Inverse Problems

Article	Citations
A Bernstein–von-Mises theorem for the Calderón problem with piecewise constant conductivities	44
An analysis of constraint-relaxation in PDE-based inverse problems	36
A Bayesian approach for CT reconstruction with defect detection for subsea pipelines	31
Flow recovery from distal pressure in linearized hemodynamics: an optimal control approach	30
Stochastic mirror descent method for linear ill-posed problems in Banach spaces	24
Recovering a function from its integrals over conical surfaces through relations with the Radon transform	24
On inverse problems for mean field games with common noise via Carleman estimate*	23
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 the convergence of PINNs for inverse source problem in the complex Ginzburg–Landau equation	21
Inversion of the fixed radius spherical mean Radon transform of F. John in	20
Uniqueness of an inverse cavity scattering problem for the time-harmonic biharmonic wave equation	18
On direct and inverse obstacle scattering problems for biharmonic waves	17
Stability of the isotropic conductivity reconstruction using magnetic resonance electrical impedance tomography (MREIT)	17
Inferring dynamical models from time-series biological data using an interpretable machine learning method based on weighted expression trees	16
Stability estimate for an inverse stochastic parabolic problem of determining unknown time-varying boundary *	16
A Kirchhoff Migration scheme for elastic obstacle identification	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
Addendum: On stochastic Kaczmarz type methods for solving large scale systems of ill-posed equations (2022 Inverse Problems 38 025003)	14
Recovering critical parameter for nonlinear Allen–Cahn equation by fully discrete continuous data assimilation algorithms *	14
Hearing the shape of a cuboid room using sparse measure recovery	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	13
Radon transform on algebraic Cormack α-curves inversion formula	13
Chilled sampling for uncertainty quantification: a motivation from a meteorological inverse problem *	13
Distributed learning with discretely observed functional data	13
Geometric approach for determining stationary phase points in radar imaging	12
Direct inversion of the Longitudinal ray transform for 2D residual elastic strain fields	12
Hyperparameter estimation using a resolution matrix for Bayesian sensing	12
A probabilistic approach to tomography and adjoint state methods, with an application to full waveform inversion in medical ultrasound	12
Efficient decomposition-based algorithms for	12
Solving the acousto-electric tomography by the adaptive Nesterov method of Kaczmarz type	11
Matrix recovery from nonconvex regularized least absolute deviations	11
A mathematical framework for nonlinear wavefront reconstruction in adaptive optics systems with Fourier-type wavefront sensing	11
On inertial iterated Tikhonov methods for solving ill-posed problems	11
A two-stage numerical approach for the sparse initial source identification of a diffusion–advection equation *	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 *	10
Stochastic asymptotical regularization for linear inverse problems	10
3D refractive index reconstruction from phaseless coherent optical microscopy data using multiple scattering-based inverse solvers—a study	10
Strong maximum a posteriori estimation in Banach spaces with Gaussian priors	10
Bayesian design of measurements for magnetorelaxometry imaging *	10
Minimizing L 1 over L 2 norms on the gradient	10
Iterative regularization in classification via hinge loss diagonal descent	10
Parameter estimation in complementarity-constrained parabolic optimal control model: application to American option implied volatility	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
Bouligand–Newton type methods for non-smooth ill-posed problems	10
Convergence analysis of the discretization of continuous-domain inverse problems	10
Low-resolution prior equilibrium network for CT reconstruction	9
A new nonconvex low-rank tensor approximation method with applications to hyperspectral images denoising	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
Nonstationary iterated Tikhonov regularization: convergence analysis via Hölder stability	9
Microwave time reversal for nondestructive testing of buried small damage in composite materials	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
On optimality and bounds for internal solutions generated from boundary data-driven Gramians	9
Uniqueness and numerical method for phaseless inverse diffraction grating problem with known superposition of incident point sources	8
Solving an inverse source problem by deep neural network method with convergence and error analysis	8
Reconstructing the image scanning microscopy dataset: an inverse problem	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
Norms in sinogram space and stability estimates for the Radon transform	8
Theory and fast learned solver for	8
Full-waveform reconstruction of microseismic events via observations of acoustic pressure in the surrounding fluid	8
Inverse source problem of sub-diffusion of variable exponent	8
Shape and orientation classification of objects based on their electromagnetic signatures using convolutional neural networks	8
Adaptive Tikhonov strategies for stochastic ensemble Kalman inversion	7
GPU accelerated 3D source free adaptive wavefield reconstruction inversion for seismic imaging	7

DRIP: deep regularizers for inverse problems	7
The initial-to-final-state inverse problem with time-independent potentials	7
Analysis of the discrepancy principle for Tikhonov regularization with oversmoothing penalty term under low order source conditions	7
Phase retrieval and phaseless inverse scattering with background information	7
Regularization graphs—a unified framework for variational regularization of inverse problems	7
Randomized block coordinate descent method for linear ill-posed problems	7
Some integral geometry problems for wave equations	7
Multi-scale CLEAN for Fourier-based hard x-ray solar imaging	7
Reconstructing the shape and material parameters of dissipative obstacles using an impedance model	7
Lipschitz stability of recovering the conductivity from internal current densities	7
Coercivity-based analysis and its application to an inverse source problem for a subdiffusion equation with time-dependent principal parts	7
Object based Bayesian full-waveform inversion for shear elastography	7
Determining anomalies in a semilinear elliptic equation by a minimal number of measurements	7
Direct sampling for recovering a clamped cavity from the biharmonic far-field data	7
Reconstruction of degenerate conductivity region for parabolic equations	7
Singular value decomposition for longitudinal, transverse and mixed ray transforms of 2D tensor fields	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
Enhanced microscale hydrodynamic near-cloaking using electro-osmosis	7
ASPIRE: iterative amortized posterior inference for Bayesian inverse problems	7
Convergence analysis of an alternating direction method of multipliers for the identification of nonsmooth diffusion parameters with total variation	6
Bayesian interface technique-based inverse estimation of closure coefficients of standard	6
Low-rank tensor completion with non-local self-similarity and multidimensional learnable transforms*	6
On the stability of recovering two sources and initial status in a stochastic hyperbolic-parabolic system	6
Mixed geometry information regularization for image deblurring with multiplicative noise	6
The C ∞	6
Uniqueness in determining rectangular grating profiles with a single incoming wave (part II): TM polarization case	6
In memoriam Pierre Sabatier	6
On uniqueness and stable estimation of multiple parameters in the Cahn–Hilliard equation	6
Generalized inexact Newton regularization for nonlinear ill-posed problems in Banach spaces	6
Importance-Aware Nonlocal Tensor Nuclear Norm for High-Dimensional Image Recovery	6
Inverse source problem for discrete Helmholtz equation	6
A numerical investigation of matched source waveform inversion applied to acoustic transmission data	6
Convergence of level sets in fractional Laplacian regularization	6
Global uniqueness for determining an inverse electromagnetic scattering medium and its physical coefficients	6
Deep neural-network based optimization for the design of a multi-element surface magnet for MRI applications	6
On Bayesian data assimilation for PDEs with ill-posed forward problems	6
Doubling inequality and strong unique continuation for an elliptic transmission problem *	6
Nearly optimal bounds for the global geometric landscape of phase retrieval	6
Non-zero constraints in elliptic PDE with random boundary values and applications to hybrid inverse problems	6
On bias and its reduction via standardization in discretized electromagnetic source localization problems	6
On the uniqueness of solutions for the basis pursuit in the continuum	6
Bayesian inversion of log-normal eikonal equations	6
Estimation of off-the grid sparse spikes with over-parametrized projected gradient descent: theory and application	5
The monotonicity method for inclusion detection and the time harmonic elastic wave equation	5
Analysis of the monotonicity method for an anisotropic scatterer with a conductive boundary	5
Heavy-ball enhanced pseudo-inverse-based hard thresholding algorithms for sparse linear inverse problems	5
Convergence study and regularizing property of a modified Robin–Robin method for the Cauchy problem in linear elasticity	5
Bayesian compressive sensing using generative models	5
Solving inverse acoustic obstacle scattering problem from phaseless far-field measurement using deep neural network surrogates*	5
Local recovery of a piecewise constant anisotropic conductivity in EIT on domains with exposed corners	5
Fourier method for inverse source problem using correlation of passive measurements*	5
An inexact proximal majorization–minimization method for a class of image reconstruction models	5
MiPhDUO: microwave imaging via physics-informed deep unrolled optimization	5
Carleman contraction mapping for a 1D inverse scattering problem with experimental time-dependent data	5
Adaptive anisotropic Bayesian meshing for inverse problems	5
Corrigendum: On uniqueness of an inverse problem in electromagnetic obstacle scattering for an impedance cylinder (2012 Inverse Problems 28 055012)	5
A mixed finite element scheme for three-dimensional Maxwell’s transmission eigenvalue problems	5
Increasing stability in the linearized inverse Schrödinger potential problem with power type nonlinearities*	5
Recovery of a coefficient in a diffusion equation from large time data*	5
Determination of discontinuous diffusion coefficients for the heat equation on a tree-shaped network	5
Multiscale hierarchical decomposition methods for ill-posed problems	5
The inverse Rytov series for diffuse optical tomography	5
Stability estimate for the broken non-abelian x-ray transform in Minkowski space	5
The lower bound of nonlocal gradient for non-convex and non-smooth image patches based regularization	5
Convergence rates of Landweber-type methods for inverse problems in Banach spaces	5
Permeability estimation of a porous structure in cancer treatment based on sampled velocity measurement*	5
Joint Gaussian dictionary learning and tomographic reconstruction	5
A probabilistic framework for uncertainty quantification in positron emission particle tracking	5
An iterative algorithm for the square-root Lasso	5
Automatic nonstationary anisotropic Tikhonov regularization through bilevel optimization	5
Heuristic rule for inexact Newton-Landweber iteration with convex penalty terms of nonlinear: ill-posed problems	5
Theoretical and numerical studies of inverse source problem for the linear parabolic equation with sparse boundary measurements	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
Vertical autofocus for the phase screen in a turbulent ionosphere	5
Simultaneous determination of different class of parameters for a diffusion equation from a single measurement	5
Inverse problem for a nonlocal diffuse optical tomography equation	5
Error estimates and converse results for a class of linear regularization methods for inverse problems in Banach spaces	5
Discrete nonlinear Fourier transforms and their inverses	4

PatchNR: learning from very few images by patch normalizing flow regularization	4
Some direct and inverse source problems in nonlinear evolutionary PDEs with Volterra operators	4
Stability of data-dependent ridge-regularization for inverse problems	4
Stability estimates for an inverse boundary value problem for biharmonic operators with first order perturbation from partial data	4
Recovery of piecewise smooth parameters in an acoustic-gravitational system of equations from exterior Cauchy data	4
Inverse scattering for the multipoint potentials of Bethe−Peierls−Thomas−Fermi type*	4
Wirtinger gradient descent methods for low-dose Poisson phase retrieval	4
Tractable optimal experimental design using transport maps*	4
Noise-robust one-bit diffraction tomography and optimal dose fractionation	4
Error estimates for Golub–Kahan bidiagonalization with Tikhonov regularization for ill–posed operator equations	4
Continuous Gaussian mixture solution for linear Bayesian inversion with application to Laplace priors	4
Uniqueness in determining rectangular grating profiles with a single incoming wave (Part I): TE polarization case	4
The inverse obstacle problem for nonlinear inclusions	4
Corrigendum: Solution of an acoustic transmission inverse problem by extended inversion (2022 Inverse Problems 38 115003)	4
One-dimensional coefficient inverse problems by transformation operators	4
An optimal transport approach for 3D electrical impedance tomography	4
Consistency of Bayesian inference with Gaussian process priors for a parabolic inverse problem	4
Reduced-order autodifferentiable ensemble Kalman filters	4
Determining initial conditions for nonlinear hyperbolic equations with time dimensional reduction and the Carleman contraction principle	4
Color image restoration based on saturation-value total variation plus L1 fidelity*	4
Determining a parabolic system by boundary observation of its non-negative solutions with biological applications	4
Microlocal properties of seven-dimensional lemon and apple Radon transforms with applications in Compton scattering tomography	4
Semi-discrete Tikhonov regularization in RKHS with large randomly distributed noise	4
Error bounds for extended source inversion applied to an acoustic transmission inverse problem	4
Accelerating ill-conditioned Hankel matrix recovery via structured Newton-like descent	4
The domain derivative in inverse obstacle scattering with nonlinear impedance boundary condition	4
Lipschitz stability of an inverse conductivity problem with two Cauchy data pairs	4
Deep Gaussian process priors for Bayesian image reconstruction	4
Stability estimates for an inverse problem for Schrödinger operators at high frequencies from arbitrary partial boundary measurements	4
On a numerical construction of doubly stochastic matrices with prescribed eigenvalues	4
Reconstruction of Voronoi diagrams: the case of inverse conductivity problems	4
An approximate analytical reconstruction method in inverse problems of cone-beam rotary computed laminography	4
A posterior contraction for Bayesian inverse problems in Banach spaces	4
Kalman-based estimation of loading conditions from ultrasonic guided wave measurements	4
A direct sampling-based deep learning approach for inverse medium scattering problems	4
The Radon transform with finitely many angles *	4
Analysis of the inverse Born series: an approach through geometric function theory	4
On a nonlinear model in domains with cavities arising from cardiac electrophysiology	4
Sparsity for dynamic inverse problems on Wasserstein curves with bounded variation	4
Determining sources in the bioluminescence tomography problem	4
Bayesian inversion with α-stable priors	4
Simultaneous recovery of a locally rough interface and the embedded obstacle with its surrounding medium	4
Assessing the potential of using a virtual Veselago lens in quantitative microwave imaging	4
Direct and inverse scattering in an optical waveguide*	4
Uncertainty quantification for goal-oriented inverse problems via variational encoder-decoder networks	4
Bilevel inverse problems in neuromorphic imaging	4
Diffraction tomography for incident Herglotz waves	4
Vector-valued spline method for the spherical multiple-shell electro-magnetoencephalography problem	4
The MLE is a reliable source: sharp performance guarantees for localization problems	4
Size estimates for nanoplates	3
The factorization method and Capon’s method for random source identification in experimental aeroacoustics	3
Precursors for synthetic aperture radar	3
Imaging in lossy media	3
Fixed-distance multipoint formulas for the scattering amplitude from phaseless measurements	3
Corrigendum: Unique reconstruction of the potential for the interior transmission eigenvalue problem for spherically stratified media (2020 Inverse Problems 36 035017)	3
Piecewise nonlinear materials and Monotonicity Principle	3
State estimation approach to dual-modal imaging of two-phase flow based on electromagnetic flow tomography and electrical tomography	3
Inverse conductivity problem with one measurement: uniqueness of multi-layer structures	3
Far field operator splitting and completion in inverse medium scattering	3
A stability result for the identification of a permeability parameter on Navier–Stokes equations	3
Discrete Calderón problem with partial data	3
V-line 2-tensor tomography in the plane	3
3D Poissonian image deblurring via patch-based tensor logarithmic Schatten-p minimization	3
Neural blind deconvolution with Poisson data	3
Determination of first order perturbation for bi-harmonic operator by asymptotic boundary spectral data	3
Inverse radiative transfer with goal-oriented hp-adaptive mesh refinement: adaptive-mesh inversion	3
Restoring the discontinuous heat equation source using sparse boundary data and dynamic sensors	3
Determining the viscosity of the Navier–Stokes equations from observations of finitely many modes	3
Initial state estimation from limited observations of the heat equation in metric graphs	3
Spectral decomposition of atomic structures in heterogeneous cryo-EM	3
An inverse Cauchy problem of a stochastic hyperbolic equation	3
Machine learning enhanced electrical impedance tomography for 2D materials	3
A novel epidemiologically informed particle filter for assessing epidemic phenomena. Application to the monkeypox outbreak of 2022	3
Inverse problem for stochastic heat equations with singular inverse-square potentials	3
Dynamic thresholding algorithm with memory for linear inverse problems	3
Convergence rate of Tikhonov regularization for identifying parameters in the elastic wave system under a positive condition	3
Microtexture region segmentation of eddy current testing data using a structural prior	3
Flash proton radiation therapy via a stochastic three-operator splitting method	3
Solution of the EEG inverse problem by random dipole sampling	3
Truncated amplitude flow with coded diffraction patterns	3
MCMC-Net: accelerating Markov Chain Monte Carlo with neural networks for inverse problems	3
fg-ORKA: fast and gridless reconstruction of moving and deforming objects in multidimensional data	3
Approximation of discontinuous inverse operators with neural networks	3
Cones with convoluted geometry that always scatter or radiate	3
Relaxation-based schemes for on-the-fly parameter estimation in dissipative dynamical systems	3
Convergence of non-linear diagonal frame filtering for regularizing inverse problems	3
Joint sparse optimization: lower-order regularization method and application in cell fate conversion	3
Ill-posedness of time-dependent inverse problems in Lebesgue-Bochner spaces	3
In memoriam Mario Bertero	3
Bayesian image segmentation under varying blur with triplet Markov random field	3
Relaxation approach for learning neural network regularizers for a class of identification problems	3
Distributed parameter identification for the Navier–Stokes equations for obstacle detection	3
Divide-and-conquer DNN approach for the inverse point source problem using a few single frequency measurements	3
Optimising seismic imaging design parameters via bilevel learning	3
Un-supervised learning for blind image deconvolution via Monte-Carlo sampling	3