Inverse Problems

Article	Citations
Multipoint formulas in inverse problems and their numerical implementation	38
A Bayesian approach for CT reconstruction with defect detection for subsea pipelines	38
Uniqueness of an inverse cavity scattering problem for the time-harmonic biharmonic wave equation	29
On direct and inverse obstacle scattering problems for biharmonic waves	27
Optimal-order convergence of Nesterov acceleration for linear ill-posed problems*	25
Flow recovery from distal pressure in linearized hemodynamics: an optimal control approach	23
Structure analysis of direct sampling method in 3D electromagnetic inverse problem: near- and far-field configuration	23
An analysis of constraint-relaxation in PDE-based inverse problems	21
Stochastic mirror descent method for linear ill-posed problems in Banach spaces	18
On inverse problems for mean field games with common noise via Carleman estimate*	18
A Bernstein–von-Mises theorem for the Calderón problem with piecewise constant conductivities	18
Imaging conductivity from current density magnitude using neural networks*	18
Recovering a function from its integrals over conical surfaces through relations with the Radon transform	17
A probabilistic approach to tomography and adjoint state methods, with an application to full waveform inversion in medical ultrasound	16
The reconstruction of surface vibrations from near-field acoustic pressure measurements under steady flow	15
Distributed learning with discretely observed functional data	15
Fictitious null spaces for improving the solution of injective inverse problems	15
Direct inversion of the Longitudinal ray transform for 2D residual elastic strain fields	15
Stability estimate for an inverse stochastic parabolic problem of determining unknown time-varying boundary *	15
Determination of a spatial load in a damped Kirchhoff–Love plate equation from final time measured data	14
Recovering critical parameter for nonlinear Allen–Cahn equation by fully discrete continuous data assimilation algorithms *	14
Uniqueness theorems for tomographic phase retrieval with few coded diffraction patterns	13
Stability of the isotropic conductivity reconstruction using magnetic resonance electrical impedance tomography (MREIT)	13
An inverse problem for generalized Kelvin–Voigt equation with p-Laplacian and damping term	13
Inferring dynamical models from time-series biological data using an interpretable machine learning method based on weighted expression trees	13

Stability of an inverse source problem for the damped biharmonic plate equation	13
Addendum: On stochastic Kaczmarz type methods for solving large scale systems of ill-posed equations (2022 Inverse Problems 38 025003)	13
A Kirchhoff Migration scheme for elastic obstacle identification	13
Chilled sampling for uncertainty quantification: a motivation from a meteorological inverse problem *	12
A dataset-free deep learning method for low-dose CT image reconstruction	12
Radon transform on algebraic Cormack α-curves inversion formula	12
Geometric approach for determining stationary phase points in radar imaging	12
A mathematical framework for nonlinear wavefront reconstruction in adaptive optics systems with Fourier-type wavefront sensing	11
Stochastic asymptotical regularization for linear inverse problems	11
3D refractive index reconstruction from phaseless coherent optical microscopy data using multiple scattering-based inverse solvers—a study	11
Maximum a posteriori estimators in ℓp are well-defined for diagonal Gaussian priors	11
Optimal regularized hypothesis testing in statistical inverse problems	11
Stability for a multi-frequency inverse random source problem	11
Reconstruction of the initial data from the trace of the solutions on an infinite time cylinder of damped wave equations *	11
Bayesian design of measurements for magnetorelaxometry imaging *	11
A two-stage numerical approach for the sparse initial source identification of a diffusion–advection equation *	11
Matrix recovery from nonconvex regularized least absolute deviations	11
Minimizing L 1 over L 2 norms on the gradient	10
Double-parameter regularization for solving the backward diffusion problem with parallel-in-time algorithm	10
Hyperparameter estimation using a resolution matrix for Bayesian sensing	10
On inertial iterated Tikhonov methods for solving ill-posed problems	10
Strong maximum a posteriori estimation in Banach spaces with Gaussian priors	9
Nonstationary iterated Tikhonov regularization: convergence analysis via Hölder stability	9
Robust signal recovery for ℓ 1–2 minimization via prior support information	9
Lipschitz stability of recovering the conductivity from internal current densities	9
Fast iterative reconstruction for multi-spectral CT by a Schmidt orthogonal modification algorithm (SOMA)	9
Unsupervised knowledge-transfer for learned image reconstruction*	9
Low-resolution prior equilibrium network for CT reconstruction	9
Iterative regularization in classification via hinge loss diagonal descent	9
Stable determination of coefficients in semilinear parabolic system with dynamic boundary conditions	9
Convergence analysis of the discretization of continuous-domain inverse problems	9
Bouligand–Newton type methods for non-smooth ill-posed problems	9
Solving the acousto-electric tomography by the adaptive Nesterov method of Kaczmarz type	9
Microwave time reversal for nondestructive testing of buried small damage in composite materials	9
A new nonconvex low-rank tensor approximation method with applications to hyperspectral images denoising	9
Reconstructing the image scanning microscopy dataset: an inverse problem	9
A statistical reconstruction model for absorption CT with source uncertainty *	9
Theory and fast learned solver for	8
Multi-scale CLEAN for Fourier-based hard x-ray solar imaging	8
Norms in sinogram space and stability estimates for the Radon transform	8
Direct sampling for recovering a clamped cavity from the biharmonic far-field data	8
Uniqueness and numerical method for phaseless inverse diffraction grating problem with known superposition of incident point sources	8
Reconstruction of degenerate conductivity region for parabolic equations	8
Some integral geometry problems for wave equations	8
Inverse problems of damped wave equations with Robin boundary conditions: an application to blood perfusion	8
DRIP: deep regularizers for inverse problems	8
Adaptive Tikhonov strategies for stochastic ensemble Kalman inversion	8
Reconstructing the shape and material parameters of dissipative obstacles using an impedance model	8
Singular value decomposition for longitudinal, transverse and mixed ray transforms of 2D tensor fields	8
Solving an inverse source problem by deep neural network method with convergence and error analysis	8

Shape and orientation classification of objects based on their electromagnetic signatures using convolutional neural networks	8
Analysis of the discrepancy principle for Tikhonov regularization with oversmoothing penalty term under low order source conditions	7
Remarks on the factorization and monotonicity method for inverse acoustic scatterings	7
Phase retrieval and phaseless inverse scattering with background information	7
The C∞ -isomorphism property for a class of singularly-weighted x-ray transforms	7
Object based Bayesian full-waveform inversion for shear elastography	7
On bias and its reduction via standardization in discretized electromagnetic source localization problems	7
Non-zero constraints in elliptic PDE with random boundary values and applications to hybrid inverse problems	7
Regularization graphs—a unified framework for variational regularization of inverse problems	7
GPU accelerated 3D source free adaptive wavefield reconstruction inversion for seismic imaging	7
Inverse source problem for discrete Helmholtz equation	7
ASPIRE: iterative amortized posterior inference for Bayesian inverse problems	7
On the stability of recovering two sources and initial status in a stochastic hyperbolic-parabolic system	7
In memoriam Pierre Sabatier	7
On the uniqueness of solutions for the basis pursuit in the continuum	7
Stability estimates for the expected utility in Bayesian optimal experimental design	7
Determining anomalies in a semilinear elliptic equation by a minimal number of measurements	7
Enhanced microscale hydrodynamic near-cloaking using electro-osmosis	7
Coercivity-based analysis and its application to an inverse source problem for a subdiffusion equation with time-dependent principal parts	7
Randomized block coordinate descent method for linear ill-posed problems	7
A stochastic gradient descent approach with partitioned-truncated singular value decomposition for large-scale inverse problems of magnetic modulus data	7
Nearly optimal bounds for the global geometric landscape of phase retrieval	7
Simultaneous determination of different class of parameters for a diffusion equation from a single measurement	6
Regularization of the factorization method applied to diffuse optical tomography	6
The lower bound of nonlocal gradient for non-convex and non-smooth image patches based regularization	6
Uniqueness in determining rectangular grating profiles with a single incoming wave (part II): TM polarization case	6
Robust kernel-based distribution regression	6
Bayesian inversion of log-normal eikonal equations	6
Generalized inexact Newton regularization for nonlinear ill-posed problems in Banach spaces	6
Deep neural-network based optimization for the design of a multi-element surface magnet for MRI applications	6
Convergence of level sets in fractional Laplacian regularization	6
Reduced order model approach for imaging with waves	6
Local saddles of relaxed averaged alternating reflections algorithms on phase retrieval	6
Fourier reconstruction for diffraction tomography of an object rotated into arbitrary orientations	5
Heuristic rule for inexact Newton-Landweber iteration with convex penalty terms of nonlinear: ill-posed problems	5
Convergence rates of Landweber-type methods for inverse problems in Banach spaces	5
Determining initial conditions for nonlinear hyperbolic equations with time dimensional reduction and the Carleman contraction principle	5
An optimal transport approach for 3D electrical impedance tomography	5
Stability estimates for an inverse boundary value problem for biharmonic operators with first order perturbation from partial data	5
Assessing the potential of using a virtual Veselago lens in quantitative microwave imaging	5
Recovery of a coefficient in a diffusion equation from large time data*	5
A direct sampling-based deep learning approach for inverse medium scattering problems	5
Theoretical and numerical studies of inverse source problem for the linear parabolic equation with sparse boundary measurements	5
Semi-discrete Tikhonov regularization in RKHS with large randomly distributed noise	5
Increasing stability in the linearized inverse Schrödinger potential problem with power type nonlinearities*	5
Local recovery of a piecewise constant anisotropic conductivity in EIT on domains with exposed corners	5
Convergence analysis of an alternating direction method of multipliers for the identification of nonsmooth diffusion parameters with total variation	5
On uniqueness and stable estimation of multiple parameters in the Cahn–Hilliard equation	5
Reduced-order autodifferentiable ensemble Kalman filters	5
The domain derivative in inverse obstacle scattering with nonlinear impedance boundary condition	5
Inverse problem for a nonlocal diffuse optical tomography equation	5
Analysis of the monotonicity method for an anisotropic scatterer with a conductive boundary	5
Kalman-based estimation of loading conditions from ultrasonic guided wave measurements	5
Stability estimate for the broken non-abelian x-ray transform in Minkowski space	5
Carleman contraction mapping for a 1D inverse scattering problem with experimental time-dependent data	5
MiPhDUO: microwave imaging via physics-informed deep unrolled optimization	5
Fourier method for inverse source problem using correlation of passive measurements*	5
Permeability estimation of a porous structure in cancer treatment based on sampled velocity measurement*	5
Bayesian interface technique-based inverse estimation of closure coefficients of standard	5
The inverse Rytov series for diffuse optical tomography	5
Crack identification in a multi-layer inhomogeneous domain using the Reciprocity Gap-Linear Sampling Method	5
The monotonicity method for inclusion detection and the time harmonic elastic wave equation	5
The MLE is a reliable source: sharp performance guarantees for localization problems	5
Adaptive anisotropic Bayesian meshing for inverse problems	5
Estimation of off-the grid sparse spikes with over-parametrized projected gradient descent: theory and application	5
Vertical autofocus for the phase screen in a turbulent ionosphere	5
Convergence study and regularizing property of a modified Robin–Robin method for the Cauchy problem in linear elasticity	5
Multiscale hierarchical decomposition methods for ill-posed problems	5
On Bayesian data assimilation for PDEs with ill-posed forward problems	5
Nonlocal low-rank regularized two-phase approach for mixed noise removal	4
Determining a parabolic system by boundary observation of its non-negative solutions with biological applications	4
On a nonlinear model in domains with cavities arising from cardiac electrophysiology	4
One-dimensional coefficient inverse problems by transformation operators	4
Wirtinger gradient descent methods for low-dose Poisson phase retrieval	4
Inverse problem of reconstruction of degenerate diffusion coefficient in a parabolic equation	4
Error estimates for Golub–Kahan bidiagonalization with Tikhonov regularization for ill–posed operator equations	4
Bayesian inversion with α-stable priors	4
A fast image reconstruction method for planar objects CT inspired by differentiation property of Fourier transform (DPFT)	4
Discrete nonlinear Fourier transforms and their inverses	4
Analysis of the inverse Born series: an approach through geometric function theory	4

Projection methods for high numerical aperture phase retrieval	4
Some direct and inverse source problems in nonlinear evolutionary PDEs with Volterra operators	4
Uniqueness in determining rectangular grating profiles with a single incoming wave (Part I): TE polarization case	4
Determining sources in the bioluminescence tomography problem	4
A variational non-linear constrained model for the inversion of FDEM data*	4
Diffraction tomography for incident Herglotz waves	4
Error bounds for extended source inversion applied to an acoustic transmission inverse problem	4
Corrigendum: Solution of an acoustic transmission inverse problem by extended inversion (2022 Inverse Problems 38 115003)	4
Lipschitz stability of an inverse conductivity problem with two Cauchy data pairs	4
PatchNR: learning from very few images by patch normalizing flow regularization	4
Joint Gaussian dictionary learning and tomographic reconstruction	4
Electric impedance tomography problem for surfaces with internal holes *	4
A probabilistic framework for uncertainty quantification in positron emission particle tracking	4
Variational regularization theory based on image space approximation rates	4
Color image restoration based on saturation-value total variation plus L1 fidelity*	4
On a numerical construction of doubly stochastic matrices with prescribed eigenvalues	4
Optimal indirect estimation for linear inverse problems with discretely sampled functional data	4
Consistency of Bayesian inference with Gaussian process priors for a parabolic inverse problem	4
Uncertainty quantification for goal-oriented inverse problems via variational encoder-decoder networks	4
The Radon transform with finitely many angles *	4
Tractable optimal experimental design using transport maps*	4
A mixed finite element scheme for three-dimensional Maxwell’s transmission eigenvalue problems	4
Corrigendum: On uniqueness of an inverse problem in electromagnetic obstacle scattering for an impedance cylinder (2012 Inverse Problems 28 055012)	4
Sound speed uncertainty in acousto-electric tomography	4