Optimizing electrode positions in 2D electrical impedance tomography using deep learning

Electrical Impedance Tomography (EIT) is a powerful tool for non-destructive evaluation, state estimation, and process tomography – among numerous other use cases. For these applications, and in order to reliably reconstruct images of a given process using EIT, we must obtain high-quality voltage measurements from the target of interest. As such, it is obvious that the locations of electrodes used for measuring plays a key role in this task. Yet, to date, methods for optimally placing electrodes either require knowledge on the EIT target (which is, in practice, never fully known) or are computationally difficult to implement numerically. In this paper, we circumvent these challenges and present a straightforward deep learning based approach for optimizing electrodes positions. It is found that the optimized electrode positions outperformed “standard” uniformly-distributed electrode layouts in all test cases. Further, it is found that the use of optimized electrode positions computed using the approach derived herein can reduce errors in EIT reconstructions as well as improve the distinguishability of EIT measurements

A quantitative evaluation of drive pattern selection for optimizing EIT-based stretchable sensors

Electrical Impedance Tomography (EIT) is a medical imaging technique that has been recently used to realize stretchable pressure sensors. In this method, voltage measurements are taken at electrodes placed at the boundary of the sensor and are used to reconstruct an image of the applied touch pressure points. The drawback in EIT-based sensors however, is their low spatial resolution due to the ill-posed nature of the EIT reconstruction. In this paper, we show our performance evaluation of different EIT drive patterns, specifically strategies for electrode selection when performing current injection and voltage measurements. We compare voltage data with Signal to Noise Ratio (SNR) and Boundary Voltage Changes (BVC), and study image quality with Size Error (SE), Position Error (PE) and Ringing (RNG) parameters, in the case of one-point and two-point simultaneous contact locations. The study shows that, in order to improve the performance of EIT based sensors, the electrode selection strategies should dynamically change correspondingly to the location of the input stimuli. In fact, the selection of a drive pattern over another can improve the target size detection and position accuracy up to 4.7% and 18% respectively

Convergence and regularization for monotonicity-based shape reconstruction in electrical impedance tomography

The inverse problem of electrical impedance tomography is severely ill-posed, meaning that, only limited information about the conductivity can in practice be recovered from boundary measurements of electric current and voltage. Recently it was shown that a simple monotonicity property of the related Neumann-to-Dirichlet map can be used to characterize shapes of inhomogeneities in a known background conductivity. In this paper we formulate a monotonicity-based shape reconstruction scheme that applies to approximative measurement models, and regularizes against noise and modelling error. We demonstrate that for admissible choices of regularization parameters the inhomogeneities are detected, and under reasonable assumptions, asymptotically exactly characterized. Moreover, we rigorously associate this result with the complete electrode model, and describe how a computationally cheap monotonicity-based reconstruction algorithm can be implemented. Numerical reconstructions from both simulated and real-life measurement data are presented

Jointly reconstructing ground motion and resistivity for ERT-based slope stability monitoring

Electrical resistivity tomography (ERT) is increasingly being used to investigate unstable slopes and monitor the hydrogeological processes within. But movement of electrodes or incorrect placement of electrodes with respect to an assumed model can introduce significant resistivity artefacts into the reconstruction. In this work, we demonstrate a joint resistivity and electrode movement reconstruction algorithm within an iterative Gauss–Newton framework. We apply this to ERT monitoring data from an active slow-moving landslide in the UK. Results show fewer resistivity artefacts and suggest that electrode movement and resistivity can be reconstructed at the same time under certain conditions. A new 2.5-D formulation for the electrode position Jacobian is developed and is shown to give accurate numerical solutions when compared to the adjoint method on 3-D models. On large finite element meshes, the calculation time of the newly developed approach was also proven to be orders of magnitude faster than the 3-D adjoint method and addressed modelling errors in the 2-D perturbation and adjoint electrode position Jacobian

A comparison of techniques to optimize measurement of voltage changes in electrical impedance tomography by minimizing phase shift errors

In electrical impedance tomography, errors due to stray capacitance may be reduced by optimization of the reference phase of the demodulator. Two possible methods, maximization of the demodulator output and minimization of reciprocity error have been assessed, applied to each electrode combination individually, or to all combinations as a whole. Using an EIT system with a single impedance measuring circuit and multiplexer to address the 16 electrodes, the methods were tested on resistor-capacitor networks, saline-filled tanks and humans during variation of the saline concentration of a constant fluid volume in the stomach. Optimization of each channel individually gave less error, particularly on humans, and maximization of the output of the demodulator was more robust. This method is, therefore, recommended to optimize systems and reduce systematic errors with similar EIT systems

Electrical Impedance Tomography: From the Traditional Design to the Novel Frontier of Wearables

Electrical impedance tomography (EIT) is a medical imaging technique based on the injection of a current or voltage pattern through electrodes on the skin of the patient, and on the reconstruction of the internal conductivity distribution from the voltages collected by the electrodes. Compared to other imaging techniques, EIT shows significant advantages: it does not use ionizing radiation, is non-invasive and is characterized by high temporal resolution. Moreover, its low cost and high portability make it suitable for real-time, bedside monitoring. However, EIT is also characterized by some technical limitations that cause poor spatial resolution. The possibility to design wearable devices based on EIT has recently given a boost to this technology. In this paper we reviewed EIT physical principles, hardware design and major clinical applications, from the classical to a wearable setup. A wireless and wearable EIT system seems a promising frontier of this technology, as it can both facilitate making clinical measurements and open novel scenarios to EIT systems, such as home monitoring

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