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We consider abstract inverse problems between infinite-dimensional Banach spaces.
A stability theorem for solutions of abstract differential equations, and its application to the study of the local behavior of solutions of elliptic equations
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Existence et approximation des solutions des équations aux dérivées partielles et des équations de convolution
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Collectively compact operator approximation theory and applications to integral equations
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On an inverse boundary value problem
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High order inverse function theorems
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A global uniqueness theorem for an inverse boundary value problem
J. Sylvester and G. Uhlmann · 1987
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Stable determination of conductivity by boundary measurements
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On the uniqueness in the inverse conductivity problem with one measurement
A. Friedman and V. Isakov · 1989
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Some inverse mapping theorems
H. Frankowska · 1990
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On the inverse conductivity problem with one measurement
V. Isakov and J. Powell · 1990
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A primer of nonlinear analysis
A. Ambrosetti and G. Prodi · 1993
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The inverse conductivity problem with one measurement: uniqueness for convex polyhedra
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A proof of the trace theorem of Sobolev spaces on Lipschitz domains
Z. Ding · 1996
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A periodic Faddeev-type solution operator
P. Hähner · 1996
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Global uniqueness for a two-dimensional inverse boundary value problem
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Electrical impedance tomography
M. Cheney, D. Isaacson, and J. C. Newell · 1999
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Completeness and total boundedness of the hausdorff metric
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M. S. Vogelius and D. Volkov · 2000
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Exponential instability in an inverse problem for the Schrödinger equation
N. Mandache · 2001
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Electrical impedance tomography
L. Borcea · 2002
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A direct impedance tomography algorithm for locating small inhomogeneities
M. Brühl, M. Hanke, and M. S. Vogelius · 2003
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Uniqueness in an inverse scattering problem within non-trapping polygonal obstacles with at most two incoming waves
J. Cheng and M. Yamamoto · 2003
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Reconstruction of small inhomogeneities from boundary measurements
H. Ammari and H. Kang · 2004
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Analytic methods for inverse scattering theory
L. Päivärinta · 2004
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Determining a sound-soft polyhedral scatterer by a single far-field measurement
G. Alessandrini and L. Rondi · 2005
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Lipschitz stability for the inverse conductivity problem
G. Alessandrini and S. Vessella · 2005
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Calderón’s inverse conductivity problem in the plane
K. Astala and L. Päivärinta · 2006
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Lipschitz stability for a stationary 2d inverse problem with unknown polygonal boundary
V. Bacchelli and S. Vessella · 2006
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A remark on a paper by Alessandrini and Vessella
L. Rondi · 2006
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Polarization and moment tensors
H. Ammari and H. Kang · 2007
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Nonlinear dimensionality reduction
J. A. Lee and M. Verleysen · 2007
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Determination of a linear crack in an elastic body from boundary measurements—Lipschitz stability
E. Beretta, E. Francini, and S. Vessella · 2008
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Recovering a potential from Cauchy data in the two-dimensional case
A. L. Bukhgeim · 2008
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Iterative regularization methods for nonlinear ill-posed problems
B. Kaltenbacher, A. Neubauer, and O. Scherzer · 2008
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Riemannian manifold learning
T. Lin and H. Zha · 2008
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Lipschitz stability for the electrostatic inverse boundary value problem with piecewise linear conductivities
G. Alessandrini, M. V. de Hoop, R. Gaburro, and E. Sincich · 2017
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Uniqueness and Lipschitz stability of an inverse boundary value problem for time-harmonic elastic waves
E. Beretta, M. V. de Hoop, E. Francini, S. Vessella, and J. Zhai · 2017
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Differentiability of the Dirichlet to Neumann map under movements of polygonal inclusions with an application to shape optimization
E. Beretta, E. Francini, and S. Vessella · 2017
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Deep convolutional neural network for inverse problems in imaging
K. H. Jin, M. T. McCann, E. Froustey, and M. Unser · 2017
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Stable determination of sound-hard polyhedral scatterers by a minimal number of scattering measurements
H. Liu, M. Petrini, L. Rondi, and J. Xiao · 2017
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R. G. Baraniuk and M. B. Wakin · 2009
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Manifold models for signals and images
G. Peyré · 2009
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Linearizing non-linear inverse problems and an application to inverse backscattering
P. Stefanov and G. Uhlmann · 2009
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Electrical impedance tomography and Calderón’s problem
G. Uhlmann · 2009
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Stability of Calderón’s inverse conductivity problem in the plane for discontinuous conductivities
A. Clop, D. Faraco, and A. Ruiz · 2010
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A global stability estimate for the Gel’fand–Calderón inverse problem in two dimensions
R. G. Novikov and M. Santacesaria · 2010
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Low dimensional manifold model for image processing
S. Osher, Z. Shi, and W. Zhu · 2017
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Learned primal-dual reconstruction
J. Adler and O. Öktem · 2018
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Lectures on elliptic methods for hybrid inverse problems
G. S. Alberti and Y. Capdeboscq · 2018
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Lipschitz stability for a piecewise linear Schrödinger potential from local Cauchy data
G. Alessandrini, M. V. de Hoop, R. Gaburro, and E. Sincich · 2018
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Using deep neural networks for inverse problems in imaging: Beyond analytical methods
A. Lucas, M. Iliadis, R. Molina, and A. K. Katsaggelos · 2018
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Calderón’s inverse problem with a finite number of measurements
G. S. Alberti and M. Santacesaria · 2019
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Solving inverse problems using data-driven models
S. Arridge, P. Maass, O. Öktem, and C.-B. Schönlieb · 2019
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Fitting a manifold of large reach to noisy data
C. Fefferman, S. Ivanov, M. Lassas, and H. Narayanan · 2019
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Uniqueness and Lipschitz stability in electrical impedance tomography with finitely many electrodes
B. Harrach · 2019
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Lipschitz stability for the finite dimensional fractional Calderón problem with finite Cauchy data
A. Rüland and E. Sincich · 2019
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Calderón’s inverse problem with a finite number of measurements II: independent data
G. S. Alberti and M. Santacesaria · 2020
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Global Lipschitz stability estimates for polygonal conductivity inclusions from boundary measurements
E. Beretta and E. Francini · 2020
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Recovering piecewise constant refractive indices by a single far-field pattern
E. Blåsten and H. Liu · 2020
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Stable determination of polygonal inclusions in calderón’s problem by a single partial boundary measurement
H. Liu and C.-H. Tsou · 2020
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On Runge approximation and Lipschitz stability for a finite-dimensional Schrödinger inverse problem
A. Rüland and E. Sincich · 2020
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Infinite dimensional compressed sensing from anisotropic measurements and applications to inverse problems in PDE
G. S. Alberti and M. Santacesaria · 2021
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Lipschitz stable determination of polygonal conductivity inclusions in a two-dimensional layered medium from the Dirichlet-to-Neumann map
E. Beretta, E. Francini, and S. Vessella · 2021
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On corners scattering stably and stable shape determination by a single far-field pattern
E. L. K. Blå sten and H. Liu · 2021
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Deep neural networks for inverse problems with pseudodifferential operators: an application to limited-angle tomography
T. A. Bubba, M. Galinier, M. Lassas, M. Prato, L. Ratti, and S. Siltanen · 2021
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Deep learning architectures for nonlinear operator functions and nonlinear inverse problems
M. V. de Hoop, M. Lassas, and C. A. Wong · 2021
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Lipschitz stability estimate and reconstruction of lamé parameters in linear elasticity
S. Eberle, B. Harrach, H. Meftahi, and T. Rezgui · 2021
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Uniqueness, stability and global convergence for a discrete inverse elliptic Robin transmission problem
B. Harrach · 2021
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Deep learning-based solvability of underdetermined inverse problems in medical imaging
C. M. Hyun, S. H. Baek, M. Lee, S. M. Lee, and J. K. Seo · 2021
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On instability mechanisms for inverse problems
H. Koch, A. Rüland, and M. Salo · 2021
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Infinite-Dimensional Inverse Problems with Finite Measurements
G. S. Alberti and M. Santacesaria · 2022
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A. Aspri, E. Beretta, E. Francini, and S. Vessella · 2022
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