Tactile sensing is fundamental to robotic systems, enabling interactions through physical contact in multiple tasks. Despite its importance, achieving high-resolution, large-area tactile sensing remains challenging. Electrical Impedance Tomography (EIT) has emerged as a promising approach for large-area, distributed tactile sensing with minimal electrode requirements which can lend itself to addressing complex contact problems in robotics. However, existing EIT-based tactile reconstruction methods often suffer from high computational costs or depend on extensive annotated simulation datasets, hindering its viability in real-world settings. To address this shortcoming, here we propose a Pre-trained Transformer for EIT-based Tactile Reconstruction (PTET), a learning-based framework that bridges the simulation-to-reality gap by leveraging self-supervised pretraining on simulation data and fine-tuning with limited real-world data. In simulations, PTET requires 99.44 percent fewer annotated samples than equivalent state-of-the-art approaches (2,500 vs. 450,000 samples) while achieving reconstruction performance improvements of up to 43.57 percent under identical data conditions. Fine-tuning with real-world data further enables PTET to overcome discrepancies between simulated and experimental datasets, achieving superior reconstruction and detail recovery in practical scenarios. The improved reconstruction accuracy, data efficiency, and robustness in real-world tasks establish it as a scalable and practical solution for tactile sensing systems in robotics, especially for object handling and adaptive grasping under varying pressure conditions.

Flexible electrical impedance tomography (EIT) offers a promising alternative to traditional tactile sensing approaches, enabling low-cost, scalable, and deformable sensor designs. Here, we propose an optimized lattice-structured flexible EIT tactile sensor incorporating a hydrogel-based conductive layer, systematically designed through three-dimensional coupling field simulations to optimize structural parameters for enhanced sensitivity and robustness. By tuning the lattice channel width and conductive layer thickness, we achieve significant improvements in tactile reconstruction quality and classification performance. Experimental results demonstrate high-quality tactile reconstruction with correlation coefficients up to 0.9275, peak signal-to-noise ratios reaching 29.0303 dB, and structural similarity indexes up to 0.9660, while maintaining low relative errors down to 0.3798. Furthermore, the optimized sensor accurately classifies 12 distinct tactile stimuli with an accuracy reaching 99.6%. These results highlight the potential of simulation-guided structural optimization for advancing flexible EIT-based tactile sensors toward practical applications in wearable systems, robotics, and human-machine interfaces.

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.

--Unsupervised learning methods, such as Deep Image Prior (DIP), have shown great potential in tomographic imaging due to their training-data-free nature and high generalization capability. IP introduces three key strategies--Unsupervised Parameter Warm-Start (UPWS), T emporal Parameter Propagation (TPP), and a customized lightweight reconstruction backbone, 3D-FastResUNet--to accelerate convergence, enforce temporal coherence, and improve computational efficiency. IP enables fast and accurate 3D time-sequence Electrical Impedance T omography (tsEIT) reconstruction. IP delivers superior image quality--with a 24.8% increase in average MSSIM and an 8.1% reduction in ERR--alongside significantly reduced computational time (7.1 faster), highlighting its promise for clinical dynamic pulmonary imaging. ULMONARY imaging plays a critical role in the early diagnosis, monitoring, and management of respiratory diseases such as pulmonary edema, chronic obstructive pulmonary disease (COPD), and acute respiratory distress syndrome (ARDS) [1]-[4]. Among available techniques, tomo-graphic imaging modalities--including Computed Tomography (CT) [5], [6] and Magnetic Resonance Imaging (MRI) [7], [8]--are widely used in clinical pulmonary imaging due to their ability to produce high-resolution anatomical images. Hao Fang, Hao Y u, Sihao Teng, Zhe Liu and Y unjie Y ang are with the SMART Group, Institute for Imaging, Data and Communications, School of Engineering, The University of Edinburgh, Edinburgh, UK. (Correspondence authors: Y unjie Y ang and Zhe Liu; Email: y.yang@ed.ac.uk and zz.liu@ed.ac.uk). Tao Zhang is with the Department of Intensive Care Unit, Tianjin Huanhu Hospital, Tianjin, China.

Electrical Impedance Tomography (EIT) is a non-invasive, low-cost bedside imaging modality with high temporal resolution, making it suitable for bedside monitoring. However, its inherently ill-posed inverse problem poses significant challenges for accurate image reconstruction. Deep learning (DL)-based approaches have shown promise but often rely on complex network architectures with a large number of parameters, limiting efficiency and scalability. Here, we propose an Ultra-Lightweight Quantum-Assisted Inference (QuantEIT) framework for EIT image reconstruction. QuantEIT leverages a Quantum-Assisted Network (QA-Net), combining parallel 2-qubit quantum circuits to generate expressive latent representations that serve as implicit nonlinear priors, followed by a single linear layer for conductivity reconstruction. This design drastically reduces model complexity and parameter number. Uniquely, QuantEIT operates in an unsupervised, training-data-free manner and represents the first integration of quantum circuits into EIT image reconstruction. Extensive experiments on simulated and real-world 2D and 3D EIT lung imaging data demonstrate that QuantEIT outperforms conventional methods, achieving comparable or superior reconstruction accuracy using only 0.2% of the parameters, with enhanced robustness to noise.

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.

This paper presents a dual-channel tactile skin that integrates Electrical Impedance Tomography (EIT) with air pressure sensing to achieve accurate multi-contact force detection. The EIT layer provides spatial contact information, while the air pressure sensor delivers precise total force measurement. Our framework combines these complementary modalities through: deep learning-based EIT image reconstruction, contact area segmentation, and force allocation based on relative conductivity intensities from EIT. The experiments demonstrated 15.1% average force estimation error in single-contact scenarios and 20.1% in multi-contact scenarios without extensive calibration data requirements. This approach effectively addresses the challenge of simultaneously localizing and quantifying multiple contact forces without requiring complex external calibration setups, paving the way for practical and scalable soft robotic skin applications.

Flexible electronic skins that simultaneously sense touch and bend are desired in several application areas, such as to cover articulated robot structures. This paper introduces a flexible tactile sensor based on Electrical Impedance Tomography (EIT), capable of simultaneously detecting and measuring contact forces and flexion of the sensor. The sensor integrates a magnetic hydrogel composite and utilizes EIT to reconstruct internal conductivity distributions. Real-time estimation is achieved through the one-step Gauss-Newton method, which dynamically updates reference voltages to accommodate sensor deformation. A convolutional neural network is employed to classify interactions, distinguishing between touch, bending, and idle states using pre-reconstructed images. Experimental results demonstrate an average touch localization error of 5.4 mm (SD 2.2 mm) and average bending angle estimation errors of 1.9$^\circ$ (SD 1.6$^\circ$). The proposed adaptive reference method effectively distinguishes between single- and multi-touch scenarios while compensating for deformation effects. This makes the sensor a promising solution for multimodal sensing in robotics and human-robot collaboration.

This paper presents a multi-resolution reconstruction method for Electrical Impedance Tomography (EIT), referred to as MR-EIT, which is capable of operating in both supervised and unsupervised learning modes. MR-EIT integrates an ordered feature extraction module and an unordered coordinate feature expression module. The former achieves the mapping from voltage to two-dimensional conductivity features through pre-training, while the latter realizes multi-resolution reconstruction independent of the order and size of the input sequence by utilizing symmetric functions and local feature extraction mechanisms. In the data-driven mode, MR-EIT reconstructs high-resolution images from low-resolution data of finite element meshes through two stages of pre-training and joint training, and demonstrates excellent performance in simulation experiments. In the unsupervised learning mode, MR-EIT does not require pre-training data and performs iterative optimization solely based on measured voltages to rapidly achieve image reconstruction from low to high resolution. It shows robustness to noise and efficient super-resolution reconstruction capabilities in both simulation and real water tank experiments. Experimental results indicate that MR-EIT outperforms the comparison methods in terms of Structural Similarity (SSIM) and Relative Image Error (RIE), especially in the unsupervised learning mode, where it can significantly reduce the number of iterations and improve image reconstruction quality.

In this book, written in Portuguese, we discuss what ill-posed problems are and how the regularization method is used to solve them. In the form of questions and answers, we reflect on the origins and future of regularization, relating the similarities and differences of its meaning in different areas, including inverse problems, statistics, machine learning, and deep learning.