Electrical Impedance Tomography with Deep Calder\'on Method

Electrical impedance tomography (EIT) is a noninvasive medical imaging modality utilizing the current-density/voltage data measured on the surface of the subject. Calder\'on's method is a relatively recent EIT imaging algorithm that is non-iterative, fast, and capable of reconstructing complex-valued electric impedances. However, due to the regularization via low-pass filtering and linearization, the reconstructed images suffer from severe blurring and underestimation of the exact conductivity values. In this work, we develop an enhanced version of Calder\'on's method, using convolution neural networks (i.e., U-net) via a postprocessing step. Specifically, we learn a U-net to postprocess the EIT images generated by Calder\'on's method so as to have better resolutions and more accurate estimates of conductivity values. We simulate chest configurations with which we generate the current-density/voltage boundary measurements and the corresponding reconstructed images by Calder\'on's method. With the paired training data, we learn the neural network and evaluate its performance on real tank measurement data. The experimental results indicate that the proposed approach indeed provides a fast and direct (complex-valued) impedance tomography imaging technique, and substantially improves the capability of the standard Calder\'on's method.Comment: 20 page

Impedance-optical Dual-modal Cell Culture Imaging with Learning-based Information Fusion

While Electrical Impedance Tomography (EIT) has found many biomedicine applications, a better resolution is needed to provide quantitative analysis for tissue engineering and regenerative medicine. This paper proposes an impedance-optical dual-modal imaging framework, which is mainly aimed at high-quality 3D cell culture imaging and can be extended to other tissue engineering applications. The framework comprises three components, i.e., an impedance-optical dual-modal sensor, the guidance image processing algorithm, and a deep learning model named multi-scale feature cross fusion network (MSFCF-Net) for information fusion. The MSFCF-Net has two inputs, i.e., the EIT measurement and a binary mask image generated by the guidance image processing algorithm, whose input is an RGB microscopic image. The network then effectively fuses the information from the two different imaging modalities and generates the final conductivity image. We assess the performance of the proposed dual-modal framework by numerical simulation and MCF-7 cell imaging experiments. The results show that the proposed method could significantly improve image quality, indicating that impedance-optical joint imaging has the potential to reveal the structural and functional information of tissue-level targets simultaneously

Electrical Impedance Tomography: A Fair Comparative Study on Deep Learning and Analytic-based Approaches

Electrical Impedance Tomography (EIT) is a powerful imaging technique with diverse applications, e.g., medical diagnosis, industrial monitoring, and environmental studies. The EIT inverse problem is about inferring the internal conductivity distribution of an object from measurements taken on its boundary. It is severely ill-posed, necessitating advanced computational methods for accurate image reconstructions. Recent years have witnessed significant progress, driven by innovations in analytic-based approaches and deep learning. This review explores techniques for solving the EIT inverse problem, focusing on the interplay between contemporary deep learning-based strategies and classical analytic-based methods. Four state-of-the-art deep learning algorithms are rigorously examined, harnessing the representational capabilities of deep neural networks to reconstruct intricate conductivity distributions. In parallel, two analytic-based methods, rooted in mathematical formulations and regularisation techniques, are dissected for their strengths and limitations. These methodologies are evaluated through various numerical experiments, encompassing diverse scenarios that reflect real-world complexities. A suite of performance metrics is employed to assess the efficacy of these methods. These metrics collectively provide a nuanced understanding of the methods' ability to capture essential features and delineate complex conductivity patterns. One novel feature of the study is the incorporation of variable conductivity scenarios, introducing a level of heterogeneity that mimics textured inclusions. This departure from uniform conductivity assumptions mimics realistic scenarios where tissues or materials exhibit spatially varying electrical properties. Exploring how each method responds to such variable conductivity scenarios opens avenues for understanding their robustness and adaptability

Expectation Propagation for Poisson Data

The Poisson distribution arises naturally when dealing with data involving counts, and it has found many applications in inverse problems and imaging. In this work, we develop an approximate Bayesian inference technique based on expectation propagation for approximating the posterior distribution formed from the Poisson likelihood function and a Laplace type prior distribution, e.g., the anisotropic total variation prior. The approach iteratively yields a Gaussian approximation, and at each iteration, it updates the Gaussian approximation to one factor of the posterior distribution by moment matching. We derive explicit update formulas in terms of one-dimensional integrals, and also discuss stable and efficient quadrature rules for evaluating these integrals. The method is showcased on two-dimensional PET images.Comment: 25 pages, to be published at Inverse Problem

Advances in Integrated Circuits and Systems for Wearable Biomedical Electrical Impedance Tomography

Electrical impedance tomography (EIT) is an impedance mapping technique that can be used to image the inner impedance distribution of the subject under test. It is non-invasive, inexpensive and radiation-free, while at the same time it can facilitate long-term and real-time dynamic monitoring. Thus, EIT lends itself particularly well to the development of a bio-signal monitoring/imaging system in the form of wearable technology. This work focuses on EIT system hardware advancement using complementary metal oxide semiconductor (CMOS) technology. It presents the design and testing of application specific integrated circuit (ASIC) and their successful use in two bio-medical applications, namely, neonatal lung function monitoring and human-machine interface (HMI) for prosthetic hand control. Each year fifteen million babies are born prematurely, and up to 30% suffer from lung disease. Although respiratory support, especially mechanical ventilation, can improve their survival, it also can cause injury to their vulnerable lungs resulting in severe and chronic pulmonary morbidity lasting into adulthood, thus an integrated wearable EIT system for neonatal lung function monitoring is urgently needed. In this work, two wearable belt systems are presented. The first belt features a miniaturized active electrode module built around an analog front-end ASIC which is fabricated with 0.35-µm high-voltage process technology with ±9 V power supplies and occupies a total die area of 3.9 mm². The ASIC offers a high power active current driver capable of up to 6 mAp-p output, and wideband active buffer for EIT recording as well as contact impedance monitoring. The belt has a bandwidth of 500 kHz, and an image frame rate of 107 frame/s. To further improve the system, the active electrode module is integrated into one ASIC. It contains a fully differential current driver, a current feedback instrumentation amplifier (IA), a digital controller and multiplexors with a total die area of 9.6 mm². Compared to the conventional active electrode architecture employed in the first EIT belt, the second belt features a new architecture. It allows programmable flexible electrode current drive and voltage sense patterns under simple digital control. It has intimate connections to the electrodes for the current drive and to the IA for direct differential voltage measurement providing superior common-mode rejection ratio (CMRR) up to 74 dB, and with active gain, the noise level can be reduced by a factor of √3 using the adjacent scan. The second belt has a wider operating bandwidth of 1 MHz and multi-frequency operation. The image frame rate is 122 frame/s, the fastest wearable EIT reported to date. It measures impedance with 98% accuracy and has less than 0.5 Ω and 1° variation across all channels. In addition the ASIC facilitates several other functionalities to provide supplementary clinical information at the bedside. With the advancement of technology and the ever-increasing fusion of computer and machine into daily life, a seamless HMI system that can recognize hand gestures and motions and allow the control of robotic machines or prostheses to perform dexterous tasks, is a target of research. Originally developed as an imaging technique, EIT can be used with a machine learning technique to track bones and muscles movement towards understanding the human user’s intentions and ultimately controlling prosthetic hand applications. For this application, an analog front-end ASIC is designed using 0.35-µm standard process technology with ±1.65 V power supplies. It comprises a current driver capable of differential drive and a low noise (9μVrms) IA with a CMRR of 80 dB. The function modules occupy an area of 0.07 mm². Using the ASIC, a complete HMI system based on the EIT principle for hand prosthesis control has been presented, and the user’s forearm inner bio-impedance redistribution is assessed. Using artificial neural networks, bio-impedance redistribution can be learned so as to recognise the user’s intention in real-time for prosthesis operation. In this work, eleven hand motions are designed for prosthesis operation. Experiments with five subjects show that the system can achieve an overall recognition accuracy of 95.8%

Interior Void Classification in Liquid Metal using Multi-Frequency Magnetic Induction Tomography with a Machine Learning Approach

Identification of gas bubble, void detection and porosity estimation are important factors in many liquid metal processes. In steel casting, the importance of flow condition and phase distribution in crucial parts, such as submerged entry nozzle (SEN) and mould raises the needs to observe the phenomena. Cross-section of flow shapes can be visualised using the magnetic induction tomography (MIT) technique. However, the inversion procedure in the image reconstruction has either limited resolution or involving post-processing stages degrading its real-time capability. Additionally, when quantifying the void fraction or porosity, the image may not be required. This work proposes an interior void classifier based on multi-frequency mutual induction measurements with eutectic alloy GaInSn as a cold liquid metal model contained in a 3D printed plastic miniature of an SEN. The sensors consist of eight coils arranged in a circle encapsulating the column, providing combinatorial detection on conductive surface and depth. The datasets are induced voltage collections of several non-metallic inclusions (NMI) patterns in liquid metal static test and used to train a machine learning model. The model architectures are a fully connected neural network (FCNN) for 1D; and a convolutional neural network (CNN) for 2D data. The classifier using 1D data has been trained to provide 95% accuracy on this dataset. On the other hand, CNN classification using multi-dimensional data produces 96% of test accuracy. Refined with representative flow scenarios, the trained model could be deployed for an intelligent online control system of the liquid metal process