Simultaneous reconstruction of outer boundary shape and admittivity distribution in electrical impedance tomography

The aim of electrical impedance tomography is to reconstruct the admittivity distribution inside a physical body from boundary measurements of current and voltage. Due to the severe ill-posedness of the underlying inverse problem, the functionality of impedance tomography relies heavily on accurate modelling of the measurement geometry. In particular, almost all reconstruction algorithms require the precise shape of the imaged body as an input. In this work, the need for prior geometric information is relaxed by introducing a Newton-type output least squares algorithm that reconstructs the admittivity distribution and the object shape simultaneously. The method is built in the framework of the complete electrode model and it is based on the Fr\'echet derivative of the corresponding current-to-voltage map with respect to the object boundary shape. The functionality of the technique is demonstrated via numerical experiments with simulated measurement data.Comment: 3 figure

Deep D-Bar: Real-Time Electrical Impedance Tomography Imaging With Deep Neural Networks

The mathematical problem for electrical impedance tomography (EIT) is a highly nonlinear ill-posed inverse problem requiring carefully designed reconstruction procedures to ensure reliable image generation. D-bar methods are based on a rigorous mathematical analysis and provide robust direct reconstructions by using a low-pass filtering of the associated nonlinear Fourier data. Similarly to low-pass filtering of linear Fourier data, only using low frequencies in the image recovery process results in blurred images lacking sharp features, such as clear organ boundaries. Convolutional neural networks provide a powerful framework for post-processing such convolved direct reconstructions. In this paper, we demonstrate that these CNN techniques lead to sharp and reliable reconstructions even for the highly nonlinear inverse problem of EIT. The network is trained on data sets of simulated examples and then applied to experimental data without the need to perform an additional transfer training. Results for absolute EIT images are presented using experimental EIT data from the ACT4 and KIT4 EIT systems

Tailored interior and boundary parameter transformations for iterative inversion in electrical impedance tomography

Electrical impedance tomography is a non-invasive method for imaging the electrical conductivity of an object from electrode measurements on its surface. The underlying mathematical problem is highly nonlinear, severely ill-posed, and several model parameters are usually not known accurately. Despite the strong nonlinearity, iterative Newton-type methods are widely used to tackle the problem numerically. This work presents and analyzes tailored transformations for the conductivity and for electrode parameters which are favourable in two regards: they remove the constrainedness of the unknown parameters and simultaneously decrease the nonlinearity of the underlying problem. We study the impact of various transformations on the nonlinearity of the problem and demonstrate improved speed of convergence for Newton-type methods while avoiding local minima in the solution space. The presented transformations can conveniently be incorporated into existing iterative solvers as they improve stability and do not require hand-tuned regularization parameters or line-search strategies, thereby bridging a gap between a variety of established conductivity estimation methods and practical applications

Model-Aware Newton-Type Inversion Scheme For Electrical Impedance Tomography

We develop a general convergence analysis for a class of inexact Newton-type regularizations for stably solving nonlinear ill-posed problems. Each of the methods under consideration consists of two components: the outer Newton iteration and an inner regularization scheme which, applied to the linearized system, provides the update. In this paper we give a novel and unified convergence analysis which is not confined to a specific inner regularization scheme but applies to a multitude of schemes including Landweber and steepest decent iterations, iterated Tikhonov method, and method of conjugate gradients

Resolution-Controlled Conductivity Discretization in Electrical Impedance Tomography

We develop a general convergence analysis for a class of inexact Newton-type regularizations for stably solving nonlinear ill-posed problems. Each of the methods under consideration consists of two components: the outer Newton iteration and an inner regularization scheme which, applied to the linearized system, provides the update. In this paper we give a novel and unified convergence analysis which is not confined to a specific inner regularization scheme but applies to a multitude of schemes including Landweber and steepest decent iterations, iterated Tikhonov method, and method of conjugate gradients

Multifrequency methods for Electrical Impedance Tomography

Multifrequency Electrical Impedance Tomography (MFEIT) is an emerging imaging modality which exploits the dependence of tissue impedance on frequency to recover images of conductivity. Given the low cost and portability of EIT scanners, MFEIT could provide emergency diagnosis of pathologies such as acute stroke, brain injury and breast cancer. Whereas time-difference, or dynamic, EIT is an established technique for monitoring lung ventilation, MFEIT has received less attention in the literature, and the imaging methodology is at an early stage of development. MFEIT holds the unique potential to form images from static data, but high sensitivity to noise and modelling errors must be overcome. The subject of this doctoral thesis is the investigation of novel techniques for including spectral information in the image reconstruction process. The aim is to improve the ill-posedness of the inverse problem and deliver the first imaging methodology with sufficient robustness for clinical application. First, a simple linear model for the conductivity is defined and a simultaneous multifrequency method is developed. Second, the method is applied to a realistic numerical model of a human head, and the robustness to modelling errors is investigated. Third, a combined image reconstruction and classification method is developed, which allows for the simultaneous recovery of the conductivity and the spectral information by introducing a Gaussian-mixture model for the conductivity. Finally, a graph-cut image segmentation technique is integrated in the imaging method. In conclusion, this work identifies spectral information as a key resource for producing MFEIT images and points to a new direction for the development of MFEIT algorithms