Inverse Problems

Article	Citations
A Bernstein–von-Mises theorem for the Calderón problem with piecewise constant conductivities	50
An analysis of constraint-relaxation in PDE-based inverse problems	44
A Bayesian approach for CT reconstruction with defect detection for subsea pipelines	35
Flow recovery from distal pressure in linearized hemodynamics: an optimal control approach	27
Stochastic mirror descent method for linear ill-posed problems in Banach spaces	27
Recovering a function from its integrals over conical surfaces through relations with the Radon transform	24
Multipoint formulas in inverse problems and their numerical implementation	23
On a quantitative partial imaging problem in vector tomography	22
Imaging conductivity from current density magnitude using neural networks*	22
An inverse potential problem for the stochastic heat equation with space-time noise	22
On inverse problems for mean field games with common noise via Carleman estimate*	22
On the convergence of PINNs for inverse source problem in the complex Ginzburg-Landau equation	21
Uniqueness of an inverse cavity scattering problem for the time-harmonic biharmonic wave equation	20
On direct and inverse obstacle scattering problems for biharmonic waves	19
Stability of the isotropic conductivity reconstruction using magnetic resonance electrical impedance tomography (MREIT)	17
Geometric approach for determining stationary phase points in radar imaging	17
Stability estimate for an inverse stochastic parabolic problem of determining unknown time-varying boundary *	16
A Kirchhoff Migration scheme for elastic obstacle identification	16
Inferring dynamical models from time-series biological data using an interpretable machine learning method based on weighted expression trees	16
Chilled sampling for uncertainty quantification: a motivation from a meteorological inverse problem *	16
Fictitious null spaces for improving the solution of injective inverse problems	15
The reconstruction of surface vibrations from near-field acoustic pressure measurements under steady flow	15
Determination of a spatial load in a damped Kirchhoff–Love plate equation from final time measured data	14
Hearing the shape of a cuboid room using sparse measure recovery	14
Addendum: On stochastic Kaczmarz type methods for solving large scale systems of ill-posed equations (2022 Inverse Problems 38 025003)	14

A probabilistic approach to tomography and adjoint state methods, with an application to full waveform inversion in medical ultrasound	14
Uniqueness theorems for tomographic phase retrieval with few coded diffraction patterns	14
A dataset-free deep learning method for low-dose CT image reconstruction	14
Direct inversion of the Longitudinal ray transform for 2D residual elastic strain fields	13
Radon transform on algebraic Cormack α-curves inversion formula	13
Recovering critical parameter for nonlinear Allen–Cahn equation by fully discrete continuous data assimilation algorithms *	13
Efficient decomposition-based algorithms for	12
Minimizing L 1 over L 2 norms on the gradient	12
Distributed learning with discretely observed functional data	12
Hyperparameter estimation using a resolution matrix for Bayesian sensing	12
A two-stage numerical approach for the sparse initial source identification of a diffusion–advection equation *	11
3D refractive index reconstruction from phaseless coherent optical microscopy data using multiple scattering-based inverse solvers—a study	11
Stability for a multi-frequency inverse random source problem	11
Solving the acousto-electric tomography by the adaptive Nesterov method of Kaczmarz type	11
On inertial iterated Tikhonov methods for solving ill-posed problems	11
A mathematical framework for nonlinear wavefront reconstruction in adaptive optics systems with Fourier-type wavefront sensing	11
Matrix recovery from nonconvex regularized least absolute deviations	11
Bayesian design of measurements for magnetorelaxometry imaging *	10
Bouligand–Newton type methods for non-smooth ill-posed problems	10
Strong maximum a posteriori estimation in Banach spaces with Gaussian priors	10
Double-parameter regularization for solving the backward diffusion problem with parallel-in-time algorithm	10
Maximum a posteriori estimators in ℓp are well-defined for diagonal Gaussian priors	10
Iterative regularization in classification via hinge loss diagonal descent	10
Reconstructing the image scanning microscopy dataset: an inverse problem	10
Reconstruction of the initial data from the trace of the solutions on an infinite time cylinder of damped wave equations *	10
Stochastic asymptotical regularization for linear inverse problems	10
Convergence analysis of the discretization of continuous-domain inverse problems	10
Parameter estimation in complementarity-constrained parabolic optimal control model: application to American option implied volatility	10
Optimal regularized hypothesis testing in statistical inverse problems	10
A new nonconvex low-rank tensor approximation method with applications to hyperspectral images denoising	9
Low-resolution prior equilibrium network for CT reconstruction	9
Nonstationary iterated Tikhonov regularization: convergence analysis via Hölder stability	9
Shape and orientation classification of objects based on their electromagnetic signatures using convolutional neural networks	9
On optimality and bounds for internal solutions generated from boundary data-driven Gramians	9
Microwave time reversal for nondestructive testing of buried small damage in composite materials	9
Statistical microlocal analysis in two-dimensional X-ray CT	9
On the required number of electrodes for uniqueness and convex reformulation in an inverse coefficient problem	9
Fast iterative reconstruction for multi-spectral CT by a Schmidt orthogonal modification algorithm (SOMA)	9
Unsupervised knowledge-transfer for learned image reconstruction*	9
Stable determination of coefficients in semilinear parabolic system with dynamic boundary conditions	9
Norms in sinogram space and stability estimates for the Radon transform	9
The initial-to-final-state inverse problem with time-independent potentials	8
Lipschitz stability of recovering the conductivity from internal current densities	8
Singular value decomposition for longitudinal, transverse and mixed ray transforms of 2D tensor fields	8
Reconstructing the shape and material parameters of dissipative obstacles using an impedance model	8
Solving an inverse source problem by deep neural network method with convergence and error analysis	8
Full-waveform reconstruction of microseismic events via observations of acoustic pressure in the surrounding fluid	8
DRIP: deep regularizers for inverse problems	8
Multi-scale CLEAN for Fourier-based hard x-ray solar imaging	8
Theory and fast learned solver for	8

Traveling wave solutions of an equation of Harry Dym type arising in the Black–Scholes framework	8
Inverse problems of damped wave equations with Robin boundary conditions: an application to blood perfusion	8
Reconstruction of degenerate conductivity region for parabolic equations	8
Regularization graphs—a unified framework for variational regularization of inverse problems	7
Randomized block coordinate descent method for linear ill-posed problems	7
Analysis of the discrepancy principle for Tikhonov regularization with oversmoothing penalty term under low order source conditions	7
Some integral geometry problems for wave equations	7
Direct sampling for recovering a clamped cavity from the biharmonic far-field data	7
Non-zero constraints in elliptic PDE with random boundary values and applications to hybrid inverse problems	7
Phase retrieval and phaseless inverse scattering with background information	7
Low-rank tensor completion with non-local self-similarity and multidimensional learnable transforms*	7
Object based Bayesian full-waveform inversion for shear elastography	7
Coercivity-based analysis and its application to an inverse source problem for a subdiffusion equation with time-dependent principal parts	7
GPU accelerated 3D source free adaptive wavefield reconstruction inversion for seismic imaging	7
Adaptive Tikhonov strategies for stochastic ensemble Kalman inversion	7
Uniqueness and numerical method for phaseless inverse diffraction grating problem with known superposition of incident point sources	7
On the stability of recovering two sources and initial status in a stochastic hyperbolic-parabolic system	7
Enhanced microscale hydrodynamic near-cloaking using electro-osmosis	7
ASPIRE: iterative amortized posterior inference for Bayesian inverse problems	7
Determining anomalies in a semilinear elliptic equation by a minimal number of measurements	7
Stability estimates for the expected utility in Bayesian optimal experimental design	7
A stochastic gradient descent approach with partitioned-truncated singular value decomposition for large-scale inverse problems of magnetic modulus data	7
The C ∞	7
Inverse source problem for discrete Helmholtz equation	6
A numerical investigation of matched source waveform inversion applied to acoustic transmission data	6
In memoriam Pierre Sabatier	6
Deep neural-network based optimization for the design of a multi-element surface magnet for MRI applications	6
Stability estimate for the broken non-abelian x-ray transform in Minkowski space	6
MiPhDUO: microwave imaging via physics-informed deep unrolled optimization	6
Simultaneous determination of different class of parameters for a diffusion equation from a single measurement	6
An inexact proximal majorization–minimization method for a class of image reconstruction models	6
Convergence of level sets in fractional Laplacian regularization	6
Mixed geometry information regularization for image deblurring with multiplicative noise	6
Bayesian inversion of log-normal eikonal equations	6
Bayesian interface technique-based inverse estimation of closure coefficients of standard	6
Vertical autofocus for the phase screen in a turbulent ionosphere	6
The inverse Rytov series for diffuse optical tomography	6
The lower bound of nonlocal gradient for non-convex and non-smooth image patches based regularization	6
Doubling inequality and strong unique continuation for an elliptic transmission problem *	6
Global uniqueness for determining an inverse electromagnetic scattering medium and its physical coefficients	6
Reduced order model approach for imaging with waves	6
Nearly optimal bounds for the global geometric landscape of phase retrieval	6
On the uniqueness of solutions for the basis pursuit in the continuum	6
On bias and its reduction via standardization in discretized electromagnetic source localization problems	6
On uniqueness and stable estimation of multiple parameters in the Cahn–Hilliard equation	6
Fourier method for inverse source problem using correlation of passive measurements*	6
Convergence analysis of an alternating direction method of multipliers for the identification of nonsmooth diffusion parameters with total variation	6
Local saddles of relaxed averaged alternating reflections algorithms on phase retrieval	6
Generalized inexact Newton regularization for nonlinear ill-posed problems in Banach spaces	6
Uniqueness in determining rectangular grating profiles with a single incoming wave (part II): TM polarization case	6
On Bayesian data assimilation for PDEs with ill-posed forward problems	6
Solving inverse acoustic obstacle scattering problem from phaseless far-field measurement using deep neural network surrogates*	5
Heuristic rule for inexact Newton-Landweber iteration with convex penalty terms of nonlinear: ill-posed problems	5
Heavy-ball enhanced pseudo-inverse-based hard thresholding algorithms for sparse linear inverse problems	5
A probabilistic framework for uncertainty quantification in positron emission particle tracking	5
Assessing the potential of using a virtual Veselago lens in quantitative microwave imaging	5
Some direct and inverse source problems in nonlinear evolutionary PDEs with Volterra operators	5
The domain derivative in inverse obstacle scattering with nonlinear impedance boundary condition	5
Joint Gaussian dictionary learning and tomographic reconstruction	5
Permeability estimation of a porous structure in cancer treatment based on sampled velocity measurement*	5
Stability estimates for an inverse boundary value problem for biharmonic operators with first order perturbation from partial data	5
Bayesian compressive sensing using generative models	5
Multiscale hierarchical decomposition methods for ill-posed problems	5
Recovery of a coefficient in a diffusion equation from large time data*	5
Local recovery of a piecewise constant anisotropic conductivity in EIT on domains with exposed corners	5
Increasing stability in the linearized inverse Schrödinger potential problem with power type nonlinearities*	5
Analysis of the monotonicity method for an anisotropic scatterer with a conductive boundary	5
PatchNR: learning from very few images by patch normalizing flow regularization	5
Analysis of the inverse Born series: an approach through geometric function theory	5
Adaptive anisotropic Bayesian meshing for inverse problems	5
Inverse problem for a nonlocal diffuse optical tomography equation	5
The monotonicity method for inclusion detection and the time harmonic elastic wave equation	5
Convergence study and regularizing property of a modified Robin–Robin method for the Cauchy problem in linear elasticity	5
Carleman contraction mapping for a 1D inverse scattering problem with experimental time-dependent data	5
Crack identification in a multi-layer inhomogeneous domain using the Reciprocity Gap-Linear Sampling Method	5
An analytical inversion formula for the overdetermined spherical section transform	5
Automatic nonstationary anisotropic Tikhonov regularization through bilevel optimization	5
Diffraction tomography for incident Herglotz waves	5
The MLE is a reliable source: sharp performance guarantees for localization problems	5
Estimation of off-the grid sparse spikes with over-parametrized projected gradient descent: theory and application	5

Kalman-based estimation of loading conditions from ultrasonic guided wave measurements	5
A mixed finite element scheme for three-dimensional Maxwell’s transmission eigenvalue problems	5
Convergence rates of Landweber-type methods for inverse problems in Banach spaces	5
Corrigendum: On uniqueness of an inverse problem in electromagnetic obstacle scattering for an impedance cylinder (2012 Inverse Problems 28 055012)	5
Theoretical and numerical studies of inverse source problem for the linear parabolic equation with sparse boundary measurements	5
Determination of discontinuous diffusion coefficients for the heat equation on a tree-shaped network	5
Deep Gaussian process priors for Bayesian image reconstruction	4
Color image restoration based on saturation-value total variation plus L1 fidelity*	4
Direct and inverse scattering in an optical waveguide*	4
Stability estimates for an inverse problem for Schrödinger operators at high frequencies from arbitrary partial boundary measurements	4
A posterior contraction for Bayesian inverse problems in Banach spaces	4
Uncertainty quantification for goal-oriented inverse problems via variational encoder-decoder networks	4
Microlocal properties of seven-dimensional lemon and apple Radon transforms with applications in Compton scattering tomography	4
Inverse scattering for the multipoint potentials of Bethe−Peierls−Thomas−Fermi type*	4
A variational non-linear constrained model for the inversion of FDEM data*	4
Accelerating ill-conditioned Hankel matrix recovery via structured Newton-like descent	4
Reconstruction of Voronoi diagrams: the case of inverse conductivity problems	4
Reduced-order autodifferentiable ensemble Kalman filters	4
Sparsity for dynamic inverse problems on Wasserstein curves with bounded variation	4
Error estimates and converse results for a class of linear regularization methods for inverse problems in Banach spaces	4
Recovery of piecewise smooth parameters in an acoustic-gravitational system of equations from exterior Cauchy data	4
The Radon transform with finitely many angles *	4
Stability of data-dependent ridge-regularization for inverse problems	4
Joint estimation of Robin coefficient and domain boundary for the Poisson problem	4
A Bayesian approach for consistent reconstruction of inclusions	4
Bilevel inverse problems in neuromorphic imaging	4
Determining sources in the bioluminescence tomography problem	4
Uniqueness in determining rectangular grating profiles with a single incoming wave (Part I): TE polarization case	4
Wirtinger gradient descent methods for low-dose Poisson phase retrieval	4
Lipschitz stability of an inverse conductivity problem with two Cauchy data pairs	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
Discrete nonlinear Fourier transforms and their inverses	4
Determining a parabolic system by boundary observation of its non-negative solutions with biological applications	4
Determining initial conditions for nonlinear hyperbolic equations with time dimensional reduction and the Carleman contraction principle	4
An optimal transport approach for 3D electrical impedance tomography	4
Vector-valued spline method for the spherical multiple-shell electro-magnetoencephalography problem	4
Simultaneous recovery of a locally rough interface and the embedded obstacle with its surrounding medium	4
Continuous Gaussian mixture solution for linear Bayesian inversion with application to Laplace priors	4
Noise-robust one-bit diffraction tomography and optimal dose fractionation	4
The inverse obstacle problem for nonlinear inclusions	4
One-dimensional coefficient inverse problems by transformation operators	4
Consistency of Bayesian inference with Gaussian process priors for a parabolic inverse problem	4
On a numerical construction of doubly stochastic matrices with prescribed eigenvalues	4
Tractable optimal experimental design using transport maps*	4
Bayesian inversion with α-stable priors	4
On a nonlinear model in domains with cavities arising from cardiac electrophysiology	4
An approximate analytical reconstruction method in inverse problems of cone-beam rotary computed laminography	4
Error estimates for Golub–Kahan bidiagonalization with Tikhonov regularization for ill–posed operator equations	4
A direct sampling-based deep learning approach for inverse medium scattering problems	4
Semi-discrete Tikhonov regularization in RKHS with large randomly distributed noise	4