Inverse Problems

Article	Citations
A Bernstein–von-Mises theorem for the Calderón problem with piecewise constant conductivities	49
An analysis of constraint-relaxation in PDE-based inverse problems	44
A Bayesian approach for CT reconstruction with defect detection for subsea pipelines	33
Imaging conductivity from current density magnitude using neural networks*	25
On a quantitative partial imaging problem in vector tomography	24
On inverse problems for mean field games with common noise via Carleman estimate*	22
Multipoint formulas in inverse problems and their numerical implementation	22
An inverse potential problem for the stochastic heat equation with space-time noise	21
On direct and inverse obstacle scattering problems for biharmonic waves	21
Uniqueness of an inverse cavity scattering problem for the time-harmonic biharmonic wave equation	20
Stochastic mirror descent method for linear ill-posed problems in Banach spaces	20
Flow recovery from distal pressure in linearized hemodynamics: an optimal control approach	20
Recovering a function from its integrals over conical surfaces through relations with the Radon transform	19
Distributed learning with discretely observed functional data	19
Direct inversion of the Longitudinal ray transform for 2D residual elastic strain fields	17
Geometric approach for determining stationary phase points in radar imaging	16
Radon transform on algebraic Cormack α-curves inversion formula	16
Stability of the isotropic conductivity reconstruction using magnetic resonance electrical impedance tomography (MREIT)	16
Stability estimate for an inverse stochastic parabolic problem of determining unknown time-varying boundary *	15
Chilled sampling for uncertainty quantification: a motivation from a meteorological inverse problem *	15
Inferring dynamical models from time-series biological data using an interpretable machine learning method based on weighted expression trees	15
Fictitious null spaces for improving the solution of injective inverse problems	14
The reconstruction of surface vibrations from near-field acoustic pressure measurements under steady flow	14
Recovering critical parameter for nonlinear Allen–Cahn equation by fully discrete continuous data assimilation algorithms *	14
A Kirchhoff Migration scheme for elastic obstacle identification	14

Addendum: On stochastic Kaczmarz type methods for solving large scale systems of ill-posed equations (2022 Inverse Problems 38 025003)	13
Uniqueness theorems for tomographic phase retrieval with few coded diffraction patterns	13
A probabilistic approach to tomography and adjoint state methods, with an application to full waveform inversion in medical ultrasound	13
Determination of a spatial load in a damped Kirchhoff–Love plate equation from final time measured data	13
Hearing the shape of a cuboid room using sparse measure recovery	13
A dataset-free deep learning method for low-dose CT image reconstruction	12
Hyperparameter estimation using a resolution matrix for Bayesian sensing	12
Efficient decomposition-based algorithms for	12
A two-stage numerical approach for the sparse initial source identification of a diffusion–advection equation *	11
A mathematical framework for nonlinear wavefront reconstruction in adaptive optics systems with Fourier-type wavefront sensing	11
Minimizing L 1 over L 2 norms on the gradient	11
3D refractive index reconstruction from phaseless coherent optical microscopy data using multiple scattering-based inverse solvers—a study	11
Solving the acousto-electric tomography by the adaptive Nesterov method of Kaczmarz type	11
Stability for a multi-frequency inverse random source problem	11
Double-parameter regularization for solving the backward diffusion problem with parallel-in-time algorithm	10
Optimal regularized hypothesis testing in statistical inverse problems	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
Matrix recovery from nonconvex regularized least absolute deviations	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
On inertial iterated Tikhonov methods for solving ill-posed problems	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
Fast iterative reconstruction for multi-spectral CT by a Schmidt orthogonal modification algorithm (SOMA)	10
Bayesian design of measurements for magnetorelaxometry imaging *	10
Low-resolution prior equilibrium network for CT reconstruction	9
Microwave time reversal for nondestructive testing of buried small damage in composite materials	9
Stable determination of coefficients in semilinear parabolic system with dynamic boundary conditions	9
Shape and orientation classification of objects based on their electromagnetic signatures using convolutional neural networks	9
Strong maximum a posteriori estimation in Banach spaces with Gaussian priors	9
A new nonconvex low-rank tensor approximation method with applications to hyperspectral images denoising	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
On optimality and bounds for internal solutions generated from boundary data-driven Gramians	9
Unsupervised knowledge-transfer for learned image reconstruction*	9
Reconstructing the image scanning microscopy dataset: an inverse problem	9
Uniqueness and numerical method for phaseless inverse diffraction grating problem with known superposition of incident point sources	9
Norms in sinogram space and stability estimates for the Radon transform	9
Inverse problems of damped wave equations with Robin boundary conditions: an application to blood perfusion	8
Multi-scale CLEAN for Fourier-based hard x-ray solar imaging	8
Direct sampling for recovering a clamped cavity from the biharmonic far-field data	8
Reconstruction of degenerate conductivity region for parabolic equations	8
Lipschitz stability of recovering the conductivity from internal current densities	8
Theory and fast learned solver for	8
Singular value decomposition for longitudinal, transverse and mixed ray transforms of 2D tensor fields	8
Full-waveform reconstruction of microseismic events via observations of acoustic pressure in the surrounding fluid	8
Adaptive Tikhonov strategies for stochastic ensemble Kalman inversion	8
DRIP: deep regularizers for inverse problems	8

Regularization graphs—a unified framework for variational regularization of inverse problems	7
A numerical investigation of matched source waveform inversion applied to acoustic transmission data	7
Analysis of the discrepancy principle for Tikhonov regularization with oversmoothing penalty term under low order source conditions	7
The initial-to-final-state inverse problem with time-independent potentials	7
A stochastic gradient descent approach with partitioned-truncated singular value decomposition for large-scale inverse problems of magnetic modulus data	7
Low-rank tensor completion with non-local self-similarity and multidimensional learnable transforms*	7
ASPIRE: iterative amortized posterior inference for Bayesian inverse problems	7
Mixed geometry information regularization for image deblurring with multiplicative noise	7
GPU accelerated 3D source free adaptive wavefield reconstruction inversion for seismic imaging	7
Some integral geometry problems for wave equations	7
Determining anomalies in a semilinear elliptic equation by a minimal number of measurements	7
Phase retrieval and phaseless inverse scattering with background information	7
Enhanced microscale hydrodynamic near-cloaking using electro-osmosis	7
Randomized block coordinate descent method for linear ill-posed problems	7
Coercivity-based analysis and its application to an inverse source problem for a subdiffusion equation with time-dependent principal parts	7
Stability estimates for the expected utility in Bayesian optimal experimental design	7
Reconstructing the shape and material parameters of dissipative obstacles using an impedance model	7
Solving an inverse source problem by deep neural network method with convergence and error analysis	7
Object based Bayesian full-waveform inversion for shear elastography	7
Doubling Inequality and Strong Unique Continuation for an Elliptic Transmission Problem∗	6
The inverse Rytov series for diffuse optical tomography	6
On Bayesian data assimilation for PDEs with ill-posed forward problems	6
Uniqueness in determining rectangular grating profiles with a single incoming wave (part II): TM polarization case	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
Convergence analysis of an alternating direction method of multipliers for the identification of nonsmooth diffusion parameters with total variation	6
Global uniqueness for determining an inverse electromagnetic scattering medium and its physical coefficients	6
Bayesian inversion of log-normal eikonal equations	6
Regularization of the factorization method applied to diffuse optical tomography	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
An inexact proximal majorization–minimization method for a class of image reconstruction models	6
Bayesian interface technique-based inverse estimation of closure coefficients of standard	6
The C ∞	6
Inverse source problem for discrete Helmholtz equation	6
On uniqueness and stable estimation of multiple parameters in the Cahn–Hilliard equation	6
Simultaneous determination of different class of parameters for a diffusion equation from a single measurement	6
The lower bound of nonlocal gradient for non-convex and non-smooth image patches based regularization	6
Reduced order model approach for imaging with waves	6
Local saddles of relaxed averaged alternating reflections algorithms on phase retrieval	6
Convergence of level sets in fractional Laplacian regularization	6
On the stability of recovering two sources and initial status in a stochastic hyperbolic-parabolic system	6
Non-zero constraints in elliptic PDE with random boundary values and applications to hybrid inverse problems	6
Nearly optimal bounds for the global geometric landscape of phase retrieval	6
In memoriam Pierre Sabatier	6
Analysis of the inverse Born series: an approach through geometric function theory	5
Joint Gaussian dictionary learning and tomographic reconstruction	5
Corrigendum: On uniqueness of an inverse problem in electromagnetic obstacle scattering for an impedance cylinder (2012 Inverse Problems 28 055012)	5
Analysis of the monotonicity method for an anisotropic scatterer with a conductive boundary	5
Projection methods for high numerical aperture phase retrieval	5
Convergence rates of Landweber-type methods for inverse problems in Banach spaces	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
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
Stability estimates for an inverse boundary value problem for biharmonic operators with first order perturbation from partial data	5
The monotonicity method for inclusion detection and the time harmonic elastic wave equation	5
Adaptive anisotropic Bayesian meshing for inverse problems	5
Sound speed uncertainty in acousto-electric tomography	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
Determination of discontinuous diffusion coefficients for the heat equation on a tree-shaped network	5
An analytical inversion formula for the overdetermined spherical section transform	5
Recovery of a coefficient in a diffusion equation from large time data*	5
Stability estimate for the broken non-abelian x-ray transform in Minkowski space	5
Permeability estimation of a porous structure in cancer treatment based on sampled velocity measurement*	5
Carleman contraction mapping for a 1D inverse scattering problem with experimental time-dependent data	5
A mixed finite element scheme for three-dimensional Maxwell’s transmission eigenvalue problems	5
Determining a parabolic system by boundary observation of its non-negative solutions with biological applications	5
Determining initial conditions for nonlinear hyperbolic equations with time dimensional reduction and the Carleman contraction principle	5
Increasing stability in the linearized inverse Schrödinger potential problem with power type nonlinearities*	5
A probabilistic framework for uncertainty quantification in positron emission particle tracking	5
Inverse problem for a nonlocal diffuse optical tomography equation	5
Crack identification in a multi-layer inhomogeneous domain using the Reciprocity Gap-Linear Sampling Method	5
Vertical autofocus for the phase screen in a turbulent ionosphere	5
MiPhDUO: microwave imaging via physics-informed deep unrolled optimization	5
Automatic nonstationary anisotropic Tikhonov regularization through bilevel optimization	5
Heavy-ball enhanced pseudo-inverse-based hard thresholding algorithms for sparse linear inverse problems	5

Continuous Gaussian mixture solution for linear Bayesian inversion with application to Laplace priors	4
Discrete nonlinear Fourier transforms and their inverses	4
Recovery of piecewise smooth parameters in an acoustic-gravitational system of equations from exterior Cauchy data	4
Uncertainty quantification for goal-oriented inverse problems via variational encoder-decoder networks	4
On a nonlinear model in domains with cavities arising from cardiac electrophysiology	4
The domain derivative in inverse obstacle scattering with nonlinear impedance boundary condition	4
A variational non-linear constrained model for the inversion of FDEM data*	4
Semi-discrete Tikhonov regularization in RKHS with large randomly distributed noise	4
The MLE is a reliable source: sharp performance guarantees for localization problems	4
A direct sampling-based deep learning approach for inverse medium scattering problems	4
Reduced-order autodifferentiable ensemble Kalman filters	4
An optimal transport approach for 3D electrical impedance tomography	4
Accelerating ill-conditioned Hankel matrix recovery via structured Newton-like descent	4
Noise-robust one-bit diffraction tomography and optimal dose fractionation	4
The inverse obstacle problem for nonlinear inclusions	4
Determining sources in the bioluminescence tomography problem	4
Tractable optimal experimental design using transport maps*	4
Deep Gaussian process priors for Bayesian image reconstruction	4
Stability of data-dependent ridge-regularization for inverse problems	4
Uniqueness in determining rectangular grating profiles with a single incoming wave (Part I): TE polarization case	4
The Radon transform with finitely many angles *	4
Corrigendum: Solution of an acoustic transmission inverse problem by extended inversion (2022 Inverse Problems 38 115003)	4
Inverse problem of reconstruction of degenerate diffusion coefficient in a parabolic equation	4
PatchNR: learning from very few images by patch normalizing flow regularization	4
Assessing the potential of using a virtual Veselago lens in quantitative microwave imaging	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
Bayesian inversion with α-stable priors	4
Lipschitz stability of an inverse conductivity problem with two Cauchy data pairs	4
Stability estimates for an inverse problem for Schrödinger operators at high frequencies from arbitrary partial boundary measurements	4
Reconstruction of Voronoi diagrams: the case of inverse conductivity problems	4
Wirtinger gradient descent methods for low-dose Poisson phase retrieval	4
Error estimates for Golub–Kahan bidiagonalization with Tikhonov regularization for ill–posed operator equations	4
Microlocal properties of seven-dimensional lemon and apple Radon transforms with applications in Compton scattering tomography	4
An approximate analytical reconstruction method in inverse problems of cone-beam rotary computed laminography	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
Consistency of Bayesian inference with Gaussian process priors for a parabolic inverse problem	4
One-dimensional coefficient inverse problems by transformation operators	4
Kalman-based estimation of loading conditions from ultrasonic guided wave measurements	4
Error bounds for extended source inversion applied to an acoustic transmission inverse problem	4
Diffraction tomography for incident Herglotz waves	4
Estimation of off-the grid sparse spikes with over-parametrized projected gradient descent: theory and application	4
Inverse scattering for the multipoint potentials of Bethe−Peierls−Thomas−Fermi type*	4
Some direct and inverse source problems in nonlinear evolutionary PDEs with Volterra operators	4
A posterior contraction for Bayesian inverse problems in Banach spaces	4
A Bayesian approach for consistent reconstruction of inclusions	4
Bilevel inverse problems in neuromorphic imaging	4
Vector-valued spline method for the spherical multiple-shell electro-magnetoencephalography problem	4
Restoring the discontinuous heat equation source using sparse boundary data and dynamic sensors	3
3D Poissonian image deblurring via patch-based tensor logarithmic Schatten-p minimization	3
Γ -convergence of Onsager–Machlup functionals: I. With applications to maximum a posteriori estimation in Bayesian inverse problems	3
Flash proton radiation therapy via a stochastic three-operator splitting method	3
Microtexture region segmentation of eddy current testing data using a structural prior	3
MCMC-Net: accelerating Markov Chain Monte Carlo with neural networks for inverse problems	3
Stochastic linear regularization methods: random discrepancy principle and applications	3
In memoriam Mario Bertero	3
Determining the viscosity of the Navier–Stokes equations from observations of finitely many modes	3
Relaxation-based schemes for on-the-fly parameter estimation in dissipative dynamical systems	3
On the uniqueness of inverse problems for the reduced wave equation with unknown embedded obstacles	3
High resolution 3D ultrasonic breast imaging by time-domain full waveform inversion	3
fg-ORKA: fast and gridless reconstruction of moving and deforming objects in multidimensional data	3
The Dantzig selector: recovery of signal via ℓ 1 − αℓ 2 minimization	3
Dynamic thresholding algorithm with memory for linear inverse problems	3
Spectral decomposition of atomic structures in heterogeneous cryo-EM	3
Optimising seismic imaging design parameters via bilevel learning	3
Distributed parameter identification for the Navier–Stokes equations for obstacle detection	3
Radial recombination for rigid rotational alignment of images and volumes	3
A stability result for the identification of a permeability parameter on Navier–Stokes equations	3
The factorization method and Capon’s method for random source identification in experimental aeroacoustics	3
Convergence of non-linear diagonal frame filtering for regularizing inverse problems	3
Ill-posedness of time-dependent inverse problems in Lebesgue-Bochner spaces	3
Solving time-fractional diffusion equations with a singular source term	3
Discrete Calderón problem with partial data	3
Joint sparse optimization: lower-order regularization method and application in cell fate conversion	3
Piecewise nonlinear materials and Monotonicity Principle	3
Corrigendum: Unique reconstruction of the potential for the interior transmission eigenvalue problem for spherically stratified media (2020 Inverse Problems 36 035017)	3
Reconstruction of the doping profile in Vlasov–Poisson system	3
Precursors for synthetic aperture radar	3
Relaxation approach for learning neural network regularizers for a class of identification problems	3
Convergence rate of Tikhonov regularization for identifying parameters in the elastic wave system under a positive condition	3
Far field operator splitting and completion in inverse medium scattering	3
Neural blind deconvolution with Poisson data	3
V-line 2-tensor tomography in the plane	3
Fixed-distance multipoint formulas for the scattering amplitude from phaseless measurements	3
Cones with convoluted geometry that always scatter or radiate	3
An optimal Bayesian strategy for comparing Wiener–Hunt deconvolution models in the absence of ground truth	3
Inverse conductivity problem with one measurement: uniqueness of multi-layer structures	3
Approximation of discontinuous inverse operators with neural networks	3
Size estimates for nanoplates	3
State estimation approach to dual-modal imaging of two-phase flow based on electromagnetic flow tomography and electrical tomography	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
Solution of an acoustic transmission inverse problem by extended inversion	3
Bayesian image segmentation under varying blur with triplet Markov random field	3