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The size estimates approach for Electrical Impedance Tomography (EIT) allows for estimating the size (area or volume) of an unknown inclusion in an electrical conductor by means of one pair of boundary measurements of voltage and current.…

Analysis of PDEs · Mathematics 2012-02-27 Giovanni Alessandrini , Antonio Bilotta , Antonino Morassi , Edi Rosset , Emilio Turco

This paper considers the problem of noise-robust neural operator approximation for the solution map of Calder\'on's inverse conductivity problem. In this continuum model of electrical impedance tomography (EIT), the boundary measurements…

Numerical Analysis · Mathematics 2025-11-26 Maarten V. de Hoop , Nikola B. Kovachki , Matti Lassas , Nicholas H. Nelsen

Electrical Resistivity Tomography (ERT) has become widely used for engineering and environmental applications in the last couple of decades due to (1) the simplification and automating of resistivity meters and (2) the new generation of…

Geophysics · Physics 2024-04-18 Deparis Jacques , Gance Julien , Orlando Leite

Electron tomography is becoming an increasingly important tool in materials science for studying the three-dimensional morphologies and chemical compositions of nanostructures. The image quality obtained by many current algorithms is…

Electromagnetic source imaging (ESI) requires solving a highly ill-posed inverse problem. To seek a unique solution, traditional ESI methods impose various forms of priors that may not accurately reflect the actual source properties, which…

Image and Video Processing · Electrical Eng. & Systems 2022-07-14 Gexin Huang , Jiawen Liang , Ke Liu , Chang Cai , ZhengHui Gu , Feifei Qi , Yuan Qing Li , Zhu Liang Yu , Wei Wu

Electrometry near a dielectric surface is performed using Rydberg electromagnetically induced transparency (EIT). The large polarizability of high n-state Rydberg atoms gives this method extreme sensitivity. We show that adsorbates on the…

Atomic Physics · Physics 2015-05-28 R. P. Abel , C. Carr , U. Krohn , C. S. Adams

This short note considerably simplifies a reconstruction method by the author (Comm. PDE, 45(9):1118--1133, 2020), for reconstructing piecewise constant layered conductivities (PCLC) from partial boundary measurements in electrical…

Analysis of PDEs · Mathematics 2022-08-24 Henrik Garde

Acousto-electric tomography (AET) is a hybrid imaging modality that combines electrical impedance tomography with focused ultrasound perturbations to obtain interior power density measurements, which provide additional information that can…

Analysis of PDEs · Mathematics 2026-03-31 Hjørdis Schlüter , Babak Maboudi Afkham

This paper is devoted to proving convergence rates of variational and iterative regularization methods under variational source conditions VSCs for inverse problems whose linearization satisfies a range invariance condition. In order to…

Numerical Analysis · Mathematics 2024-03-28 Barbara Kaltenbacher

In optical tomography a physical body is illuminated with near-infrared light and the resulting outward photon flux is measured at the object boundary. The goal is to reconstruct internal optical properties of the body, such as absorption…

Numerical Analysis · Mathematics 2016-01-20 Antti Hannukainen , Lauri Harhanen , Nuutti Hyvönen , Helle Majander

Edge detection is crucial in image processing, but existing methods often produce overly detailed edge maps, affecting clarity. Fixed-window statistical testing faces issues like scale mismatch and computational redundancy. To address…

Computer Vision and Pattern Recognition · Computer Science 2025-05-05 Ruyu Yan , Da-Qing Zhang

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…

Image and Video Processing · Electrical Eng. & Systems 2024-09-18 Hao Fang , Zhe Liu , Yi Feng , Zhen Qiu , Pierre Bagnaninchi , Yunjie Yang

In this work, we propose a new approach for efficient edge-preserving image deconvolution. Our algorithm is based on a novel type of explicit image filter - guided filter. The guided filter can be used as an edge-preserving smoothing…

Computer Vision and Pattern Recognition · Computer Science 2016-09-08 Hang Yang , Ming Zhu , Zhongbo Zhang , Heyan Huang

This paper introduces a method for approximately eliminating the effect that conductivity changes outside the region of interest have in electrical impedance tomography, allowing to form a local reconstruction in the region of interest…

Numerical Analysis · Mathematics 2026-01-21 A. Jääskeläinen , A. Vavilov , J. Toivanen , A. Hänninen , V. Kolehmainen , N. Hyvönen

Inter subject variability of the electrical conductivity of brain, skull and skin strongly limits the accuracy by which current sources underlying electro-encephalography (EEG) can be localized in the brain. This inter subject variability…

Medical imaging is nowadays a pillar in diagnostics and therapeutic follow-up. Current research tries to integrate established - but ionizing - tomographic techniques with technologies offering reduced radiation exposure. Diffuse Optical…

Numerical Analysis · Mathematics 2024-02-15 Alessandro Benfenati , Paola Causin , Martina Quinteri

Electron tomography (ET) has become a standard technique for 3D characterization of materials at the nano-scale. Traditional reconstruction algorithms such as weighted back projection suffer from disruptive artifacts with insufficient…

Computer Vision and Pattern Recognition · Computer Science 2019-04-05 Yi Jiang , Elliot Padgett , Robert Hovden , David A. Muller

Purpose: To investigate deep learning electrical properties tomography (EPT) for application on different simulated and in-vivo datasets including pathologies for obtaining quantitative brain conductivity maps. Methods: 3D patch-based…

The electrical impedance tomography (EIT) problem of estimating the unknown conductivity distribution inside a domain from boundary current or voltage measurements requires the solution of a nonlinear inverse problem. Sparsity promoting…

Numerical Analysis · Mathematics 2024-05-27 Daniela Calvetti , Monica Pragliola , Erkki Somersalo

Electrical Impedance Tomography (EIT) is a functional imaging method that is being developed for bedside use in critical care medicine. Aiming at improving the chest anatomical resolution of EIT images we developed a fuzzy model based on…