Inverse Problems

Article	Citations
A Bernstein–von-Mises theorem for the Calderón problem with piecewise constant conductivities	59
Flow recovery from distal pressure in linearized hemodynamics: an optimal control approach	40
Recovering a function from its integrals over conical surfaces through relations with the Radon transform	36
Multipoint formulas in inverse problems and their numerical implementation	28
On inverse problems for mean field games with common noise via Carleman estimate*	26
Stochastic mirror descent method for linear ill-posed problems in Banach spaces	25
Uniqueness of an inverse cavity scattering problem for the time-harmonic biharmonic wave equation	24
An inverse potential problem for the stochastic heat equation with space-time noise	23
Imaging conductivity from current density magnitude using neural networks*	22
On direct and inverse obstacle scattering problems for biharmonic waves	22
On a quantitative partial imaging problem in vector tomography	21
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	21
An analysis of constraint-relaxation in PDE-based inverse problems	19
A Bayesian approach for CT reconstruction with defect detection for subsea pipelines	19
Stability estimate for an inverse stochastic parabolic problem of determining unknown time-varying boundary *	18
Recovering critical parameter for nonlinear Allen–Cahn equation by fully discrete continuous data assimilation algorithms *	17
Fictitious null spaces for improving the solution of injective inverse problems	16
Inferring dynamical models from time-series biological data using an interpretable machine learning method based on weighted expression trees	16
Uniqueness theorems for tomographic phase retrieval with few coded diffraction patterns	15
The reconstruction of surface vibrations from near-field acoustic pressure measurements under steady flow	15
Distributed learning with discretely observed functional data	15
Hearing the shape of a cuboid room using sparse measure recovery	15
Chilled sampling for uncertainty quantification: a motivation from a meteorological inverse problem *	14
Geometric approach for determining stationary phase points in radar imaging	14

A dataset-free deep learning method for low-dose CT image reconstruction	14
Range characterization of the x-ray transform of symmetric complex valued tensor fields	13
Direct inversion of the Longitudinal ray transform for 2D residual elastic strain fields	13
Stability of the isotropic conductivity reconstruction using magnetic resonance electrical impedance tomography (MREIT)	13
Radon transform on algebraic Cormack α-curves inversion formula	13
A Kirchhoff Migration scheme for elastic obstacle identification	13
Hyperparameter estimation using a resolution matrix for Bayesian sensing	12
Phase retrieval of quaternion signals via augmented Gauss–Newton method	12
A mathematical framework for nonlinear wavefront reconstruction in adaptive optics systems with Fourier-type wavefront sensing	12
Maximum a posteriori estimators in ℓp are well-defined for diagonal Gaussian priors	12
Efficient decomposition-based algorithms for	12
Solving the acousto-electric tomography by the adaptive Nesterov method of Kaczmarz type	11
Optimal regularized hypothesis testing in statistical inverse problems	11
Parameter estimation in complementarity-constrained parabolic optimal control model: application to American option implied volatility	11
Bayesian design of measurements for magnetorelaxometry imaging *	11
Minimizing L 1 over L 2 norms on the gradient	11
Reconstruction of the initial data from the trace of the solutions on an infinite time cylinder of damped wave equations *	11
Stochastic asymptotical regularization for linear inverse problems	11
3D refractive index reconstruction from phaseless coherent optical microscopy data using multiple scattering-based inverse solvers—a study	11
Double-parameter regularization for solving the backward diffusion problem with parallel-in-time algorithm	11
On inertial iterated Tikhonov methods for solving ill-posed problems	11
Stability for a multi-frequency inverse random source problem	11
Matrix recovery from nonconvex regularized least absolute deviations	11
A two-stage numerical approach for the sparse initial source identification of a diffusion–advection equation *	11
Reconstructing the image scanning microscopy dataset: an inverse problem	10
Bouligand–Newton type methods for non-smooth ill-posed problems	10
On the required number of electrodes for uniqueness and convex reformulation in an inverse coefficient problem	10
Statistical microlocal analysis in two-dimensional x-ray CT	10
On optimality and bounds for internal solutions generated from boundary data-driven Gramians	10
Iterative regularization in classification via hinge loss diagonal descent	10
Low-resolution prior equilibrium network for CT reconstruction	10
Least-squares reverse time migration based on second-order Born approximation	10
Strong maximum a posteriori estimation in Banach spaces with Gaussian priors	10
Unsupervised knowledge-transfer for learned image reconstruction*	10
Convergence analysis of the discretization of continuous-domain inverse problems	9
Fast iterative reconstruction for multi-spectral CT by a Schmidt orthogonal modification algorithm (SOMA)	9
Shape and orientation classification of objects based on their electromagnetic signatures using convolutional neural networks	9
Microwave time reversal for nondestructive testing of buried small damage in composite materials	9
Inverse source problem of sub-diffusion of variable exponent	9
A new nonconvex low-rank tensor approximation method with applications to hyperspectral images denoising	9
Traveling wave solutions of an equation of Harry Dym type arising in the Black–Scholes framework	9
Stable determination of coefficients in semilinear parabolic system with dynamic boundary conditions	9
Identification problems for anisotropic time-fractional subdiffusion equations	9
Norms in sinogram space and stability estimates for the Radon transform	9
Nonstationary iterated Tikhonov regularization: convergence analysis via Hölder stability	9
In memoriam Edward Roy Pike	8
Lipschitz stability of recovering the conductivity from internal current densities	8
Reconstruction of degenerate conductivity region for parabolic equations	8
Singular value decomposition for longitudinal, transverse and mixed ray transforms of 2D tensor fields	8
The initial-to-final-state inverse problem with time-independent potentials	8

Levenberg–Marquardt hard thresholding pursuit for sparse bilinear inverse problems	8
Stability estimates for the expected utility in Bayesian optimal experimental design	8
Uniqueness and numerical method for phaseless inverse diffraction grating problem with known superposition of incident point sources	8
Direct sampling for recovering a clamped cavity from the biharmonic far-field data	8
GPU accelerated 3D source free adaptive wavefield reconstruction inversion for seismic imaging	8
On the inverse transmission eigenvalue problem with a piecewise <	8
Inverse problems of damped wave equations with Robin boundary conditions: an application to blood perfusion	8
DRIP: deep regularizers for inverse problems	8
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
Some integral geometry problems for wave equations	7
Coercivity-based analysis and its application to an inverse source problem for a subdiffusion equation with time-dependent principal parts	7
ASPIRE: iterative amortized posterior inference for Bayesian inverse problems	7
Enhanced microscale hydrodynamic near-cloaking using electro-osmosis	7
A numerical investigation of matched source waveform inversion applied to acoustic transmission data	7
Determining anomalies in a semilinear elliptic equation by a minimal number of measurements	7
Reconstructing the shape and material parameters of dissipative obstacles using an impedance model	7
A learning-based hybrid reconstruction scheme for an inverse boundary value problem	7
Randomized block coordinate descent method for linear ill-posed problems	7
Mixed geometry information regularization for image deblurring with multiplicative noise	7
Importance-aware nonlocal tensor nuclear norm for high-dimensional image recovery	7
The C ∞	7
Multi-scale CLEAN for Fourier-based hard x-ray solar imaging	7
Theory and fast learned solver for	7
Full-waveform reconstruction of microseismic events via observations of acoustic pressure in the surrounding fluid	7
On the uniqueness of solutions for the basis pursuit in the continuum	7
Non-zero constraints in elliptic PDE with random boundary values and applications to hybrid inverse problems	7
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
Low-rank tensor completion with non-local self-similarity and multidimensional learnable transforms*	6
Nearly optimal bounds for the global geometric landscape of phase retrieval	6
Object based Bayesian full-waveform inversion for shear elastography	6
Doubling inequality and strong unique continuation for an elliptic transmission problem *	6
Automatic nonstationary anisotropic Tikhonov regularization through bilevel optimization	6
On bias and its reduction via standardization in discretized electromagnetic source localization problems	6
Convergence of level sets in fractional Laplacian regularization	6
Bayesian interface technique-based inverse estimation of closure coefficients of standard	6
Uniqueness in determining rectangular grating profiles with a single incoming wave (part II): TM polarization case	6
Inverse source problem for discrete Helmholtz equation	6
Generalized spherical mean associated with the generalized Darboux equation and its applications	6
Phase retrieval and phaseless inverse scattering with background information	6
Rothe's method in direct and time-dependent inverse source problems for a semilinear pseudo-parabolic equation	6
Stability estimate for the broken non-abelian x-ray transform in Minkowski space	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
Bayesian inversion of log-normal eikonal equations	6
In memoriam Pierre Sabatier	6
On Bayesian data assimilation for PDEs with ill-posed forward problems	6
Regularization graphs—a unified framework for variational regularization of inverse problems	6
A stochastic gradient descent approach with partitioned-truncated singular value decomposition for large-scale inverse problems of magnetic modulus data	6
Analysis of beam hardening streaks in tomography	6
On uniqueness and stable estimation of multiple parameters in the Cahn–Hilliard equation	6
The inverse Rytov series for diffuse optical tomography	6
Vertical autofocus for the phase screen in a turbulent ionosphere	6
Heavy-ball enhanced pseudo-inverse-based hard thresholding algorithms for sparse linear inverse problems	5
Analysis of the inverse Born series: an approach through geometric function theory	5
Convergence study and regularizing property of a modified Robin–Robin method for the Cauchy problem in linear elasticity	5
Sparsity for dynamic inverse problems on Wasserstein curves with bounded variation	5
Recovery of a coefficient in a diffusion equation from large time data*	5
Semi-discrete Tikhonov regularization in RKHS with large randomly distributed noise	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
An iterative algorithm for the square-root Lasso	5
Kalman-based estimation of loading conditions from ultrasonic guided wave measurements	5
Fused L	5
A direct sampling-based deep learning approach for inverse medium scattering problems	5
Fourier method for inverse source problem using correlation of passive measurements*	5
The domain derivative in inverse obstacle scattering with nonlinear impedance boundary condition	5
The monotonicity method for inclusion detection and the time harmonic elastic wave equation	5
An optimal transport approach for 3D electrical impedance tomography	5
Analysis of the monotonicity method for an anisotropic scatterer with a conductive boundary	5
Stability estimates for an inverse boundary value problem for biharmonic operators with first order perturbation from partial data	5
A localized consensus-based sampling algorithm	5
Determining initial conditions for nonlinear hyperbolic equations with time dimensional reduction and the Carleman contraction principle	5
Corrigendum: On uniqueness of an inverse problem in electromagnetic obstacle scattering for an impedance cylinder (2012 Inverse Problems  28 055012)	5
Multiscale hierarchical decomposition methods for ill-posed problems	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
Adaptive anisotropic Bayesian meshing for inverse problems	5
Deep Gaussian process priors for Bayesian image reconstruction	5

Estimation of off-the grid sparse spikes with over-parametrized projected gradient descent: theory and application	5
Assessing the potential of using a virtual Veselago lens in quantitative microwave imaging	5
Theoretical and numerical studies of inverse source problem for the linear parabolic equation with sparse boundary measurements	5
Joint Gaussian dictionary learning and tomographic reconstruction	5
Bayesian compressive sensing using generative models	5
Diffraction tomography for incident Herglotz waves	5
MiPhDUO: microwave imaging via physics-informed deep unrolled optimization	5
Determining a parabolic system by boundary observation of its non-negative solutions with biological applications	5
Determination of discontinuous diffusion coefficients for the heat equation on a tree-shaped network	5
Error estimates and converse results for a class of linear regularization methods for inverse problems in Banach spaces	5
Convergence rates of Landweber-type methods for inverse problems in Banach spaces	5
An analytical inversion formula for the overdetermined spherical section transform	5
A mixed finite element scheme for three-dimensional Maxwell’s transmission eigenvalue problems	5
The MLE is a reliable source: sharp performance guarantees for localization problems	5
PatchNR: learning from very few images by patch normalizing flow regularization	5
A probabilistic framework for uncertainty quantification in positron emission particle tracking	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
On the convergence of stochastic variance reduced gradient for linear inverse problems *	5
Reduced-order autodifferentiable ensemble Kalman filters	5
Error estimates for Golub–Kahan bidiagonalization with Tikhonov regularization for ill–posed operator equations	4
A novel epidemiologically informed particle filter for assessing epidemic phenomena. Application to the monkeypox outbreak of 2022	4
One-dimensional coefficient inverse problems by transformation operators	4
Radial recombination for rigid rotational alignment of images and volumes	4
Reconstruction of multilayered periodic structures from one-sided acoustic near-field data	4
Joint sparse optimization: lower-order regularization method and application in cell fate conversion	4
On a nonlinear model in domains with cavities arising from cardiac electrophysiology	4
The inverse obstacle problem for nonlinear inclusions	4
The Radon transform with finitely many angles *	4
A Bayesian approach for consistent reconstruction of inclusions	4
Bayesian inversion with α-stable priors	4
Uniqueness in determining rectangular grating profiles with a single incoming wave (Part I): TE polarization case	4
Direct and inverse scattering in an optical waveguide*	4
VARPROX: a primal-dual variable projection method for the minimization of penalized separable non-linear least squares	4
Discrete inverse problems with internal functionals*	4
An approximate analytical reconstruction method in inverse problems of cone-beam rotary computed laminography	4
Image analysis and resolution for detection-based synthetic-aperture passive source localization	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
Bayesian view on the training of invertible residual networks for solving linear inverse problems *	4
Vector-valued spline method for the spherical multiple-shell electro-magnetoencephalography problem	4
In memoriam Mario Bertero	4
Microlocal properties of seven-dimensional lemon and apple Radon transforms with applications in Compton scattering tomography	4
Approximation of discontinuous inverse operators with neural networks	4
Uncertainty quantification for goal-oriented inverse problems via variational encoder-decoder networks	4
The implementation in STIR of four analytical algorithms for 2D PET and 2D SPECT reconstruction	4
Recovery of piecewise smooth parameters in an acoustic-gravitational system of equations from exterior Cauchy data	4
Noise-robust one-bit diffraction tomography and optimal dose fractionation	4
On a numerical construction of doubly stochastic matrices with prescribed eigenvalues	4
Corrigendum: Solution of an acoustic transmission inverse problem by extended inversion (2022 Inverse Problems 38 115003)	4
A posterior contraction for Bayesian inverse problems in Banach spaces	4
TRAC method in dissipative media—a first analysis in frequency domain and homogeneous media	4
Corrigendum: Unique reconstruction of the potential for the interior transmission eigenvalue problem for spherically stratified media (2020 Inverse Problems 36 035017)	4
An inverse Cauchy problem of a stochastic hyperbolic equation	4
Tractable optimal experimental design using transport maps*	4
Accelerating ill-conditioned Hankel matrix recovery via structured Newton-like descent	4
Simultaneous reconstruction of an obstacle and its wavenumber for the Helmholtz equation: a robust optimization approach	4
Color image restoration based on saturation-value total variation plus L1 fidelity*	4
Solving time-fractional diffusion equations with a singular source term	4
Lipschitz stability of an inverse conductivity problem with two Cauchy data pairs	4
State estimation approach to dual-modal imaging of two-phase flow based on electromagnetic flow tomography and electrical tomography	4
Error bounds for extended source inversion applied to an acoustic transmission inverse problem	4
An optimal Bayesian strategy for comparing Wiener–Hunt deconvolution models in the absence of ground truth	4
Moments, time-inversion and source identification for the heat equation	4
Continuous Gaussian mixture solution for linear Bayesian inversion with application to Laplace priors	4
Discrete nonlinear Fourier transforms and their inverses	4
HyDeFuse: provably convergent denoiser-driven hyperspectral fusion	4
Reconstruction of Voronoi diagrams: the case of inverse conductivity problems	4
Bilevel inverse problems in neuromorphic imaging	4
Stability estimates for an inverse problem for Schrödinger operators at high frequencies from arbitrary partial boundary measurements	4
Imaging in lossy media	4
Determining sources in the bioluminescence tomography problem	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
Convergence rate of Tikhonov regularization for identifying parameters in the elastic wave system under a positive condition	3
An inverse source problem for semilinear stochastic hyperbolic equations	3
Microtexture region segmentation of eddy current testing data using a structural prior	3
Recovery of the matrix potential of the one-dimensional Dirac equation from spectral data	3
Neural blind deconvolution with Poisson data	3
Determination of first order perturbation for bi-harmonic operator by asymptotic boundary spectral data	3
Divide-and-conquer DNN approach for the inverse point source problem using a few single frequency measurements	3
Inverse scattering problem for the third-order equation on the line *	3
Pseudo-differential integral autoencoder network for inverse PDE operators	3
Optimising seismic imaging design parameters via bilevel learning	3
3D Poissonian image deblurring via patch-based tensor logarithmic Schatten-p minimization	3
The factorization method and Capon’s method for random source identification in experimental aeroacoustics	3
Monotonicity of the Laplace transform for tomography in dissipative systems	3
Solution of the EEG inverse problem by random dipole sampling	3
Nonlinearity helps the convergence of the inverse Born series	3
Fast ℓ	3
Convergence analysis of regularised Nyström method for functional linear regression	3
Inverse radiative transfer with goal-oriented hp-adaptive mesh refinement: adaptive-mesh inversion	3
Dynamic thresholding algorithm with memory for linear inverse problems	3
V-line 2-tensor tomography in the plane	3
MCMC-Net: accelerating Markov Chain Monte Carlo with neural networks for inverse problems	3