Inverse Problems

Article	Citations
Recovering a function from its integrals over conical surfaces through relations with the Radon transform	71
On the convergence of PINNs for inverse source problem in the complex Ginzburg–Landau equation	44
Multipoint formulas in inverse problems and their numerical implementation	39
On a quantitative partial imaging problem in vector tomography	30
Flow recovery from distal pressure in linearized hemodynamics: an optimal control approach	29
Uniqueness of an inverse cavity scattering problem for the time-harmonic biharmonic wave equation	27
On direct and inverse obstacle scattering problems for biharmonic waves	26
A Bernstein–von-Mises theorem for the Calderón problem with piecewise constant conductivities	25
An analysis of constraint-relaxation in PDE-based inverse problems	23
A Bayesian approach for CT reconstruction with defect detection for subsea pipelines	23
Determination of physical coefficients at boundary for the Brinkman equations	22
An inverse potential problem for the stochastic heat equation with space-time noise	22
Inversion of the fixed radius spherical mean Radon transform of F. John in	21
On inverse problems for mean field games with common noise via Carleman estimate*	19
Stochastic mirror descent method for linear ill-posed problems in Banach spaces	19
A dataset-free deep learning method for low-dose CT image reconstruction	18
Distributed learning with discretely observed functional data	18
Chilled sampling for uncertainty quantification: a motivation from a meteorological inverse problem *	16
Inferring dynamical models from time-series biological data using an interpretable machine learning method based on weighted expression trees	15
The reconstruction of surface vibrations from near-field acoustic pressure measurements under steady flow	15
A Kirchhoff Migration scheme for elastic obstacle identification	15
Fictitious null spaces for improving the solution of injective inverse problems	15
Radon transform on algebraic Cormack α-curves inversion formula	14
Geometric approach for determining stationary phase points in radar imaging	14
Stability of the isotropic conductivity reconstruction using magnetic resonance electrical impedance tomography (MREIT)	14

Range characterization of the x-ray transform of symmetric complex valued tensor fields	14
Hearing the shape of a cuboid room using sparse measure recovery	14
Stability estimate for an inverse stochastic parabolic problem of determining unknown time-varying boundary *	14
Recovering critical parameter for nonlinear Allen–Cahn equation by fully discrete continuous data assimilation algorithms *	13
Efficient decomposition-based algorithms for	13
Direct inversion of the Longitudinal ray transform for 2D residual elastic strain fields	13
On parameter identification in three-dimensional elasticity and discretisation with physics-informed neural networks	12
Parameter estimation in complementarity-constrained parabolic optimal control model: application to American option implied volatility	12
Solving the acousto-electric tomography by the adaptive Nesterov method of Kaczmarz type	12
On inertial iterated Tikhonov methods for solving ill-posed problems	12
3D refractive index reconstruction from phaseless coherent optical microscopy data using multiple scattering-based inverse solvers—a study	12
Stability for a multi-frequency inverse random source problem	12
Hyperparameter estimation using a resolution matrix for Bayesian sensing	12
Bayesian design of measurements for magnetorelaxometry imaging *	11
Maximum a posteriori estimators in ℓp are well-defined for diagonal Gaussian priors	11
Optimal regularized hypothesis testing in statistical inverse problems	11
Bouligand–Newton type methods for non-smooth ill-posed problems	11
Strong maximum a posteriori estimation in Banach spaces with Gaussian priors	11
Reconstruction of the initial data from the trace of the solutions on an infinite time cylinder of damped wave equations *	11
Phase retrieval of quaternion signals via augmented Gauss–Newton method	11
Stochastic asymptotical regularization for linear inverse problems	11
Iterative regularization in classification via hinge loss diagonal descent	11
Primal-dual finite element methods for the direct reconstruction of material coefficients in stationary elliptic problems	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
Double-parameter regularization for solving the backward diffusion problem with parallel-in-time algorithm	11
A two-stage numerical approach for the sparse initial source identification of a diffusion–advection equation *	11
Statistical microlocal analysis in two-dimensional x-ray CT	11
Unsupervised knowledge-transfer for learned image reconstruction*	10
Nonstationary iterated Tikhonov regularization: convergence analysis via Hölder stability	10
Fast iterative reconstruction for multi-spectral CT by a Schmidt orthogonal modification algorithm (SOMA)	10
On the required number of electrodes for uniqueness and convex reformulation in an inverse coefficient problem	10
Stable determination of coefficients in semilinear parabolic system with dynamic boundary conditions	10
Reconstructing the image scanning microscopy dataset: an inverse problem	10
On optimality and bounds for internal solutions generated from boundary data-driven Gramians	10
Least-squares reverse time migration based on second-order Born approximation	10
Convergence analysis of the discretization of continuous-domain inverse problems	10
Multi-scale CLEAN for Fourier-based hard x-ray solar imaging	9
On the inverse transmission eigenvalue problem with a piecewise <	9
Identification problems for anisotropic time-fractional subdiffusion equations	9
The initial-to-final-state inverse problem with time-independent potentials	9
Full-waveform reconstruction of microseismic events via observations of acoustic pressure in the surrounding fluid	9
Traveling wave solutions of an equation of Harry Dym type arising in the Black–Scholes framework	9
Microwave time reversal for nondestructive testing of buried small damage in composite materials	9
Low-resolution prior equilibrium network for CT reconstruction	9
Inverse source problem of sub-diffusion of variable exponent	9
Levenberg–Marquardt hard thresholding pursuit for sparse bilinear inverse problems	9
A new nonconvex low-rank tensor approximation method with applications to hyperspectral images denoising	9
Norms in sinogram space and stability estimates for the Radon transform	9
Determining anomalies in a semilinear elliptic equation by a minimal number of measurements	8

Singular value decomposition for longitudinal, transverse and mixed ray transforms of 2D tensor fields	8
Shape and orientation classification of objects based on their electromagnetic signatures using convolutional neural networks	8
Reconstructing the shape and material parameters of dissipative obstacles using an impedance model	8
Stability estimates for the expected utility in Bayesian optimal experimental design	8
Theory and fast learned solver for	8
Inverse problems of damped wave equations with Robin boundary conditions: an application to blood perfusion	8
In memoriam Edward Roy Pike	8
DRIP: deep regularizers for inverse problems	8
Reconstruction of degenerate conductivity region for parabolic equations	8
A learning-based hybrid reconstruction scheme for an inverse boundary value problem	8
Inverse problem for the Navier–Stokes equations and identification of immersed obstacles in the Mediterranean Sea	7
On the uniqueness of solutions for the basis pursuit in the continuum	7
Object based Bayesian full-waveform inversion for shear elastography	7
Regularization graphs—a unified framework for variational regularization of inverse problems	7
Probabilistic approach to black-box binary optimization with budget constraints: Application to sensor placement	7
Lipschitz stability of recovering the conductivity from internal current densities	7
Corrigendum: Inverse conductivity problem with one measurement: uniqueness of multi-layer structures (2024 Inverse Problems 40 085005)	7
Enhanced microscale hydrodynamic near-cloaking using electro-osmosis	7
Mixed geometry information regularization for image deblurring with multiplicative noise	7
ASPIRE: iterative amortized posterior inference for Bayesian inverse problems	7
Generalized spherical mean associated with the generalized Darboux equation and its applications	7
Coercivity-based analysis and its application to an inverse source problem for a subdiffusion equation with time-dependent principal parts	7
Analysis of the discrepancy principle for Tikhonov regularization with oversmoothing penalty term under low order source conditions	7
Solving an inverse source problem by deep neural network method with convergence and error analysis	7
Non-zero constraints in elliptic PDE with random boundary values and applications to hybrid inverse problems	7
Importance-aware nonlocal tensor nuclear norm for high-dimensional image recovery	7
Doubling inequality and strong unique continuation for an elliptic transmission problem *	7
Nearly optimal bounds for the global geometric landscape of phase retrieval	7
Low-rank tensor completion with non-local self-similarity and multidimensional learnable transforms*	7
Inverse source problem for discrete Helmholtz equation	7
Phase retrieval and phaseless inverse scattering with background information	7
Uniqueness and numerical method for phaseless inverse diffraction grating problem with known superposition of incident point sources	7
Direct sampling for recovering a clamped cavity from the biharmonic far-field data	7
GPU accelerated 3D source free adaptive wavefield reconstruction inversion for seismic imaging	7
The C ∞	7
A numerical investigation of matched source waveform inversion applied to acoustic transmission data	7
Randomized block coordinate descent method for linear ill-posed problems	7
On the convergence of stochastic variance reduced gradient for linear inverse problems *	6
A localized consensus-based sampling algorithm	6
Convergence rates of Landweber-type methods for inverse problems in Banach spaces	6
Local recovery of a piecewise constant anisotropic conductivity in EIT on domains with exposed corners	6
An interpretable neural network for diffeomorphic image registration: theory and application	6
An inexact proximal majorization–minimization method for a class of image reconstruction models	6
Bayesian inversion of log-normal eikonal equations	6
Convergence analysis of an alternating direction method of multipliers for the identification of nonsmooth diffusion parameters with total variation	6
An analytical inversion formula for the overdetermined spherical section transform	6
Solving inverse acoustic obstacle scattering problem from phaseless far-field measurement using deep neural network surrogates*	6
Stability estimate for the broken non-abelian x-ray transform in Minkowski space	6
Fourier method for inverse source problem using correlation of passive measurements*	6
An iterative algorithm for the square-root Lasso	6
Determination of discontinuous diffusion coefficients for the heat equation on a tree-shaped network	6
Convergence of level sets in fractional Laplacian regularization	6
On bias and its reduction via standardization in discretized electromagnetic source localization problems	6
Global uniqueness for determining an inverse electromagnetic scattering medium and its physical coefficients	6
In memoriam Pierre Sabatier	6
Heuristic rule for inexact Newton-Landweber iteration with convex penalty terms of nonlinear: ill-posed problems	6
Bayesian interface technique-based inverse estimation of closure coefficients of standard	6
A morphology-adaptive random feature method for inverse source problem of the Helmholtz equation	6
Bayesian compressive sensing using generative models	6
Multiscale hierarchical decomposition methods for ill-posed problems	6
Heavy-ball enhanced pseudo-inverse-based hard thresholding algorithms for sparse linear inverse problems	6
Recovery of a coefficient in a diffusion equation from large time data*	6
Vertical autofocus for the phase screen in a turbulent ionosphere	6
Analysis of beam hardening streaks in tomography	6
Rothe’s method in direct and time-dependent inverse source problems for a semilinear pseudo-parabolic equation	6
Uniqueness in determining rectangular grating profiles with a single incoming wave (part II): TM polarization case	6
On uniqueness and stable estimation of multiple parameters in the Cahn–Hilliard equation	6
Crack identification in a multi-layer inhomogeneous domain using the Reciprocity Gap-Linear Sampling Method	6
Inverse problem for a nonlocal diffuse optical tomography equation	6
Determining sources in the bioluminescence tomography problem	5
A mixed finite element scheme for three-dimensional Maxwell’s transmission eigenvalue problems	5
The domain derivative in inverse obstacle scattering with nonlinear impedance boundary condition	5
Sparsity for dynamic inverse problems on Wasserstein curves with bounded variation	5
Deep Gaussian process priors for Bayesian image reconstruction	5
Analysis of the monotonicity method for an anisotropic scatterer with a conductive boundary	5
Estimation of off-the grid sparse spikes with over-parametrized projected gradient descent: theory and application	5
Identification of space-dependent coefficients in two competing terms of a nonlinear subdiffusion equation	5
The inverse Rytov series for diffuse optical tomography	5
Error estimates and converse results for a class of linear regularization methods for inverse problems in Banach spaces	5
Stability estimates for an inverse boundary value problem for biharmonic operators with first order perturbation from partial data	5

Lipschitz stability of an inverse conductivity problem with two Cauchy data pairs	5
Wirtinger gradient descent methods for low-dose Poisson phase retrieval	5
Corrigendum: Solution of an acoustic transmission inverse problem by extended inversion (2022 Inverse Problems 38 115003)	5
An optimal transport approach for 3D electrical impedance tomography	5
Bayesian inversion with α-stable priors	5
PatchNR: learning from very few images by patch normalizing flow regularization	5
Determining a parabolic system by boundary observation of its non-negative solutions with biological applications	5
Some direct and inverse source problems in nonlinear evolutionary PDEs with Volterra operators	5
Corrigendum: On uniqueness of an inverse problem in electromagnetic obstacle scattering for an impedance cylinder (2012 Inverse Problems 28 055012)	5
The monotonicity method for inclusion detection and the time harmonic elastic wave equation	5
Uniqueness in determining rectangular grating profiles with a single incoming wave (Part I): TE polarization case	5
Kalman-based estimation of loading conditions from ultrasonic guided wave measurements	5
Adaptive anisotropic Bayesian meshing for inverse problems	5
Automatic nonstationary anisotropic Tikhonov regularization through bilevel optimization	5
MiPhDUO: microwave imaging via physics-informed deep unrolled optimization	5
Reduced-order autodifferentiable ensemble Kalman filters	5
Fused L	5
Inverse scattering for the multipoint potentials of Bethe−Peierls−Thomas−Fermi type*	5
Reconstruction of multilayered periodic structures from one-sided acoustic near-field data	5
The Radon transform with finitely many angles *	5
The MLE is a reliable source: sharp performance guarantees for localization problems	5
On a numerical construction of doubly stochastic matrices with prescribed eigenvalues	5
A probabilistic framework for uncertainty quantification in positron emission particle tracking	5
Inverse problems for time-fractional Schrödinger equations	5
Assessing the potential of using a virtual Veselago lens in quantitative microwave imaging	5
An approximate analytical reconstruction method in inverse problems of cone-beam rotary computed laminography	5
Determining initial conditions for nonlinear hyperbolic equations with time dimensional reduction and the Carleman contraction principle	5
Semi-discrete Tikhonov regularization in RKHS with large randomly distributed noise	5
Diffraction tomography for incident Herglotz waves	5
Theoretical and numerical studies of inverse source problem for the linear parabolic equation with sparse boundary measurements	5
Inverse Problems for Dynamic History-Dependent Variational-Hemivariational Inequalities with Time-Dependent Parameters	5
A direct sampling-based deep learning approach for inverse medium scattering problems	5
Accelerating ill-conditioned Hankel matrix recovery via structured Newton-like descent	5
On a nonlinear model in domains with cavities arising from cardiac electrophysiology	5
Uncertainty quantification for goal-oriented inverse problems via variational encoder-decoder networks	5
Recovery of piecewise smooth parameters in an acoustic-gravitational system of equations from exterior Cauchy data	5
Joint Gaussian dictionary learning and tomographic reconstruction	5
Robust multi-subspace tensor dictionary learning for multi-temporal image reconstruction	4
A novel Newton method for inverse elastic scattering problems	4
Bilevel inverse problems in neuromorphic imaging	4
Far field operator splitting by principal component pursuit	4
Approximation of discontinuous inverse operators with neural networks	4
Carleman estimate with piecewise weight and applications to inverse problems for first-order transport equations	4
Solving time-fractional diffusion equations with a singular source term	4
Potential coefficient identification problem in parabolic equation with deep neural networks	4
HyDeFuse: provably convergent denoiser-driven hyperspectral fusion	4
Error bounds for extended source inversion applied to an acoustic transmission inverse problem	4
A reformulation of the equation error approach for direct inversion from full-field interior data	4
The inverse obstacle problem for nonlinear inclusions	4
Distributed spectral pairwise ranking algorithms	4
Noise-robust one-bit diffraction tomography and optimal dose fractionation	4
Inverse problem for stochastic heat equations with singular inverse-square potentials	4
Tractable optimal experimental design using transport maps*	4
Joint sparse optimization: lower-order regularization method and application in cell fate conversion	4
Moments, time-inversion and source identification for the heat equation	4
Stability analysis of a new curl-based full field reconstruction method in 2D isotropic nearly-incompressible elasticity	4
A novel epidemiologically informed particle filter for assessing epidemic phenomena. Application to the monkeypox outbreak of 2022	4
Multi-resolution deconvolution	4
A posterior contraction for Bayesian inverse problems in Banach spaces	4
Determination of a small elliptical anomaly in electrical impedance tomography using minimal measurements	4
In memoriam Mario Bertero	4
Inverse medium scattering problems with Kalman filter techniques	4
Bayesian view on the training of invertible residual networks for solving linear inverse problems *	4
Corrigendum: Unique reconstruction of the potential for the interior transmission eigenvalue problem for spherically stratified media (2020 Inverse Problems 36 035017)	4
Numerical analysis of simultaneous reconstruction of initial condition and potential in subdiffusion	4
A Bayesian approach for consistent reconstruction of inclusions	4
Sampling complexity on phase retrieval from masked Fourier measurements via Wirtinger flow*	4
Stability estimates for an inverse problem for Schrödinger operators at high frequencies from arbitrary partial boundary measurements	4
The elastic ray transform	4
Reconstruction of Voronoi diagrams: the case of inverse conductivity problems	4
TRAC method in dissipative media—a first analysis in frequency domain and homogeneous media	4
One-dimensional coefficient inverse problems by transformation operators	4
IP-basis PINNs: efficient multi-query inverse parameter estimation	4
An inverse Cauchy problem of a stochastic hyperbolic equation	4
Image analysis and resolution for detection-based synthetic-aperture passive source localization	4
Radial recombination for rigid rotational alignment of images and volumes	4
State estimation approach to dual-modal imaging of two-phase flow based on electromagnetic flow tomography and electrical tomography	4
Stochastic linear regularization methods: random discrepancy principle and applications	4
An optimal Bayesian strategy for comparing Wiener–Hunt deconvolution models in the absence of ground truth	4
Subsampling in ensemble Kalman inversion	4
Locally-supervised global image restoration	4
Solution of an acoustic transmission inverse problem by extended inversion	4
Simultaneous reconstruction of an obstacle and its wavenumber for the Helmholtz equation: a robust optimization approach	4
The implementation in STIR of four analytical algorithms for 2D PET and 2D SPECT reconstruction	4
Subgradient-based Lavrentiev regularisation of monotone ill-posed problems	4
Continuous Gaussian mixture solution for linear Bayesian inversion with application to Laplace priors	4
VARPROX: a primal-dual variable projection method for the minimization of penalized separable non-linear least squares	4
CORRIGENDUM: Inversion of the fixed radius spherical mean Radon transform of F. John in	4
Conditional stability and the numerical solution of the backward problem in dynamical cardiac electrophysiology modeling	4
Error estimates for Golub–Kahan bidiagonalization with Tikhonov regularization for ill–posed operator equations	4
Relaxation-based schemes for on-the-fly parameter estimation in dissipative dynamical systems	4
Stability of data-dependent ridge-regularization for inverse problems	4
Imaging in lossy media	4
Direct and inverse scattering in an optical waveguide*	4
Determination of first order perturbation for bi-harmonic operator by asymptotic boundary spectral data	3