Inverse Problems

Article	Citations
Recovering a function from its integrals over conical surfaces through relations with the Radon transform	64
On the convergence of PINNs for inverse source problem in the complex Ginzburg–Landau equation	42
An inverse potential problem for the stochastic heat equation with space-time noise	37
On inverse problems for mean field games with common noise via Carleman estimate*	29
Multipoint formulas in inverse problems and their numerical implementation	27
Inversion of the fixed radius spherical mean Radon transform of F. John in	26
An analysis of constraint-relaxation in PDE-based inverse problems	25
A Bayesian approach for CT reconstruction with defect detection for subsea pipelines	23
On a quantitative partial imaging problem in vector tomography	23
Flow recovery from distal pressure in linearized hemodynamics: an optimal control approach	22
Uniqueness of an inverse cavity scattering problem for the time-harmonic biharmonic wave equation	21
On direct and inverse obstacle scattering problems for biharmonic waves	20
Stochastic mirror descent method for linear ill-posed problems in Banach spaces	19
Imaging conductivity from current density magnitude using neural networks*	19
A Bernstein–von-Mises theorem for the Calderón problem with piecewise constant conductivities	18
Chilled sampling for uncertainty quantification: a motivation from a meteorological inverse problem *	16
A dataset-free deep learning method for low-dose CT image reconstruction	16
Distributed learning with discretely observed functional data	16
Inferring dynamical models from time-series biological data using an interpretable machine learning method based on weighted expression trees	15
A Kirchhoff Migration scheme for elastic obstacle identification	15
Range characterization of the x-ray transform of symmetric complex valued tensor fields	14
Stability of the isotropic conductivity reconstruction using magnetic resonance electrical impedance tomography (MREIT)	14
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
Hearing the shape of a cuboid room using sparse measure recovery	14

Geometric approach for determining stationary phase points in radar imaging	13
Recovering critical parameter for nonlinear Allen–Cahn equation by fully discrete continuous data assimilation algorithms *	13
Radon transform on algebraic Cormack α-curves inversion formula	13
Uniqueness theorems for tomographic phase retrieval with few coded diffraction patterns	13
Stability estimate for an inverse stochastic parabolic problem of determining unknown time-varying boundary *	13
Direct inversion of the Longitudinal ray transform for 2D residual elastic strain fields	13
Efficient decomposition-based algorithms for	12
Stochastic asymptotical regularization for linear inverse problems	12
Parameter estimation in complementarity-constrained parabolic optimal control model: application to American option implied volatility	12
3D refractive index reconstruction from phaseless coherent optical microscopy data using multiple scattering-based inverse solvers—a study	12
Hyperparameter estimation using a resolution matrix for Bayesian sensing	12
Maximum a posteriori estimators in ℓp are well-defined for diagonal Gaussian priors	11
Optimal regularized hypothesis testing in statistical inverse problems	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
Phase retrieval of quaternion signals via augmented Gauss–Newton method	11
Bayesian design of measurements for magnetorelaxometry imaging *	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
Reconstruction of the initial data from the trace of the solutions on an infinite time cylinder of damped wave equations *	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
Bouligand–Newton type methods for non-smooth ill-posed problems	10
Strong maximum a posteriori estimation in Banach spaces with Gaussian priors	10
On the required number of electrodes for uniqueness and convex reformulation in an inverse coefficient problem	10
Matrix recovery from nonconvex regularized least absolute deviations	10
Iterative regularization in classification via hinge loss diagonal descent	10
On optimality and bounds for internal solutions generated from boundary data-driven Gramians	10
Fast iterative reconstruction for multi-spectral CT by a Schmidt orthogonal modification algorithm (SOMA)	10
Primal-dual finite element methods for the direct reconstruction of material coefficients in stationary elliptic problems	10
Statistical microlocal analysis in two-dimensional x-ray CT	10
Low-resolution prior equilibrium network for CT reconstruction	10
Unsupervised knowledge-transfer for learned image reconstruction*	10
Microwave time reversal for nondestructive testing of buried small damage in composite materials	9
Identification problems for anisotropic time-fractional subdiffusion equations	9
Inverse source problem of sub-diffusion of variable exponent	9
The initial-to-final-state inverse problem with time-independent potentials	9
Least-squares reverse time migration based on second-order Born approximation	9
A new nonconvex low-rank tensor approximation method with applications to hyperspectral images denoising	9
Convergence analysis of the discretization of continuous-domain inverse problems	9
Reconstructing the image scanning microscopy dataset: an inverse problem	9
Traveling wave solutions of an equation of Harry Dym type arising in the Black–Scholes framework	9
Nonstationary iterated Tikhonov regularization: convergence analysis via Hölder stability	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
Multi-scale CLEAN for Fourier-based hard x-ray solar imaging	9
On the inverse transmission eigenvalue problem with a piecewise <	8
Some integral geometry problems for wave equations	8
Theory and fast learned solver for	8
Direct sampling for recovering a clamped cavity from the biharmonic far-field data	8

Levenberg–Marquardt hard thresholding pursuit for sparse bilinear inverse problems	8
Stability estimates for the expected utility in Bayesian optimal experimental design	8
DRIP: deep regularizers for inverse problems	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
Lipschitz stability of recovering the conductivity from internal current densities	8
Determining anomalies in a semilinear elliptic equation by a minimal number of measurements	8
In memoriam Edward Roy Pike	8
Shape and orientation classification of objects based on their electromagnetic signatures using convolutional neural networks	8
Full-waveform reconstruction of microseismic events via observations of acoustic pressure in the surrounding fluid	7
Reconstruction of degenerate conductivity region for parabolic equations	7
Analysis of the discrepancy principle for Tikhonov regularization with oversmoothing penalty term under low order source conditions	7
Regularization graphs—a unified framework for variational regularization of inverse problems	7
Randomized block coordinate descent method for linear ill-posed problems	7
ASPIRE: iterative amortized posterior inference for Bayesian inverse problems	7
Mixed geometry information regularization for image deblurring with multiplicative noise	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
Uniqueness and numerical method for phaseless inverse diffraction grating problem with known superposition of incident point sources	7
The C ∞	7
A numerical investigation of matched source waveform inversion applied to acoustic transmission data	7
On the uniqueness of solutions for the basis pursuit in the continuum	7
Inverse problems of damped wave equations with Robin boundary conditions: an application to blood perfusion	7
Solving an inverse source problem by deep neural network method with convergence and error analysis	7
A learning-based hybrid reconstruction scheme for an inverse boundary value problem	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
Importance-aware nonlocal tensor nuclear norm for high-dimensional image recovery	7
An interpretable neural network for diffeomorphic image registration: theory and application	6
The inverse Rytov series for diffuse optical tomography	6
Doubling inequality and strong unique continuation for an elliptic transmission problem *	6
On Bayesian data assimilation for PDEs with ill-posed forward problems	6
Object based Bayesian full-waveform inversion for shear elastography	6
Generalized spherical mean associated with the generalized Darboux equation and its applications	6
Uniqueness in determining rectangular grating profiles with a single incoming wave (part II): TM polarization case	6
Bayesian compressive sensing using generative models	6
Convergence rates of Landweber-type methods for inverse problems in Banach spaces	6
On bias and its reduction via standardization in discretized electromagnetic source localization problems	6
Simultaneous determination of different class of parameters for a diffusion equation from a single measurement	6
On uniqueness and stable estimation of multiple parameters in the Cahn–Hilliard equation	6
In memoriam Pierre Sabatier	6
Low-rank tensor completion with non-local self-similarity and multidimensional learnable transforms*	6
An inexact proximal majorization–minimization method for a class of image reconstruction models	6
Nearly optimal bounds for the global geometric landscape of phase retrieval	6
Convergence analysis of an alternating direction method of multipliers for the identification of nonsmooth diffusion parameters with total variation	6
On the convergence of stochastic variance reduced gradient for linear inverse problems *	6
Stability estimate for the broken non-abelian x-ray transform in Minkowski space	6
Bayesian interface technique-based inverse estimation of closure coefficients of standard	6
Bayesian inversion of log-normal eikonal equations	6
Analysis of beam hardening streaks in tomography	6
Global uniqueness for determining an inverse electromagnetic scattering medium and its physical coefficients	6
Enhanced microscale hydrodynamic near-cloaking using electro-osmosis	6
Inverse source problem for discrete Helmholtz equation	6
Convergence of level sets in fractional Laplacian regularization	6
Rothe’s method in direct and time-dependent inverse source problems for a semilinear pseudo-parabolic equation	6
An iterative algorithm for the square-root Lasso	6
Convergence study and regularizing property of a modified Robin–Robin method for the Cauchy problem in linear elasticity	6
An optimal transport approach for 3D electrical impedance tomography	5
Heavy-ball enhanced pseudo-inverse-based hard thresholding algorithms for sparse linear inverse problems	5
Inverse problem for a nonlocal diffuse optical tomography equation	5
Some direct and inverse source problems in nonlinear evolutionary PDEs with Volterra operators	5
Automatic nonstationary anisotropic Tikhonov regularization through bilevel optimization	5
The domain derivative in inverse obstacle scattering with nonlinear impedance boundary condition	5
Crack identification in a multi-layer inhomogeneous domain using the Reciprocity Gap-Linear Sampling Method	5
Heuristic rule for inexact Newton-Landweber iteration with convex penalty terms of nonlinear: ill-posed problems	5
Kalman-based estimation of loading conditions from ultrasonic guided wave measurements	5
On a numerical construction of doubly stochastic matrices with prescribed eigenvalues	5
Tractable optimal experimental design using transport maps*	5
The monotonicity method for inclusion detection and the time harmonic elastic wave equation	5
Local recovery of a piecewise constant anisotropic conductivity in EIT on domains with exposed corners	5
Reduced-order autodifferentiable ensemble Kalman filters	5
A morphology-adaptive random feature method for inverse source problem of the Helmholtz equation	5
Fused L	5
Stability estimates for an inverse boundary value problem for biharmonic operators with first order perturbation from partial data	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
Theoretical and numerical studies of inverse source problem for the linear parabolic equation with sparse boundary measurements	5
Assessing the potential of using a virtual Veselago lens in quantitative microwave imaging	5
Determination of discontinuous diffusion coefficients for the heat equation on a tree-shaped network	5
Solving inverse acoustic obstacle scattering problem from phaseless far-field measurement using deep neural network surrogates*	5

Sparsity for dynamic inverse problems on Wasserstein curves with bounded variation	5
A probabilistic framework for uncertainty quantification in positron emission particle tracking	5
Uniqueness in determining rectangular grating profiles with a single incoming wave (Part I): TE polarization case	5
An approximate analytical reconstruction method in inverse problems of cone-beam rotary computed laminography	5
PatchNR: learning from very few images by patch normalizing flow regularization	5
A localized consensus-based sampling algorithm	5
Semi-discrete Tikhonov regularization in RKHS with large randomly distributed noise	5
Determining a parabolic system by boundary observation of its non-negative solutions with biological applications	5
The MLE is a reliable source: sharp performance guarantees for localization problems	5
Diffraction tomography for incident Herglotz waves	5
Recovery of a coefficient in a diffusion equation from large time data*	5
Estimation of off-the grid sparse spikes with over-parametrized projected gradient descent: theory and application	5
Fourier method for inverse source problem using correlation of passive measurements*	5
Error estimates and converse results for a class of linear regularization methods for inverse problems in Banach spaces	5
MiPhDUO: microwave imaging via physics-informed deep unrolled optimization	5
An analytical inversion formula for the overdetermined spherical section transform	5
Vertical autofocus for the phase screen in a turbulent ionosphere	5
Determining initial conditions for nonlinear hyperbolic equations with time dimensional reduction and the Carleman contraction principle	5
Deep Gaussian process priors for Bayesian image reconstruction	5
A direct sampling-based deep learning approach for inverse medium scattering problems	5
A mixed finite element scheme for three-dimensional Maxwell’s transmission eigenvalue problems	5
Multiscale hierarchical decomposition methods for ill-posed problems	5
Joint Gaussian dictionary learning and tomographic reconstruction	5
Adaptive anisotropic Bayesian meshing for inverse problems	5
Wirtinger gradient descent methods for low-dose Poisson phase retrieval	4
Radial recombination for rigid rotational alignment of images and volumes	4
Reconstruction of Voronoi diagrams: the case of inverse conductivity problems	4
Distributed spectral pairwise ranking algorithms	4
A Bayesian approach for consistent reconstruction of inclusions	4
Inverse problem for stochastic heat equations with singular inverse-square potentials	4
One-dimensional coefficient inverse problems by transformation operators	4
Joint sparse optimization: lower-order regularization method and application in cell fate conversion	4
Error bounds for extended source inversion applied to an acoustic transmission inverse problem	4
Locally-Supervised Global Image Restoration	4
Moments, time-inversion and source identification for the heat equation	4
Relaxation-based schemes for on-the-fly parameter estimation in dissipative dynamical systems	4
Uncertainty quantification for goal-oriented inverse problems via variational encoder-decoder networks	4
Image analysis and resolution for detection-based synthetic-aperture passive source localization	4
The Radon transform with finitely many angles *	4
Corrigendum: Unique reconstruction of the potential for the interior transmission eigenvalue problem for spherically stratified media (2020 Inverse Problems 36 035017)	4
The inverse obstacle problem for nonlinear inclusions	4
Continuous Gaussian mixture solution for linear Bayesian inversion with application to Laplace priors	4
Bilevel inverse problems in neuromorphic imaging	4
Lipschitz stability of an inverse conductivity problem with two Cauchy data pairs	4
VARPROX: a primal-dual variable projection method for the minimization of penalized separable non-linear least squares	4
Noise-robust one-bit diffraction tomography and optimal dose fractionation	4
The elastic ray transform	4
Direct and inverse scattering in an optical waveguide*	4
TRAC method in dissipative media—a first analysis in frequency domain and homogeneous media	4
Stability estimates for an inverse problem for Schrödinger operators at high frequencies from arbitrary partial boundary measurements	4
A novel epidemiologically informed particle filter for assessing epidemic phenomena. Application to the monkeypox outbreak of 2022	4
Stability of data-dependent ridge-regularization for inverse problems	4
Stability analysis of a new curl-based full field reconstruction method in 2D isotropic nearly-incompressible elasticity	4
On a nonlinear model in domains with cavities arising from cardiac electrophysiology	4
Bayesian view on the training of invertible residual networks for solving linear inverse problems *	4
Discrete nonlinear Fourier transforms and their inverses	4
State estimation approach to dual-modal imaging of two-phase flow based on electromagnetic flow tomography and electrical tomography	4
Recovery of piecewise smooth parameters in an acoustic-gravitational system of equations from exterior Cauchy data	4
Approximation of discontinuous inverse operators with neural networks	4
Bayesian inversion with α-stable priors	4
An optimal Bayesian strategy for comparing Wiener–Hunt deconvolution models in the absence of ground truth	4
Accelerating ill-conditioned Hankel matrix recovery via structured Newton-like descent	4
A novel Newton method for inverse elastic scattering problems	4
Vector-valued spline method for the spherical multiple-shell electro-magnetoencephalography problem	4
Subgradient-based Lavrentiev regularisation of monotone ill-posed problems	4
HyDeFuse: provably convergent denoiser-driven hyperspectral fusion	4
Conditional stability and the numerical solution of the backward problem in dynamical cardiac electrophysiology modeling	4
The implementation in STIR of four analytical algorithms for 2D PET and 2D SPECT reconstruction	4
Discrete inverse problems with internal functionals*	4
Color image restoration based on saturation-value total variation plus L1 fidelity*	4
A reformulation of the equation error approach for direct inversion from full-field interior data	4
Error estimates for Golub–Kahan bidiagonalization with Tikhonov regularization for ill–posed operator equations	4
Simultaneous reconstruction of an obstacle and its wavenumber for the Helmholtz equation: a robust optimization approach	4
Reconstruction of multilayered periodic structures from one-sided acoustic near-field data	4
Solving time-fractional diffusion equations with a singular source term	4
Corrigendum: Solution of an acoustic transmission inverse problem by extended inversion (2022 Inverse Problems 38 115003)	4
In memoriam Mario Bertero	4
Determining sources in the bioluminescence tomography problem	4
An inverse Cauchy problem of a stochastic hyperbolic equation	4
Inverse scattering for the multipoint potentials of Bethe−Peierls−Thomas−Fermi type*	4
A posterior contraction for Bayesian inverse problems in Banach spaces	4
Convergence analysis of regularised Nyström method for functional linear regression	3
Recovery of the matrix potential of the one-dimensional Dirac equation from spectral data	3
V-line 2-tensor tomography in the plane	3
Neural blind deconvolution with Poisson data	3
Dynamic thresholding algorithm with memory for linear inverse problems	3
Relaxation approach for learning neural network regularizers for a class of identification problems	3
MCMC-Net: accelerating Markov Chain Monte Carlo with neural networks for inverse problems	3
Optimising seismic imaging design parameters via bilevel learning	3
Divide-and-conquer DNN approach for the inverse point source problem using a few single frequency measurements	3
Determination of first order perturbation for bi-harmonic operator by asymptotic boundary spectral data	3
3D Poissonian image deblurring via patch-based tensor logarithmic Schatten-p minimization	3
Solution of the EEG inverse problem by random dipole sampling	3
Monotonicity of the Laplace transform for tomography in dissipative systems	3
Inverse radiative transfer with goal-oriented hp-adaptive mesh refinement: adaptive-mesh inversion	3