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

Supporting community engagement through teaching, student projects and research

The Education Acts statutory obligations for ITPs are not supported by the Crown funding model. Part of the statutory role of an ITP is “... promotes community learning and by research, particularly applied and technological research ...” [The education act 1989]. In relation to this a 2017 TEC report highlighted impaired business models and an excessive administrative burden as restrictive and impeding success. Further restrictions are seen when considering ITPs attract < 3 % of the available TEC funding for research, and ~ 20 % available TEC funding for teaching, despite having overall student efts of ~ 26 % nationally. An attempt to improve performance and engage through collaboration (community, industry, tertiary) at our institution is proving successful. The cross-disciplinary approach provides students high level experience and the technical stretch needed to be successful engineers, technologists and technicians. This study presents one of the methods we use to collaborate externally through teaching, student projects and research

Conditioning electrical impedance mammography system

A multi-frequency Electrical Impedance Mammography (EIM) system has been developed to evaluate the conductivity and permittivity spectrums of breast tissues, which aims to improve early detection of breast cancer as a non-invasive, relatively low cost and label-free screening (or pre-screening) method. Multi-frequency EIM systems typically employ current excitations and measure differential potentials from the subject under test. Both the output impedance and system performance (SNR and accuracy) depend on the total output resistance, stray and output capacitances, capacitance at the electrode level, crosstalk at the chip and PCB levels. This makes the system design highly complex due to the impact of the unwanted capacitive effects, which substantially reduce the output impedance of stable current sources and bandwidth of the data that can be acquired. To overcome these difficulties, we present new methods to design a high performance, wide bandwidth EIM system using novel second generation current conveyor operational amplifiers based on a gyrator (OCCII-GIC) combination with different current excitation systems to cancel unwanted capacitive effects from the whole system. We reconstructed tomography images using a planar E-phantom consisting of an RSC circuit model, which represents the resistance of extra-cellular (R), intra-cellular (S) and membrane capacitance (C) of the breast tissues to validate the performance of the system. The experimental results demonstrated that an EIM system with the new design achieved a high output impedance of 10MΩ at 1MHz to at least 3MΩ at 3MHz frequency, with an average SNR and modelling accuracy of over 80dB and 99%, respectively

A Versatile and Reproducible Multi-Frequency Electrical Impedance Tomography System

A highly versatile Electrical Impedance Tomography (EIT) system, nicknamed the ScouseTom, has been developed. The system allows control over current amplitude, frequency, number of electrodes, injection protocol and data processing. Current is injected using a Keithley 6221 current source, and voltages are recorded with a 24-bit EEG system with minimum bandwidth of 3.2 kHz. Custom PCBs interface with a PC to control the measurement process, electrode addressing and triggering of external stimuli. The performance of the system was characterised using resistor phantoms to represent human scalp recordings, with an SNR of 77.5 dB, stable across a four hour recording and 20 Hz to 20 kHz. In studies of both haeomorrhage using scalp electrodes, and evoked activity using epicortical electrode mats in rats, it was possible to reconstruct images matching established literature at known areas of onset. Data collected using scalp electrode in humans matched known tissue impedance spectra and was stable over frequency. The experimental procedure is software controlled and is readily adaptable to new paradigms. Where possible, commercial or open-source components were used, to minimise the complexity in reproduction. The hardware designs and software for the system have been released under an open source licence, encouraging contributions and allowing for rapid replication

Active complex electrode (ACE1) electrical impedance tomography system & anatomically inspired modeling of electrode-skin contact impedance, The

Includes bibliographical references.2016 Summer.Electrical Impedance Tomography (EIT) is a technique used to image the varying electrical properties of biological tissues or tissue conductivity and permittivity. There are many clinical uses of EIT, but as a newer imaging modality, there is interest in improving hardware to acquire EIT data, creating models of the system and generating high quality images. The two main contributions of this work include: (1) EIT hardware advancements and (2) software modeling to simulate measured human subject data. Specifically, this dissertation includes the design and testing of Colorado State University's first EIT system, the pairwise current injection active complex electrode (ACE1) system for phasic voltage measurement. The ACE1 system was primarily designed for thoracic EIT applications, and its performance and limitations were tested through a variety of experiments. Additionally, the EIT forward problem was used to investigate electrode-skin contact impedance

Parallel algorithms for three dimensional electrical impedance tomography

This thesis is concerned with Electrical Impedance Tomography (EIT), an imaging technique in which pictures of the electrical impedance within a volume are formed from current and voltage measurements made on the surface of the volume. The focus of the thesis is the mathematical and numerical aspects of reconstructing the impedance image from the measured data (the reconstruction problem). The reconstruction problem is mathematically difficult and most reconstruction algorithms are computationally intensive. Many of the potential applications of EIT in medical diagnosis and industrial process control depend upon rapid reconstruction of images. The aim of this investigation is to find algorithms and numerical techniques that lead to fast reconstruction while respecting the real mathematical difficulties involved. A general framework for Newton based reconstruction algorithms is developed which describes a large number of the reconstruction algorithms used by other investigators. Optimal experiments are defined in terms of current drive and voltage measurement patterns and it is shown that adaptive current reconstruction algorithms are a special case of their use. This leads to a new reconstruction algorithm using optimal experiments which is considerably faster than other methods of the Newton type. A tomograph is tested to measure the magnitude of the major sources of error in the data used for image reconstruction. An investigation into the numerical stability of reconstruction algorithms identifies the resulting uncertainty in the impedance image. A new data collection strategy and a numerical forward model are developed which minimise the effects of, previously, major sources of error. A reconstruction program is written for a range of Multiple Instruction Multiple Data, (MIMD), distributed memory, parallel computers. These machines promise high computational power for low cost and so look promising as components in medical tomographs. The performance of several reconstruction algorithms on these computers is analysed in detail

A computational model for real-time calculation of electric field due to transcranial magnetic stimulation in clinics

The aim of this paper is to propose an approach for an accurate and fast (real-time) computation of the electric field induced inside the whole brain volume during a transcranial magnetic stimulation (TMS) procedure. The numerical solution implements the admittance method for a discretized realistic brain model derived from Magnetic Resonance Imaging (MRI). Results are in a good agreement with those obtained using commercial codes and require much less computational time. An integration of the developed codewith neuronavigation toolswill permit real-time evaluation of the stimulated brain regions during the TMSdelivery, thus improving the efficacy of clinical applications

The Development of a Flexible Sensor for Continuum Soft-Bodied Robots

In this thesis, we investigate, develop, and verify an approach to sense over soft and flexible materials based on the use of a tomographic technique known as Electrical Impedance Tomography

Nonstationary shape estimation in electrical impedance tomography using a parametric level set-based extended Kalman filter approach

This paper presents a parametric level set based reconstruction method for non-stationary applications using electrical impedance tomography (EIT). Owing to relatively low signal to noise ratios in EIT measurement systems and the diffusive nature of EIT, reconstructed images often suffer from low spatial resolution. In addressing these challenges, we propose a computationally efficient shape-estimation approach where the conductivity distribution to be reconstructed is assumed to be piecewise constant, and the region boundaries are assumed to be non-stationary in the sense that the characteristics of region boundaries change during measurement time. The EIT inverse problem is formulated as a state estimation problem in which the system is modeled with a state equation and an observation equation. Given the temporal evolution model of the boundaries and observation model, the objective is to estimate a sequence of states for the nonstationary region boundaries. The implementation of the approach is based on the finite element method and a parametric representation of the region boundaries using level set functions. The performance of the proposed approach is evaluated with simulated examples of thorax imaging, using noisy synthetic data and experimental data from a laboratory setting. In addition, robustness studies of the approach w.r.t the modeling errors caused by inaccurately known boundary shape, non-homogeneous background and varying conductivity values of the targets are carried out and it is found that the proposed approach tolerates such kind of modeling errors, leading to good reconstructions in non-stationary situations