paper we propose a boundary element-based method which utilizes data also from internal electrodes in the image reconstruction. The proposed approach assumes that the internal geometry is known a priori and only the conductivities of the predetermined regions are estimated. Two-dimensional simulations with four additional sources/measurement locations show clear improvement in the reconstructed images when the results are compared to those based only on boundary data. Copyright © 2001 John Wiley & Sons, Ltd.
TL;DR: This work proposes a new computational approach which does not require the use of surface interpolation but does it implicitly and uses only the recorded data at the electrodes and refers to this method as the systematic approach (SA).
Abstract: Estimation of current or potential distribution on the cortex is used to obtain information about neural sources from the scalp recorded electroencephalogram. If the active sources in the brain are superficial, the estimated field distribution on the cortex also yields information about the active source configuration. In these cases, these methods can be used as source localization methods. In this study, we concentrate on finite-element-based cortex potential estimation. Usually these methods require surface interpolation of the recorded voltages at the electrodes onto the entire scalp surface. We propose a new computational approach which does not require the use of surface interpolation but does it implicitly and uses only the recorded data at the electrodes. We refer to this method as the systematic approach (SA). We compare the SA with the surface interpolation approach (IA) and show that the SA is able to produce somewhat better accuracy than the IA. However, the main asset is that the sensitivity of the cortical potential maps to the regularization parameter is significantly lower than with the IA.
02 Feb 2001
TL;DR: In this paper, the authors consider how the inaccuracies in the fluid dynamical model affect the state estimates in process tomography and consider the case of the electric imaging of the moving fluid.
Abstract: Process tomography consists of tomographic imaging of systems, such as process pipes in industry. One typical feature for the industrial processes is that the state of the system changes fast. If the changes are very fast in comparison to data acquisition rate, the ordinary computational methods in tomography can not provide feasible reconstructions. We use state estimation in process tomography and take into account the time dependence of the object. Especially, we consider the case of the electric imaging of the moving fluid. We use the convection-diffusion equation in modeling time dependence of the target. The Kalman smoother algorithm is used for estimating the state of the object. We have previously shown that the state estimation works well in process tomography in the cases in which the fluid dynamics of the system is modeled correctly. However, in the real case the velocity field can not usually be determined accurately. This may be caused e.g. by complex nature of the flow, the turbulence, discretization, etc. In this paper we consider how the inaccuracies in the fluid dynamical model affect the state estimates in process tomography.© (2001) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.