The D-bar method for electrical impedance tomography—demystified

JL Mueller, S Siltanen - Inverse problems, 2020 - iopscience.iop.org
Electrical impedance tomography (EIT) is an imaging modality where a patient or object is
probed using harmless electric currents. The currents are fed through electrodes placed on …

[LIVRE][B] Linear and nonlinear inverse problems with practical applications

JL Mueller, S Siltanen - 2012 - SIAM
Inverse problems arise from the need to interpret indirect and incomplete measurements. As
an area of contemporary mathematics, the field of inverse problems is strongly driven by …

[LIVRE][B] Electrical impedance tomography: methods, history and applications

A Adler, D Holder - 2021 - books.google.com
With contributions from leading international researchers, this second edition of Electrical
Impedance Tomography: Methods, History and Applications has been fully updated …

Uniqueness and Lipschitz stability in electrical impedance tomography with finitely many electrodes

B Harrach - Inverse problems, 2019 - iopscience.iop.org
For the linearized reconstruction problem in electrical impedance tomography with the
complete electrode model, Lechleiter and Rieder (2008 Inverse Problems 24 065009) have …

Electrical impedance tomography

A Adler, R Gaburro, W Lionheart - 2015 - eprints.maths.manchester.ac.uk
Electrical Impedance tomography Adler, Andy and Gaburro, Romina and Lionheart, William
2015 MIMS EPrint: 2020.23 Manchester Ins Page 1 Electrical Impedance tomography Adler …

Monotonicity-based inversion of the fractional Schrödinger equation II. General potentials and stability

B Harrach, YH Lin - SIAM Journal on Mathematical Analysis, 2020 - SIAM
In this work, we use monotonicity-based methods for the fractional Schrödinger equation
with general potentials q in L^ ∞ (Omega) in a Lipschitz bounded open set Omega ⊂ R^ n …

Local analysis of inverse problems: Hölder stability and iterative reconstruction

MV De Hoop, L Qiu, O Scherzer - Inverse Problems, 2012 - iopscience.iop.org
We consider a class of inverse problems defined by a nonlinear map** from parameter or
model functions to the data, where the inverse map** is Hölder continuous with respect to …

Mathematical analysis of a model-constrained inverse problem for the reconstruction of early states of prostate cancer growth

E Beretta, C Cavaterra, M Fornoni, G Lorenzo… - SIAM Journal on Applied …, 2024 - SIAM
The availability of cancer measurements over time enables the personalized assessment of
tumor growth and therapeutic response dynamics. However, many tumors are treated after …

Calderón's inverse problem with a finite number of measurements

GS Alberti, M Santacesaria - Forum of mathematics, sigma, 2019 - cambridge.org
We prove that an L∞ potential in the Schrödinger equation in three and higher dimensions
can be uniquely determined from a finite number of boundary measurements, provided it …

Modeling active electrolocation in weakly electric fish

H Ammari, T Boulier, J Garnier - SIAM Journal on Imaging Sciences, 2013 - SIAM
In this paper, we provide a mathematical model for the electrolocation in weakly electric
fishes. We first investigate the forward complex conductivity problem and derive the …