Multi-frequency Electrical Impedance Tomography (mfEIT) represents a promising biomedical imaging modality that enables the estimation of tissue conductivities across a range of frequencies. Addressing this challenge, we present a novel variational network, a model-based learning paradigm that strategically merges the advantages and interpretability of classical iterative reconstruction with the power of deep learning. This approach integrates graph neural networks (GNNs) within the iterative Proximal Regularized Gauss Newton (PRGN) framework. By unrolling the PRGN algorithm, where each iteration corresponds to a network layer, we leverage the physical insights of nonlinear model fitting alongside the GNN's capacity to capture inter-frequency correlations. Notably, the GNN architecture preserves the irregular triangular mesh structure used in the solution of the nonlinear forward model, enabling accurate reconstruction of overlapping tissue fraction concentrations.

Electrical impedance tomography (EIT) is a non-invasive imaging method with diverse applications, including medical imaging and non-destructive testing. The inverse problem of reconstructing internal electrical conductivity from boundary measurements is nonlinear and highly ill-posed, making it difficult to solve accurately. In recent years, there has been growing interest in combining analytical methods with machine learning to solve inverse problems. In this paper, we propose a method for estimating the convex hull of inclusions from boundary measurements by combining the enclosure method proposed by Ikehata with neural networks. We demonstrate its performance using experimental data. Compared to the classical enclosure method with least squares fitting, the learned convex hull achieves superior performance on both simulated and experimental data.

Objective: To develop a fast image reconstruction method for stroke monitoring with electrical impedance tomography with image quality comparable to computationally expensive nonlinear model-based methods. Methods: A post-processing approach with graph convolutional networks is employed. Utilizing the flexibility of the graph setting, a graph U-net is trained on linear difference reconstructions from 2D simulated stroke data and applied to fully 3D images from realistic simulated and experimental data. An additional network, trained on 3D vs. 2D images, is also considered for comparison. Results: Post-processing the linear difference reconstructions through the graph U-net significantly improved the image quality, resulting in images comparable to, or better than, the time-intensive nonlinear reconstruction method (a few minutes vs. several hours). Conclusion: Pairing a fast reconstruction method, such as linear difference imaging, with post-processing through a graph U-net provided significant improvements, at a negligible computational cost. Training in the graph framework vs classic pixel-based setting (CNN) allowed the ability to train on 2D cross-sectional images and process 3D volumes providing a nearly 50x savings in data simulation costs with no noticeable loss in quality. Significance: The proposed approach of post-processing a linear difference reconstruction with the graph U-net could be a feasible approach for on-line monitoring of hemorrhagic stroke.

Flexible electrical impedance tomography (EIT) is an emerging technology for tactile sensing in human-machine interfaces (HMI). It offers a unique alternative to traditional array-based tactile sensors with its flexible, scalable, and cost-effective one-piece design. This paper proposes a lattice-patterned flexible EIT tactile sensor with a hydrogel-based conductive layer, designed for enhanced sensitivity while maintaining durability. We conducted simulation studies to explore the influence of lattice width and conductive layer thickness on sensor performance, establishing optimized sensor design parameters for enhanced functionality. Experimental evaluations demonstrate the sensor's capacity to detect diverse tactile patterns with a high accuracy. The practical utility of the sensor is demonstrated through its integration within an HMI setup to control a virtual game, showcasing its potential for dynamic, multi-functional tactile interactions in real-time applications. This study reinforces the potential of EIT-based flexible tactile sensors, establishing a foundation for future advancements in wearable, adaptable HMI technologies.

Electrical Impedance Tomography (EIT)-inspired tactile sensors are gaining attention in robotic tactile sensing due to their cost-effectiveness, safety, and scalability with sparse electrode configurations. This paper presents a data augmentation strategy for learning-based tactile reconstruction that amplifies the original single-frame signal measurement into 32 distinct, effective signal data for training. This approach supplements uncollected conditions of position information, resulting in more accurate and high-resolution tactile reconstructions. Data augmentation for EIT significantly reduces the required EIT measurements and achieves promising performance with even limited samples. Simulation results show that the proposed method improves the correlation coefficient by over 12% and reduces the relative error by over 21% under various noise levels. Furthermore, we demonstrate that a standard deep neural network (DNN) utilizing the proposed data augmentation reduces the required data down to 1/31 while achieving a similar tactile reconstruction quality. Real-world tests further validate the approach's effectiveness on a flexible EIT-based tactile sensor. These results could help address the challenge of training tactile sensing networks with limited available measurements, improving the accuracy and applicability of EIT-based tactile sensing systems.

Multi-frequency Electrical Impedance Tomography (mfEIT) is a promising biomedical imaging technique that estimates tissue conductivities across different frequencies. Current state-of-the-art (SOTA) algorithms, which rely on supervised learning and Multiple Measurement Vectors (MMV), require extensive training data, making them time-consuming, costly, and less practical for widespread applications. Moreover, the dependency on training data in supervised MMV methods can introduce erroneous conductivity contrasts across frequencies, posing significant concerns in biomedical applications. To address these challenges, we propose a novel unsupervised learning approach based on Multi-Branch Attention Image Prior (MAIP) for mfEIT reconstruction. Our method employs a carefully designed Multi-Branch Attention Network (MBA-Net) to represent multiple frequency-dependent conductivity images and simultaneously reconstructs mfEIT images by iteratively updating its parameters. By leveraging the implicit regularization capability of the MBA-Net, our algorithm can capture significant inter- and intra-frequency correlations, enabling robust mfEIT reconstruction without the need for training data. Through simulation and real-world experiments, our approach demonstrates performance comparable to, or better than, SOTA algorithms while exhibiting superior generalization capability. These results suggest that the MAIP-based method can be used to improve the reliability and applicability of mfEIT in various settings.

In this work, we consider the non-invasive medical imaging modality of Electrical Impedance Tomography, where the problem is to recover the conductivity in a medium from a set of data that arises out of a current-to-voltage map (Neumann-to-Dirichlet operator) defined on the boundary of the medium. We formulate this inverse problem as an operator-learning problem where the goal is to learn the implicitly defined operator-to-function map between the space of Neumann-to-Dirichlet operators to the space of admissible conductivities. Subsequently, we use an operator-learning architecture, popularly called DeepONets, to learn this operator-to-function map. Thus far, most of the operator learning architectures have been implemented to learn operators between function spaces. In this work, we generalize the earlier works and use a DeepONet to actually learn an operator-to-function map. We provide a Universal Approximation Theorem type result which guarantees that this implicitly defined operator-to-function map between the the space of Neumann-to-Dirichlet operator to the space of conductivity function can be approximated to an arbitrary degree using such a DeepONet. Furthermore, we provide a computational implementation of our proposed approach and compare it against a standard baseline. We show that the proposed approach achieves good reconstructions and outperforms the baseline method in our experiments.

Electrical impedance tomography (EIT) plays a crucial role in non-invasive imaging, with both medical and industrial applications. In this paper, we present three data-driven reconstruction methods for EIT imaging. These three approaches were originally submitted to the Kuopio tomography challenge 2023 (KTC2023). First, we introduce a post-processing approach, which achieved first place at KTC2023. Further, we present a fully learned and a conditional diffusion approach. All three methods are based on a similar neural network as a backbone and were trained using a synthetically generated data set, providing with an opportunity for a fair comparison of these different data-driven reconstruction methods.

This study proposes an unsupervised sequence-to-sequence learning approach that automatically assesses the motion-induced reliability degradation of the cardiac volume signal (CVS) in multi-channel electrical impedance-based hemodynamic monitoring. The proposed method attempts to tackle shortcomings in existing learning-based assessment approaches, such as the requirement of manual annotation for motion influence and the lack of explicit mechanisms for realizing motion-induced abnormalities under contextual variations in CVS over time. By utilizing long-short term memory and variational auto-encoder structures, an encoder--decoder model is trained not only to self-reproduce an input sequence of the CVS but also to extrapolate the future in a parallel fashion. By doing so, the model can capture contextual knowledge lying in a temporal CVS sequence while being regularized to explore a general relationship over the entire time-series. A motion-influenced CVS of low-quality is detected, based on the residual between the input sequence and its neural representation with a cut--off value determined from the two-sigma rule of thumb over the training set. Our experimental observations validated two claims: (i) in the learning environment of label-absence, assessment performance is achievable at a competitive level to the supervised setting, and (ii) the contextual information across a time series of CVS is advantageous for effectively realizing motion-induced unrealistic distortions in signal amplitude and morphology. We also investigated the capability as a pseudo-labeling tool to minimize human-craft annotation by preemptively providing strong candidates for motion-induced anomalies. Empirical evidence has shown that machine-guided annotation can reduce inevitable human-errors during manual assessment while minimizing cumbersome and time-consuming processes.

Breast cancer is one of the most threatening diseases in women's life; thus, the early and accurate diagnosis plays a key role in reducing the risk of death in a patient's life. Mammography stands as the reference technique for breast cancer screening; nevertheless, many countries still lack access to mammograms due to economic, social, and cultural issues. Latest advances in computational tools, infrared cameras and devices for bio-impedance quantification, have given a chance to emerge other reference techniques like thermography, infrared thermography, electrical impedance tomography and biomarkers found in blood tests, therefore being faster, reliable and cheaper than other methods. In the last two decades, the techniques mentioned above have been considered as parallel and extended approaches for breast cancer diagnosis, as well many authors concluded that false positives and false negatives rates are significantly reduced. Moreover, when a screening method works together with a computational technique, it generate a "computer-aided diagnosis" system. The present work aims to review the last breakthroughs about the three techniques mentioned earlier, suggested machine learning techniques for breast cancer diagnosis, thus, describing the benefits of some methods in relation with other ones, such as, logistic regression, decision trees, random forest, deep and convolutional neural networks. With this, we studied several hyper-parameters optimization approaches with parzen tree optimizers to improve the performance of baseline models. An exploratory data analysis for each database and a benchmark of convolutional neural networks for the database of thermal images are presented.