A Bayesian approach for consistent reconstruction of inclusions
From MaRDI portal
Publication:6149891
DOI10.1088/1361-6420/ad2531arXiv2308.13673OpenAlexW4391465074WikidataQ128699125 ScholiaQ128699125MaRDI QIDQ6149891
Aksel Kaastrup Rasmussen, Babak Maboudi Afkham, Kim Knudsen, Tanja Tarvainen
Publication date: 5 March 2024
Published in: Inverse Problems (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2308.13673
Asymptotic properties of nonparametric inference (62G20) Bayesian inference (62F15) Monte Carlo methods (65C05) Inverse problems for PDEs (35R30) Numerical solution to inverse problems in abstract spaces (65J22)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- An Explicit Link between Gaussian Fields and Gaussian Markov Random Fields: The Stochastic Partial Differential Equation Approach
- The Bayesian formulation of EIT: analysis and algorithms
- A Bayesian level set method for geometric inverse problems
- Spectral gaps for a Metropolis-Hastings algorithm in infinite dimensions
- Whittle-Matérn priors for Bayesian statistical inversion with applications in electrical impedance tomography
- Applications of CGO solutions to coupled-physics inverse problems
- On statistical Calderón problems
- Bernstein-von Mises theorems for statistical inverse problems. I: Schrödinger equation
- Adaptive Bayesian estimation using a Gaussian random field with inverse gamma bandwidth
- Stability of Calderón's inverse conductivity problem in the plane for discontinuous conductivities
- Partial differential equations. I: Basic theory
- Granulometric smoothing
- Hierarchical Bayesian level set inversion
- Statistical and computational inverse problems.
- A Bayesian level set method for an inverse medium scattering problem in acoustics
- A Bayesian level set method for the shape reconstruction of inverse scattering problems in elasticity
- Some stability inequalities for hybrid inverse problems
- The interior inverse scattering problem for a two-layered cavity using the Bayesian method
- Hyperparameter estimation in Bayesian MAP estimation: parameterizations and consistency
- Discretization-invariant Bayesian inversion and Besov space priors
- Dimension-independent likelihood-informed MCMC
- Posterior contraction rates for the Bayesian approach to linear ill-posed inverse problems
- MAP estimators for piecewise continuous inversion
- Inverse problems: A Bayesian perspective
- Mathematics of Hybrid Imaging: A Brief Review
- An Analysis of Infinite Dimensional Bayesian Inverse Shape Acoustic Scattering and Its Numerical Approximation
- Quantitative thermo-acoustics and related problems
- A level-set approach for inverse problems involving obstacles Fadil SANTOSA
- Reconstructing absorption and scattering distributions in quantitative photoacoustic tomography
- Mathematical Foundations of Infinite-Dimensional Statistical Models
- Level Sets and Extrema of Random Processes and Fields
- Besov Spaces on Domains in ℝ d
- Parameterizations for ensemble Kalman inversion
- THE SOBOLEV NORM OF CHARACTERISTIC FUNCTIONS WITH APPLICATIONS TO THE CALDERON INVERSE PROBLEM
- Convergence Rates for Penalized Least Squares Estimators in PDE Constrained Regression Problems
- Bayesian approach to inverse scattering with topological priors
- Consistent Inversion of Noisy <scp>Non‐Abelian X‐Ray</scp> Transforms
- Bayesian approach to inverse time-harmonic acoustic scattering with phaseless far-field data
- Consistency of Bayesian inference with Gaussian process priors in an elliptic inverse problem
- Foundations of Modern Probability
- An upper bound on the volume of the symmetric difference of a body and a congruent copy
- Analysis of Boundary Effects on PDE-Based Sampling of Whittle--Matérn Random Fields
- Posterior consistency for Bayesian inverse problems through stability and regression results
- Uniqueness of reconstruction and an inversion procedure for thermoacoustic and photoacoustic tomography with variable sound speed
- A series solution and a fast algorithm for the inversion of the spherical mean Radon transform
- Stable Determination of an Inclusion by Boundary Measurements
- Fundamentals of Nonparametric Bayesian Inference
- MCMC methods for functions: modifying old algorithms to make them faster
- Uncertainty Quantification of Inclusion Boundaries in the Context of X-Ray Tomography
- Bayesian non-linear statistical inverse problems
- A statistical framework for domain shape estimation in Stokes flows
This page was built for publication: A Bayesian approach for consistent reconstruction of inclusions