Design and application of a multi-modal process tomography system

This paper presents a design and application study of an integrated multi-modal system designed to support a range of common modalities: electrical resistance, electrical capacitance and ultrasonic tomography. Such a system is designed for use with complex processes that exhibit behaviour changes over time and space, and thus demand equally diverse sensing modalities. A multi-modal process tomography system able to exploit multiple sensor modes must permit the integration of their data, probably centred upon a composite process model. The paper presents an overview of this approach followed by an overview of the systems engineering and integrated design constraints. These include a range of hardware oriented challenges: the complexity and specificity of the front end electronics for each modality; the need for front end data pre-processing and packing; the need to integrate the data to facilitate data fusion; and finally the features to enable successful fusion and interpretation. A range of software aspects are also reviewed: the need to support differing front-end sensors for each modality in a generic fashion; the need to communicate with front end data pre-processing and packing systems; the need to integrate the data to allow data fusion; and finally to enable successful interpretation. The review of the system concepts is illustrated with an application to the study of a complex multi-component process

A schema for generic process tomography sensors

A schema is introduced that aims to facilitate the widespread exploitation of the science of process tomography (PT) that promises a unique multidimensional sensing opportunity. Although PT has been developed to an advanced state, applications have been laboratory or pilot-plant based, configured on an end-to-end basis, and limited typically to the formation of images that attempt to represent process contents. The schema facilitates the fusion of multidimensional internal process state data in terms of a model that yields directly usable process information, either for design model confirmation or for effective plant monitoring or control, here termed a reality visualization model (RVM). A generic view leads to a taxonomy of process types and their respective RVM. An illustrative example is included and a review of typical sensor system components is given

Sparsity prior for electrical impedance tomography with partial data

This paper focuses on prior information for improved sparsity reconstruction in electrical impedance tomography with partial data, i.e. data measured only on subsets of the boundary. Sparsity is enforced using an $\ell_1$ norm of the basis coefficients as the penalty term in a Tikhonov functional, and prior information is incorporated by applying a spatially distributed regularization parameter. The resulting optimization problem allows great flexibility with respect to the choice of measurement boundaries and incorporation of prior knowledge. The problem is solved using a generalized conditional gradient method applying soft thresholding. Numerical examples show that the addition of prior information in the proposed algorithm gives vastly improved reconstructions even for the partial data problem. The method is in addition compared to a total variation approach.Comment: 17 pages, 12 figure

The Factorization method for three dimensional Electrical Impedance Tomography

The use of the Factorization method for Electrical Impedance Tomography has been proved to be very promising for applications in the case where one wants to find inhomogeneous inclusions in a known background. In many situations, the inspected domain is three dimensional and is made of various materials. In this case, the main challenge in applying the Factorization method consists in computing the Neumann Green's function of the background medium. We explain how we solve this difficulty and demonstrate the capability of the Factorization method to locate inclusions in realistic inhomogeneous three dimensional background media from simulated data obtained by solving the so-called complete electrode model. We also perform a numerical study of the stability of the Factorization method with respect to various modelling errors.Comment: 16 page

Design of sensor electronics for electrical capacitance tomography

The design of the sensor electronics for a tomographic imaging system based on electrical capacitance sensors is described. The performance of the sensor electronics is crucial to the performance of the imaging system. The problems associated with such a measurement process are discussed and solutions to these are described. Test results show that the present design has a resolution of 0.3 femtofarad. (For a 12-electrode system imaging an oil/gas flow, this represents a 2% gas void fraction change at the centre of the pipe) with a low noise level of 0.08 fF (RMS value), a large dynamic range of 76 dB and a data acquisition speed of 6600 measurements per second. This enables sensors with up to 12 electrodes to be used in a system with a maximum imaging rate of 100 frames per second, and thus provides an improved image resolution over the earlier 8-electrode system and an adequate electrode area to give sufficient measurement sensitivit

Expectation Propagation for Nonlinear Inverse Problems -- with an Application to Electrical Impedance Tomography

In this paper, we study a fast approximate inference method based on expectation propagation for exploring the posterior probability distribution arising from the Bayesian formulation of nonlinear inverse problems. It is capable of efficiently delivering reliable estimates of the posterior mean and covariance, thereby providing an inverse solution together with quantified uncertainties. Some theoretical properties of the iterative algorithm are discussed, and the efficient implementation for an important class of problems of projection type is described. The method is illustrated with one typical nonlinear inverse problem, electrical impedance tomography with complete electrode model, under sparsity constraints. Numerical results for real experimental data are presented, and compared with that by Markov chain Monte Carlo. The results indicate that the method is accurate and computationally very efficient.Comment: Journal of Computational Physics, to appea

Application and comparison of three tomographic techniques for detection of decay in trees

This paper reports application of electric, ultrasonic, and georadar tomography for detection of decay in trees and their comparison with the traditional penetrometer. Their feasibility in arboriculture is also evaluated, critically considering some "open problems." The experiments were carried out in an urban environment on two plane (Platanus hybrida Brot.) trees. Both trees, after felling, showed extensive white rot in the central cylinder. The electric tomography revealed low resistivity zones roughly centered in the trunk. A comparison with the successively cut sections showed a fine correspondence to decayed areas and a strong correspondence between high moisture zones and low resistivity zones. Ultrasonic tomography demonstrated to be a very effective tool for the detection of internal decay, accurately locating the position of the anomalies and estimating their size, shape, and characteristic in terms of mechanical properties. With the georadar technique, the high contrast of electromagnetic impedance measured between the inner decayed section and the outside sound section allowed the detection of the interface between the sound and decayed section of the tree, using radar acquisition in reflection modality. The penetrometer profiles detected the low-resistance areas inside the two trunk

Distinguishability revisited: depth dependent bounds on reconstruction quality in electrical impedance tomography

The reconstruction problem in electrical impedance tomography is highly ill-posed, and it is often observed numerically that reconstructions have poor resolution far away from the measurement boundary but better resolution near the measurement boundary. The observation can be quantified by the concept of distinguishability of inclusions. This paper provides mathematically rigorous results supporting the intuition. Indeed, for a model problem lower and upper bounds on the distinguishability of an inclusion are derived in terms of the boundary data. These bounds depend explicitly on the distance of the inclusion to the boundary, i.e. the depth of the inclusion. The results are obtained for disk inclusions in a homogeneous background in the unit disk. The theoretical bounds are verified numerically using a novel, exact characterization of the forward map as a tridiagonal matrix.Comment: 25 pages, 6 figure