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Infinite-dimensional inverse problems with finite measurements (Q2069717)

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English	Infinite-dimensional inverse problems with finite measurements	scientific article

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scholarly article

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Infinite-dimensional inverse problems with finite measurements (English)

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Giovanni S. Alberti

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Matteo Santacesaria

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Archive for Rational Mechanics and Analysis

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publication date

21 January 2022

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full work available at URL

https://arxiv.org/abs/1906.10028

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zbMATH Keywords

abstract inverse problems

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convergent reconstruction algorithm

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Landweber iteration

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MaRDI profile type

MaRDI publication profile

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A generalized sampling theorem for stable reconstructions in arbitrary bases

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Generalized sampling and infinite-dimensional compressed sensing

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Beyond Consistent Reconstructions: Optimality and Sharp Bounds for Generalized Sampling, and Application to the Uniform Resampling Problem

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BREAKING THE COHERENCE BARRIER: A NEW THEORY FOR COMPRESSED SENSING

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Solving ill-posed inverse problems using iterative deep neural networks

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CALDERÓN’S INVERSE PROBLEM WITH A FINITE NUMBER OF MEASUREMENTS

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

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Stable determination of conductivity by boundary measurements

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Determining Linear Cracks by Boundary Measurements: Lipschitz Stability

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Uniqueness for the electrostatic inverse boundary value problem with piecewise constant anisotropic conductivities

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Lipschitz stability for the electrostatic inverse boundary value problem with piecewise linear conductivities

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Lipschitz stability for a piecewise linear Schrödinger potential from local Cauchy data

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Determining a sound-soft polyhedral scatterer by a single far-field measurement

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Lipschitz stability for the inverse conductivity problem

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Theory of Reproducing Kernels

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Solving inverse problems using data-driven models

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Calderón's inverse conductivity problem in the plane

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Lipschitz stability for a stationary 2D inverse problem with unknown polygonal boundary

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Hybrid inverse problems and internal functionals

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Characterization of Sobolev spaces on the sphere

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Lipschitz stability for a hyperbolic inverse problem by finite local boundary data

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

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Global Lipschitz stability estimates for polygonal conductivity inclusions from boundary measurements

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Lipschitz continuous dependence of piecewise constant Lamé coefficients from boundary data: the case of non-flat interfaces

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Uniqueness and Lipschitz stability for the identification of Lamé parameters from boundary measurements

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Stable Determination of Polyhedral Interfaces from Boundary Data for the Helmholtz Equation

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Lipschitz Stability of an Inverse Boundary Value Problem for a Schrödinger-Type Equation

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On corners scattering stably and stable shape determination by a single far-field pattern

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Electrical impedance tomography

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A remark on Lipschitz stability for inverse problems

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A characterization of Sobolev spaces on the sphere and an extension of Stolarsky's invariance principle to arbitrary smoothness

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Stability of the Calderón problem for less regular conductivities

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GLOBAL UNIQUENESS FOR THE CALDERÓN PROBLEM WITH LIPSCHITZ CONDUCTIVITIES

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The Calderón problem for the fractional Schrödinger equation with drift

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Electrical Impedance Tomography

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Stability for the inverse potential problem by finite measurements on the boundary

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Uniqueness in an inverse scattering problem within non-trapping polygonal obstacles with at most two incoming waves

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Stability of Calderón's inverse conductivity problem in the plane for discontinuous conductivities

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Inverse acoustic and electromagnetic scattering theory

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Besov priors for Bayesian inverse problems

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Reproducing kernel Hilbert spaces on manifolds: Sobolev and diffusion spaces

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Lipschitz stability for the inverse conductivity problem for a conformal class of anisotropic conductivities

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Elliptic partial differential equations of second order

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Necessary and sufficient conditions for linear convergence of ℓ1-regularization

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The residual method for regularizing ill-posed problems

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Uniqueness in Calderón's problem for conductivities with unbounded gradient

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

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Uniqueness, stability and global convergence for a discrete inverse elliptic Robin transmission problem

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Global Uniqueness and Lipschitz-Stability for the Inverse Robin Transmission Problem

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Introduction to Inverse Problems for Differential Equations

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Local analysis of inverse problems: Hölder stability and iterative reconstruction

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An analysis of a multi-level projected steepest descent iteration for nonlinear inverse problems in Banach spaces subject to stability constraints

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Shape Identification in Inverse Medium Scattering Problems with a Single Far-Field Pattern

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Iterative regularization methods for nonlinear ill-posed problems

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Analysis of regularized inversion of data corrupted by white Gaussian noise

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An introduction to the mathematical theory of inverse problems

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Mathematics of Photoacoustic and Thermoacoustic Tomography

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Stabilizing inverse problems by internal data

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Discretization-invariant Bayesian inversion and Besov space priors

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Newton regularizations for impedance tomography: convergence by local injectivity

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Sampling analysis in the complex reproducing kernel Hilbert space

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Stable determination of sound-hard polyhedral scatterers by a minimal number of scattering measurements

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Exponential instability in an inverse problem for the Schrödinger equation

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Iteratively regularized Landweber iteration method: convergence analysis via Hölder stability

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Linear and Nonlinear Inverse Problems with Practical Applications

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Global uniqueness for a two-dimensional inverse boundary value problem

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A remark on a paper by Alessandrini and Vessella

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Lipschitz stability for the finite dimensional fractional Calderón problem with finite Cauchy data

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Nonconvergence results for the application of least-squares estimation to ill-posed problems

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Stability of the inverse problem in potential scattering at fixed energy

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Travel time tomography

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A global uniqueness theorem for an inverse boundary value problem

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Electrical impedance tomography and Calderón's problem

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Error bounds for approximations with deep ReLU networks

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Identifiers

zbMATH Open document ID

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Mathematics Subject Classification ID

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zbMATH DE Number

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10.1007/S00205-021-01718-4

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Sitelinks

Mathematics(1 entry)

mardi Publication:2069717

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