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Purpose: Point-of-care MRI requires operation outside of a faraday shielded room normally used to block image-degrading electromagnetic Interference (EMI). To address this, we introduce the EDITER method, an external sensor based dynamic…

The Pulmonary Function Test (PFT) is an widely utilized and rigorous classification test for lung function evaluation, serving as a comprehensive tool for lung diagnosis. Meanwhile, Electrical Impedance Tomography (EIT) is a rapidly…

Image and Video Processing · Electrical Eng. & Systems 2023-07-04 Shuzhe Chen , Li Li , Zhichao Lin , Ke Zhang , Ying Gong , Lu Wang , Xu Wu , Maokun Li , Yuanlin Song , Fan Yang , Shenheng Xu

This paper introduces a constructive method for approximating relative continuum measurements in two-dimensional electrical impedance tomography based on data originating from either the point electrode model or the complete electrode…

Numerical Analysis · Mathematics 2021-03-09 Henrik Garde , Nuutti Hyvönen

Image reconstruction of EIT mathematically is a typical nonlinear and severely ill-posed inverse problem. Appropriate priors or penalties are required to enable the reconstruction. The commonly used L2-norm can enforce the stability to…

Numerical Analysis · Mathematics 2018-03-13 Jing Wang , Bo Han , Wei Wang

This work considers finding optimal positions for the electrodes within the Bayesian paradigm based on available prior information on the conductivity; the aim is to place the electrodes so that the posterior density of the (discretized)…

Optimization and Control · Mathematics 2014-09-11 Nuutti Hyvönen , Aku Seppänen , Stratos Staboulis

Scanning transmission electron microscopy (STEM) has been extensively used for imaging complex materials down to atomic resolution. The most commonly employed STEM modality, annular dark-field imaging, produces easily-interpretable…

Owing to recent advances in thoracic electrical impedance tomography, a patient's hemodynamic function can be noninvasively and continuously estimated in real-time by surveilling a cardiac volume signal associated with stroke volume and…

Signal Processing · Electrical Eng. & Systems 2023-01-05 Chang Min Hyun , Tae Jun Jang , Jeongchan Nam , Hyeuknam Kwon , Kiwan Jeon , Kyunghun Lee

Two reconstruction methods of Electrical Impedance Tomography (EIT) are numerically compared for nonsmooth conductivities in the plane based on the use of complex geometrical optics (CGO) solutions to D-bar equations involving the global…

Analysis of PDEs · Mathematics 2015-06-17 Kari Astala , Lassi Päivärinta , Juan Manuel Reyes , Samuli Siltanen

This work considers using reduced basis techniques in connection to (smoothened) total variation regularization in electrical impedance tomography, but analogous ideas can also be used for other inverse elliptic boundary value problems. It…

Numerical Analysis · Mathematics 2026-02-18 A. Hannukainen , N. Hyvönen , V. Toresen

Electrical impedance tomography aims at reconstructing the interior electrical conductivity from surface measurements of currents and voltages. As the current-voltage pairs depend nonlinearly on the conductivity, impedance tomography leads…

Numerical Analysis · Mathematics 2017-05-31 Nuutti Hyvönen , Lauri Mustonen

This paper treats the inverse problem of retrieving the electrical conductivity of a material starting from boundary measurements in the framework of Electrical Resistance Tomography (ERT). In particular, the focus is on non-iterative…

Numerical Analysis · Mathematics 2026-05-15 Antonello Tamburrino , Vincenzo Mottola

This article considers the inverse problem of Magnet resonance electrical impedance tomography (MREIT) in two dimensions. A rigorous mathematical framework for this inverse problem as well as the existing Harmonic $B_z$ Algorithm as a…

Numerical Analysis · Mathematics 2018-04-17 Dominik Garmatter , Bastian Harrach

In this work we consider the inverse problem of reconstructing the optical properties of a layered medium from an elastography measurement where optical coherence tomography is used as the imaging method. We hereby model the sample as a…

Numerical Analysis · Mathematics 2024-02-23 Peter Elbau , Leonidas Mindrinos , Leopold Veselka

We show how to eliminate the error caused by an incorrectly modeled boundary in electrical impedance tomography (EIT). In practical measurements, one usually lacks the exact knowledge of the boundary. Because of this the numerical…

Analysis of PDEs · Mathematics 2007-05-23 Ville Kolehmainen , Matti Lassas , Petri Ola

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 focuses on prior information for improved sparsity reconstruction in electrical impedance tomography with partial data, i.e. data measured only on subsets of the boundary. Sparsity is enforced using an $\ell_1$ norm of the basis…

Numerical Analysis · Mathematics 2016-01-20 Henrik Garde , Kim Knudsen

For the linearized reconstruction problem in Electrical Impedance Tomography (EIT) with the Complete Electrode Model (CEM), Lechleiter and Rieder (2008 Inverse Problems 24 065009) have shown that a piecewise polynomial conductivity on a…

Analysis of PDEs · Mathematics 2019-01-04 Bastian Harrach

The ill-posedness of Calder\'on's inverse conductivity problem, responsible for the poor spatial resolution of Electrical Impedance Tomography (EIT), has been an impetus for the development of hybrid imaging techniques, which compensate for…

Analysis of PDEs · Mathematics 2021-04-28 Allan Greenleaf , Matti Lassas , Matteo Santacesaria , Samuli Siltanen , Gunther Uhlmann

Adequate characterization of two-dimensional materials with low energy barriers for impurity adsorption is key for advancing applications based on catalysis, sensing, and surface functionalization. However, first-principles methods, such as…

The multifrequency electrical impedance tomography is considered in order to image a conductivity inclusion inside a homogeneous background medium by injecting one current. An original spectral decomposition of the solution of the forward…

Analysis of PDEs · Mathematics 2016-09-23 Habib Ammari , Faouzi Triki