Infinite-dimensional inverse problems with finite measurements
From MaRDI portal
Publication:2069717
DOI10.1007/s00205-021-01718-4zbMath1481.35390arXiv1906.10028OpenAlexW3213855703MaRDI QIDQ2069717
Giovanni S. Alberti, Matteo Santacesaria
Publication date: 21 January 2022
Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1906.10028
Boundary value problems for second-order elliptic equations (35J25) Scattering theory for PDEs (35P25) Inverse problems for PDEs (35R30) Nonlinear ill-posed problems (47J06) Sampling theory in information and communication theory (94A20) Inverse problems (including inverse scattering) in optics and electromagnetic theory (78A46)
Related Items
Lipschitz Stable Determination of Polyhedral Conductivity Inclusions from Local Boundary Measurements ⋮ Nonstationary iterated Tikhonov regularization: convergence analysis via Hölder stability ⋮ A Bernstein–von-Mises theorem for the Calderón problem with piecewise constant conductivities ⋮ Inverse problems on low-dimensional manifolds ⋮ Calderón's inverse problem with a finite number of measurements II: independent data ⋮ Inverse medium scattering problems with Kalman filter techniques ⋮ On (global) unique continuation properties of the fractional discrete Laplacian ⋮ Stability Estimates for the Inverse Fractional Conductivity Problem ⋮ Computational aspects of electromagnetic tomography ⋮ CALDERÓN’S INVERSE PROBLEM WITH A FINITE NUMBER OF MEASUREMENTS ⋮ Local recovery of a piecewise constant anisotropic conductivity in EIT on domains with exposed corners ⋮ Deep neural networks can stably solve high-dimensional, noisy, non-linear inverse problems
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A characterization of Sobolev spaces on the sphere and an extension of Stolarsky's invariance principle to arbitrary smoothness
- The residual method for regularizing ill-posed problems
- Besov priors for Bayesian inverse problems
- Uniqueness and Lipschitz stability for the identification of Lamé parameters from boundary measurements
- Uniqueness in Calderón's problem for conductivities with unbounded gradient
- Generalized sampling and infinite-dimensional compressed sensing
- Lipschitz stability for the electrostatic inverse boundary value problem with piecewise linear conductivities
- A global uniqueness theorem for an inverse boundary value problem
- A generalized sampling theorem for stable reconstructions in arbitrary bases
- Stability of the Calderón problem for less regular conductivities
- Stable determination of sound-hard polyhedral scatterers by a minimal number of scattering measurements
- Iterative regularization methods for nonlinear ill-posed problems
- Stability of Calderón's inverse conductivity problem in the plane for discontinuous conductivities
- Nonconvergence results for the application of least-squares estimation to ill-posed problems
- Elliptic partial differential equations of second order
- Stability of the inverse problem in potential scattering at fixed energy
- Global uniqueness for a two-dimensional inverse boundary value problem
- Uniqueness, stability and global convergence for a discrete inverse elliptic Robin transmission problem
- The Calderón problem for the fractional Schrödinger equation with drift
- Characterization of Sobolev spaces on the sphere
- Discretization-invariant Bayesian inversion and Besov space priors
- Error bounds for approximations with deep ReLU networks
- Travel time tomography
- Lipschitz stability for the finite dimensional fractional Calderón problem with finite Cauchy data
- A remark on Lipschitz stability for inverse problems
- A remark on a paper by Alessandrini and Vessella
- Calderón's inverse conductivity problem in the plane
- Statistical inverse problems: discretization, model reduction and inverse crimes
- An analysis of a multi-level projected steepest descent iteration for nonlinear inverse problems in Banach spaces subject to stability constraints
- Lipschitz stability for the inverse conductivity problem
- Infinite dimensional compressed sensing from anisotropic measurements and applications to inverse problems in PDE
- Iteratively regularized Landweber iteration method: convergence analysis via Hölder stability
- Stability for the inverse potential problem by finite measurements on the boundary
- Exponential instability in an inverse problem for the Schrödinger equation
- Mathematics of Photoacoustic and Thermoacoustic Tomography
- Inverse Boundary Value Problem For The Helmholtz Equation: Quantitative Conditional Lipschitz Stability Estimates
- Lipschitz Stability of an Inverse Boundary Value Problem for a Schrödinger-Type Equation
- Beyond Consistent Reconstructions: Optimality and Sharp Bounds for Generalized Sampling, and Application to the Uniform Resampling Problem
- Local analysis of inverse problems: Hölder stability and iterative reconstruction
- Lipschitz continuous dependence of piecewise constant Lamé coefficients from boundary data: the case of non-flat interfaces
- BREAKING THE COHERENCE BARRIER: A NEW THEORY FOR COMPRESSED SENSING
- Uniqueness and Lipschitz stability of an inverse boundary value problem for time-harmonic elastic waves
- Multi-source quantitative photoacoustic tomography in a diffusive regime
- Necessary and sufficient conditions for linear convergence of ℓ1-regularization
- Unique determination of periodic polyhedral structures by scattered electromagnetic fields
- Lipschitz Stability for the Electrical Impedance Tomography Problem: The Complex Case
- Stabilizing inverse problems by internal data
- Lipschitz stability for a stationary 2D inverse problem with unknown polygonal boundary
- Lipschitz stability for a hyperbolic inverse problem by finite local boundary data
- Stable Determination of Polyhedral Interfaces from Boundary Data for the Helmholtz Equation
- Shape Identification in Inverse Medium Scattering Problems with a Single Far-Field Pattern
- GLOBAL UNIQUENESS FOR THE CALDERÓN PROBLEM WITH LIPSCHITZ CONDUCTIVITIES
- Newton regularizations for impedance tomography: convergence by local injectivity
- Inverse diffusion theory of photoacoustics
- Determination of a Linear Crack in an Elastic Body from Boundary Measurements—Lipschitz Stability
- Electrical impedance tomography and Calderón's problem
- Electrical Impedance Tomography
- Uniqueness in an inverse scattering problem within non-trapping polygonal obstacles with at most two incoming waves
- Sampling analysis in the complex reproducing kernel Hilbert space
- Solving ill-posed inverse problems using iterative deep neural networks
- Uniqueness for the electrostatic inverse boundary value problem with piecewise constant anisotropic conductivities
- Uniqueness and Lipschitz stability in electrical impedance tomography with finitely many electrodes
- Global Uniqueness and Lipschitz-Stability for the Inverse Robin Transmission Problem
- Linear and Nonlinear Inverse Problems with Practical Applications
- Determining a sound-soft polyhedral scatterer by a single far-field measurement
- Lipschitz stability for a piecewise linear Schrödinger potential from local Cauchy data
- Stable determination of conductivity by boundary measurements
- Electrical impedance tomography
- Determining Linear Cracks by Boundary Measurements: Lipschitz Stability
- Introduction to Inverse Problems for Differential Equations
- Reproducing kernel Hilbert spaces on manifolds: Sobolev and diffusion spaces
- Global Lipschitz stability estimates for polygonal conductivity inclusions from boundary measurements
- Recovering piecewise constant refractive indices by a single far-field pattern
- On corners scattering stably and stable shape determination by a single far-field pattern
- Lipschitz stability for the inverse conductivity problem for a conformal class of anisotropic conductivities
- Solving inverse problems using data-driven models
- CALDERÓN’S INVERSE PROBLEM WITH A FINITE NUMBER OF MEASUREMENTS
- Hybrid inverse problems and internal functionals
- Inverse transport theory of photoacoustics
- Analysis of regularized inversion of data corrupted by white Gaussian noise
- Theory of Reproducing Kernels
- Inverse acoustic and electromagnetic scattering theory
- Inverse problems for partial differential equations
- An introduction to the mathematical theory of inverse problems