4.5 Article

SERIES REVERSION IN CALDERON'S PROBLEM

相关参考文献

注意:仅列出部分参考文献,下载原文获取全部文献信息。
Article Mathematics, Applied

Calderon's inverse problem with a finite number of measurements II: independent data

Giovanni S. Alberti et al.

Summary: This paper proves a local Lipschitz stability estimate for Gel'fand-Calderon's inverse problem for the Schrodinger equation, and proposes a new iterative reconstruction scheme.

APPLICABLE ANALYSIS (2022)

Article Mathematics, Applied

CONTACT ADAPTING ELECTRODE MODEL FOR ELECTRICAL IMPEDANCE TOMOGRAPHY

J. Darde et al.

Summary: This study proposes a new robust modeling method for contact electrodes in electrical impedance tomography. By assuming approximate knowledge about the electrodes' whereabouts and using a boundary admittivity function to determine their actual locations, the proposed method enables simultaneous reconstruction of the positions and strengths of the contacts.

SIAM JOURNAL ON APPLIED MATHEMATICS (2022)

Article Mathematics, Applied

Infinite dimensional compressed sensing from anisotropic measurements and applications to inverse problems in PDE

Giovanni S. Alberti et al.

Summary: This study investigates a compressed sensing problem with measurement and sparsifying systems assumed to be frames of the underlying Hilbert space of signals, providing explicit bounds on the number of measurements needed for stable recovery based on mutual coherence. It also discusses the efficiency of nonuniform sampling strategies and applications to inverse problems in partial differential equations, with a focus on electrical impedance tomography.

APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS (2021)

Article Mathematics, Applied

Mimicking relative continuum measurements by electrode data in two-dimensional electrical impedance tomography

Henrik Garde et al.

Summary: 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 model. The upper bounds for the corresponding approximation errors explicitly depend on the number (and size) of the employed electrodes as well as on the regularity of the continuum current that is mimicked. In particular, if the input current and the object boundary are infinitely smooth, the discrepancy associated with the point electrode model converges to zero faster than any negative power of the number of electrodes.

NUMERISCHE MATHEMATIK (2021)

Article Mathematics, Applied

OPTIMAL DEPTH-DEPENDENT DISTINGUISHABILITY BOUNDS FOR ELECTRICAL IMPEDANCE TOMOGRAPHY IN ARBITRARY DIMENSION

Henrik Garde et al.

SIAM JOURNAL ON APPLIED MATHEMATICS (2020)

Article Mathematics, Applied

ON REGULARITY OF THE LOGARITHMIC FORWARD MAP OF ELECTRICAL IMPEDANCE TOMOGRAPHY

Henrik Garde et al.

SIAM JOURNAL ON MATHEMATICAL ANALYSIS (2020)

Article Mathematics, Applied

Reconstruction of piecewise constant layered conductivities in electrical impedance tomography

Henrik Garde

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS (2020)

Article Mathematics, Applied

MONOTONICITY-BASED RECONSTRUCTION OF EXTREME INCLUSIONS IN ELECTRICAL IMPEDANCE TOMOGRAPHY

Valentina Candiani et al.

SIAM JOURNAL ON MATHEMATICAL ANALYSIS (2020)

Article Mathematics, Applied

CALDERON'S INVERSE PROBLEM WITH A FINITE NUMBER OF MEASUREMENTS

Giovanni S. Alberti et al.

FORUM OF MATHEMATICS SIGMA (2019)

Article Mathematics, Applied

EIT IN A LAYERED ANISOTROPIC MEDIUM

Giovanni Alessandrini et al.

INVERSE PROBLEMS AND IMAGING (2018)

Article Mathematics, Applied

ENHANCING D-BAR RECONSTRUCTIONS FOR ELECTRICAL IMPEDANCE TOMOGRAPHY WITH CONFORMAL MAPS

Nuutti Hyvonen et al.

INVERSE PROBLEMS AND IMAGING (2018)

Article Mathematics, Applied

SMOOTHENED COMPLETE ELECTRODE MODEL

Nuutti Hyvonen et al.

SIAM JOURNAL ON APPLIED MATHEMATICS (2017)

Article Mathematics, Applied

GLOBAL UNIQUENESS FOR THE CALDERON PROBLEM WITH LIPSCHITZ CONDUCTIVITIES

Pedro Caro et al.

FORUM OF MATHEMATICS PI (2016)

Article Mathematics

The Neumann-to-Dirichlet map in two dimensions

O. Yu. Imanuvilov et al.

ADVANCES IN MATHEMATICS (2015)

Article Mathematics, Applied

MONOTONICITY-BASED SHAPE RECONSTRUCTION IN ELECTRICAL IMPEDANCE TOMOGRAPHY

Bastian Harrach et al.

SIAM JOURNAL ON MATHEMATICAL ANALYSIS (2013)

Article Mathematics, Applied

THE CALDERON PROBLEM WITH PARTIAL DATA ON MANIFOLDS AND APPLICATIONS

Carlos Kenig et al.

ANALYSIS & PDE (2013)

Article Mathematics, Applied

Inverse Born series for the Calderon problem

Simon Arridge et al.

INVERSE PROBLEMS (2012)

Article Mathematics, Applied

Reconstruction in the Calderon Problem with Partial Data

Adrian Nachman et al.

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS (2010)

Article Mathematics

THE CALDERON PROBLEM WITH PARTIAL DATA IN TWO DIMENSIONS

Oleg Yu. Imanuvilov et al.

JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY (2010)

Article Mathematics, Applied

EXACT SHAPE-RECONSTRUCTION BY ONE-STEP LINEARIZATION IN ELECTRICAL IMPEDANCE TOMOGRAPHY

Bastian Harrach et al.

SIAM JOURNAL ON MATHEMATICAL ANALYSIS (2010)

Review Mathematics, Applied

Electrical impedance tomography and Calderon's problem

G. Uhlmann

INVERSE PROBLEMS (2009)

Article Mathematics, Applied

APPROXIMATING IDEALIZED BOUNDARY DATA OF ELECTRIC IMPEDANCE TOMOGRAPHY BY ELECTRODE MEASUREMENTS

Nuutti Hyvonen

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES (2009)

Article Mathematics

ON THE LINEARIZED LOCAL CALDERON PROBLEM

David Dos Santos Ferreira et al.

MATHEMATICAL RESEARCH LETTERS (2009)

Article Mathematics, Applied

Newton regularizations for impedance tomography: convergence by local injectivity

Armin Lechleiter et al.

INVERSE PROBLEMS (2008)

Article Mathematics, Applied

On uniqueness in the inverse conductivity problem with local data

Victor Isakov

INVERSE PROBLEMS AND IMAGING (2007)

Article Mathematics

Calderon's inverse conductivity problem in the plane

Kari Astala et al.

ANNALS OF MATHEMATICS (2006)

Article Mathematics, Applied

Calderon's inverse problem for anisotropic conductivity in the plane

K Astala et al.

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS (2005)

Article Mathematics, Applied

Recent progress in electrical impedance tomography

M Hanke et al.

INVERSE PROBLEMS (2003)

Correction Mathematics, Applied

Electrical impedance tomography (vol 18, pg 99, 2002)

L Borcea

INVERSE PROBLEMS (2003)

Review Mathematics, Applied

Electrical impedance tomography

L Borcea

INVERSE PROBLEMS (2002)