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Communications in Partial Differential Equations Volume 36, 2011 - Issue 10
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Original Articles

Lipschitz Stability for the Electrical Impedance Tomography Problem: The Complex Case

Elena Beretta Dipartimento di Matematica “G. Castelnuovo”, Università di Roma “La Sapienza”, Rome, ItalyCorrespondence[email protected]
&
Elisa Francini Dipartimento di Matematica “U. Dini”, Università di Firenze, Firenze, Italy
Pages 1723-1749 | Received 30 Jul 2010, Accepted 31 Dec 2010, Published online: 08 Sep 2011

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H. Meftahi & A. Potschka. (2023) Elastic shear modulus and density profiles inversion: Lipschitz stability results. Applicable Analysis 0:0, pages 1-16.
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Elena Beretta & Elisa Francini. (2022) Global Lipschitz stability estimates for polygonal conductivity inclusions from boundary measurements. Applicable Analysis 101:10, pages 3536-3549.
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Olga Doeva, Romina Gaburro, William R. B. Lionheart & Clifford J. Nolan. (2022) Lipschitz stability at the boundary for time-harmonic diffuse optical tomography. Applicable Analysis 101:10, pages 3697-3715.
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Giovanni S. Alberti & Matteo Santacesaria. (2022) Calderón's inverse problem with a finite number of measurements II: independent data. Applicable Analysis 101:10, pages 3636-3654.
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Angkana Rüland & Eva Sincich. (2022) On Runge approximation and Lipschitz stability for a finite-dimensional Schrödinger inverse problem. Applicable Analysis 101:10, pages 3655-3666.
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Elena Beretta, Elisa Francini & Sergio Vessella. (2019) A transmission problem on a polygonal partition: regularity and shape differentiability. Applicable Analysis 98:10, pages 1862-1874.
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Elena Beretta, MaartenV. de Hoop, Elisa Francini & Sergio Vessella. (2015) Stable Determination of Polyhedral Interfaces from Boundary Data for the Helmholtz Equation. Communications in Partial Differential Equations 40:7, pages 1365-1392.
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Habib Ammari, Josselin Garnier, Loc Hoang Nguyen & Laurent Seppecher. (2013) Reconstruction of a Piecewise Smooth Absorption Coefficient by an Acousto-Optic Process. Communications in Partial Differential Equations 38:10, pages 1737-1762.
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Articles from other publishers (44)

Sonia Foschiatti. (2024) Lipschitz stability estimate for the simultaneous recovery of two coefficients in the anisotropic Schrödinger type equation via local Cauchy data. Journal of Mathematical Analysis and Applications 531:1, pages 127753.
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Vanessa Markaki, Drosos Kourounis & Antonios Charalambopoulos. (2023) On the identification of Lamé parameters in linear isotropic elasticity via a weighted self-guided TV-regularization method. Journal of Inverse and Ill-posed Problems 0:0.
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Jiali Xu & Xiang Xu. (2023) On Uniqueness of Recovering Coefficients from Localized Dirichlet-to-Neumann Map for Piecewise Homogeneous Piezoelectricity. SIAM Journal on Mathematical Analysis 55:2, pages 571-602.
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Maarten V de Hoop, Takashi Furuya, Ching-Lung Lin, Gen Nakamura & Manmohan Vashisth. (2023) Local recovery of a piecewise constant anisotropic conductivity in EIT on domains with exposed corners. Inverse Problems 39:2, pages 025005.
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Giovanni S Alberti, Ángel Arroyo & Matteo Santacesaria. (2022) Inverse problems on low-dimensional manifolds. Nonlinearity 36:1, pages 734-808.
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Andrea Aspri, Elena Beretta, Elisa Francini & Sergio Vessella. (2022) Lipschitz Stable Determination of Polyhedral Conductivity Inclusions from Local Boundary Measurements. SIAM Journal on Mathematical Analysis 54:5, pages 5182-5222.
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Fagueye Ndiaye. (2022) Inverse Problem for the Schrödinger Equation in Dimension 3. Journal of Mathematics 2022, pages 1-8.
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Jason Curran, Romina Gaburro, Clifford Nolan & Erkki Somersalo. (2022) Time-harmonic diffuse optical tomography: Hölder stability of the derivatives of the optical properties of a medium at the boundary. Inverse Problems and Imaging 0:0, pages 0.
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Gaurav Mittal & Ankik Kumar Giri. (2022) Convergence rates for iteratively regularized Gauss–Newton method subject to stability constraints. Journal of Computational and Applied Mathematics 400, pages 113744.
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Giovanni S. Alberti & Matteo Santacesaria. (2021) Infinite-Dimensional Inverse Problems with Finite Measurements. Archive for Rational Mechanics and Analysis 243:1, pages 1-31.
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Sonia Foschiatti, Romina Gaburro & Eva Sincich. (2021) Stability for the Calderón’s problem for a class of anisotropic conductivities via an ad hoc misfit functional. Inverse Problems 37:12, pages 125007.
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Snezhana Hristova, Stepan Tersian & Radoslava Terzieva. (2021) Lipschitz Stability in Time for Riemann–Liouville Fractional Differential Equations. Fractal and Fractional 5:2, pages 37.
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Ravi Agarwal, Snezhana Hristova & Donal O’Regan. (2021) Lyapunov Functions and Lipschitz Stability for Riemann–Liouville Non-Instantaneous Impulsive Fractional Differential Equations. Symmetry 13:4, pages 730.
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Gaurav Mittal & Ankik Kumar Giri. (2021) Iteratively regularized Landweber iteration method: Convergence analysis via Hölder stability. Applied Mathematics and Computation 392, pages 125744.
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Peijun Li, Jian Zhai & Yue Zhao. (2021) Lipschitz stability for an inverse source scattering problem at a fixed frequency * . Inverse Problems 37:2, pages 025003.
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Houcine Meftahi. (2021) Uniqueness, Lipschitz Stability, and Reconstruction for the Inverse Optical Tomography Problem. SIAM Journal on Mathematical Analysis 53:6, pages 6326-6354.
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Elena Beretta, Elisa Francini & Sergio Vessella. (2021) Lipschitz Stable Determination of Polygonal Conductivity Inclusions in a Two-Dimensional Layered Medium from the Dirichlet-to-Neumann Map. SIAM Journal on Mathematical Analysis 53:4, pages 4303-4327.
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Giovanni S. Alberti & Matteo Santacesaria. (2021) Infinite dimensional compressed sensing from anisotropic measurements and applications to inverse problems in PDE. Applied and Computational Harmonic Analysis 50, pages 105-146.
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Bastian Harrach. (2020) Uniqueness, stability and global convergence for a discrete inverse elliptic Robin transmission problem. Numerische Mathematik 147:1, pages 29-70.
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Mai Thi Kim Dung & Dang Anh Tuan. (2020) Calderón’s Problem for Some Classes of Conductivities in Circularly Symmetric Domains. Acta Mathematica Vietnamica 45:4, pages 849-863.
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J L Mueller & S Siltanen. (2020) The D-bar method for electrical impedance tomography—demystified. Inverse Problems 36:9, pages 093001.
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George Lytle, Peter Perry & Samuli Siltanen. (2020) Nachman’s reconstruction method for the Calderón problem with discontinuous conductivities. Inverse Problems 36:3, pages 035018.
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Bastian Harrach & Yi-Hsuan Lin. (2020) Monotonicity-Based Inversion of the Fractional Schrödinger Equation II. General Potentials and Stability. SIAM Journal on Mathematical Analysis 52:1, pages 402-436.
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Bastian Harrach. (2019) Uniqueness and Lipschitz stability in electrical impedance tomography with finitely many electrodes. Inverse Problems 35:2, pages 024005.
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Bastian Harrach & Houcine Meftahi. (2019) Global Uniqueness and Lipschitz-Stability for the Inverse Robin Transmission Problem. SIAM Journal on Applied Mathematics 79:2, pages 525-550.
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GIOVANNI S. ALBERTI & MATTEO SANTACESARIA. (2019) CALDERÓN’S INVERSE PROBLEM WITH A FINITE NUMBER OF MEASUREMENTS. Forum of Mathematics, Sigma 7.
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Cătălin I. Cârstea, Naofumi Honda & Gen Nakamura. (2018) Uniqueness in the Inverse Boundary Value Problem for Piecewise Homogeneous Anisotropic Elasticity. SIAM Journal on Mathematical Analysis 50:3, pages 3291-3302.
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Giovanni Alessandrini, Maarten V de Hoop & Romina Gaburro. (2017) Uniqueness for the electrostatic inverse boundary value problem with piecewise constant anisotropic conductivities. Inverse Problems 33:12, pages 125013.
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Giovanni Alessandrini, Maarten V. de Hoop, Romina Gaburro & Eva Sincich. (2017) Lipschitz stability for the electrostatic inverse boundary value problem with piecewise linear conductivities. Journal de Mathématiques Pures et Appliquées 107:5, pages 638-664.
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Kiril Datchev & Maarten V de Hoop. (2016) Iterative reconstruction of the wave speed for the wave equation with bounded frequency boundary data. Inverse Problems 32:2, pages 025008.
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Elena Beretta, Maarten V. de Hoop, Florian Faucher & Otmar Scherzer. (2016) Inverse Boundary Value Problem For The Helmholtz Equation: Quantitative Conditional Lipschitz Stability Estimates. SIAM Journal on Mathematical Analysis 48:6, pages 3962-3983.
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Romina Gaburro & Eva Sincich. (2015) Lipschitz stability for the inverse conductivity problem for a conformal class of anisotropic conductivities. Inverse Problems 31:1, pages 015008.
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Maarten V. de Hoop, Lingyun Qiu & Otmar Scherzer. (2014) An analysis of a multi-level projected steepest descent iteration for nonlinear inverse problems in Banach spaces subject to stability constraints. Numerische Mathematik 129:1, pages 127-148.
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Andy Adler, Romina Gaburro & William Lionheart. 2015. Handbook of Mathematical Methods in Imaging. Handbook of Mathematical Methods in Imaging 701 762 .
Elena Beretta, Elisa Francini & Sergio Vessella. (2014) Uniqueness and Lipschitz stability for the identification of Lamé parameters from boundary measurements. Inverse Problems & Imaging 8:3, pages 611-644.
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W. Naetar & O. Scherzer. (2014) Quantitative Photoacoustic Tomography with Piecewise Constant Material Parameters. SIAM Journal on Imaging Sciences 7:3, pages 1755-1774.
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Andy Adler, Romina Gaburro & William Lionheart. 2020. Handbook of Mathematical Methods in Imaging. Handbook of Mathematical Methods in Imaging 1 57 .
Matteo Santacesaria. (2012) New global stability estimates for the Calderón problem in two dimensions. Journal of the Institute of Mathematics of Jussieu 12:3, pages 553-569.
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Elena Beretta, Maarten V. de Hoop & Lingyun Qiu. (2013) Lipschitz Stability of an Inverse Boundary Value Problem for a Schrödinger-Type Equation. SIAM Journal on Mathematical Analysis 45:2, pages 679-699.
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Habib Ammari, Thomas Boulier & Josselin Garnier. (2013) Modeling Active Electrolocation in Weakly Electric Fish. SIAM Journal on Imaging Sciences 6:1, pages 285-321.
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Maarten V de Hoop, Lingyun Qiu & Otmar Scherzer. (2012) Local analysis of inverse problems: Hölder stability and iterative reconstruction. Inverse Problems 28:4, pages 045001.
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Bastian Harrach. (2012) Simultaneous determination of the diffusion and absorption coefficient from boundary data. Inverse Problems & Imaging 6:4, pages 663-679.
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