Inverse Problems

Article	Citations
A Bayesian approach for CT reconstruction with defect detection for subsea pipelines	40
Multipoint formulas in inverse problems and their numerical implementation	38
Uniqueness of an inverse cavity scattering problem for the time-harmonic biharmonic wave equation	31
On direct and inverse obstacle scattering problems for biharmonic waves	28
Structure analysis of direct sampling method in 3D electromagnetic inverse problem: near- and far-field configuration	27
On inverse problems for mean field games with common noise via Carleman estimate*	23
An analysis of constraint-relaxation in PDE-based inverse problems	23
A Bernstein–von-Mises theorem for the Calderón problem with piecewise constant conductivities	21
Recovering a function from its integrals over conical surfaces through relations with the Radon transform	20
Imaging conductivity from current density magnitude using neural networks*	19
A probabilistic approach to tomography and adjoint state methods, with an application to full waveform inversion in medical ultrasound	18
Flow recovery from distal pressure in linearized hemodynamics: an optimal control approach	18
Stochastic mirror descent method for linear ill-posed problems in Banach spaces	18
Direct inversion of the Longitudinal ray transform for 2D residual elastic strain fields	16
Distributed learning with discretely observed functional data	16
Stability of an inverse source problem for the damped biharmonic plate equation	16
Determination of a spatial load in a damped Kirchhoff–Love plate equation from final time measured data	15
Fictitious null spaces for improving the solution of injective inverse problems	15
Recovering critical parameter for nonlinear Allen–Cahn equation by fully discrete continuous data assimilation algorithms *	15
The reconstruction of surface vibrations from near-field acoustic pressure measurements under steady flow	15
Uniqueness theorems for tomographic phase retrieval with few coded diffraction patterns	14
An inverse problem for generalized Kelvin–Voigt equation with p-Laplacian and damping term	14
Stability of the isotropic conductivity reconstruction using magnetic resonance electrical impedance tomography (MREIT)	14
A Kirchhoff Migration scheme for elastic obstacle identification	14
Inferring dynamical models from time-series biological data using an interpretable machine learning method based on weighted expression trees	14

Geometric approach for determining stationary phase points in radar imaging	13
Addendum: On stochastic Kaczmarz type methods for solving large scale systems of ill-posed equations (2022 Inverse Problems 38 025003)	13
Chilled sampling for uncertainty quantification: a motivation from a meteorological inverse problem *	13
Radon transform on algebraic Cormack α-curves inversion formula	13
A dataset-free deep learning method for low-dose CT image reconstruction	12
Stability for a multi-frequency inverse random source problem	12
Optimal regularized hypothesis testing in statistical inverse problems	12
Bayesian design of measurements for magnetorelaxometry imaging *	12
Stability estimate for an inverse stochastic parabolic problem of determining unknown time-varying boundary *	12
Reconstruction of the initial data from the trace of the solutions on an infinite time cylinder of damped wave equations *	11
Maximum a posteriori estimators in ℓp are well-defined for diagonal Gaussian priors	11
A mathematical framework for nonlinear wavefront reconstruction in adaptive optics systems with Fourier-type wavefront sensing	11
Stochastic asymptotical regularization for linear inverse problems	11
Matrix recovery from nonconvex regularized least absolute deviations	11
Hyperparameter estimation using a resolution matrix for Bayesian 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
On inertial iterated Tikhonov methods for solving ill-posed problems	11
Solving the acousto-electric tomography by the adaptive Nesterov method of Kaczmarz type	11
Double-parameter regularization for solving the backward diffusion problem with parallel-in-time algorithm	11
Unsupervised knowledge-transfer for learned image reconstruction*	10
Nonstationary iterated Tikhonov regularization: convergence analysis via Hölder stability	10
A statistical reconstruction model for absorption CT with source uncertainty *	10
A two-stage numerical approach for the sparse initial source identification of a diffusion–advection equation *	10
Bouligand–Newton type methods for non-smooth ill-posed problems	10
Strong maximum a posteriori estimation in Banach spaces with Gaussian priors	10
Iterative regularization in classification via hinge loss diagonal descent	9
Lipschitz stability of recovering the conductivity from internal current densities	9
Reconstructing the shape and material parameters of dissipative obstacles using an impedance model	9
Reconstructing the image scanning microscopy dataset: an inverse problem	9
Microwave time reversal for nondestructive testing of buried small damage in composite materials	9
Robust signal recovery for ℓ 1–2 minimization via prior support information	9
A new nonconvex low-rank tensor approximation method with applications to hyperspectral images denoising	9
Multi-scale CLEAN for Fourier-based hard x-ray solar imaging	9
Low-resolution prior equilibrium network for CT reconstruction	9
Convergence analysis of the discretization of continuous-domain inverse problems	9
Stable determination of coefficients in semilinear parabolic system with dynamic boundary conditions	9
Reconstruction of degenerate conductivity region for parabolic equations	9
Adaptive Tikhonov strategies for stochastic ensemble Kalman inversion	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	8
DRIP: deep regularizers for inverse problems	8
Theory and fast learned solver for	8
Uniqueness and numerical method for phaseless inverse diffraction grating problem with known superposition of incident point sources	8
Remarks on the factorization and monotonicity method for inverse acoustic scatterings	8
GPU accelerated 3D source free adaptive wavefield reconstruction inversion for seismic imaging	8
Singular value decomposition for longitudinal, transverse and mixed ray transforms of 2D tensor fields	8
Determining anomalies in a semilinear elliptic equation by a minimal number of measurements	8
Direct sampling for recovering a clamped cavity from the biharmonic far-field data	8
Solving an inverse source problem by deep neural network method with convergence and error analysis	8

Some integral geometry problems for wave equations	8
Norms in sinogram space and stability estimates for the Radon transform	8
Inverse problems of damped wave equations with Robin boundary conditions: an application to blood perfusion	8
Stability estimates for the expected utility in Bayesian optimal experimental design	8
ASPIRE: iterative amortized posterior inference for Bayesian inverse problems	8
Generalized inexact Newton regularization for nonlinear ill-posed problems in Banach spaces	7
Phase retrieval and phaseless inverse scattering with background information	7
Local saddles of relaxed averaged alternating reflections algorithms on phase retrieval	7
Analysis of the discrepancy principle for Tikhonov regularization with oversmoothing penalty term under low order source conditions	7
Reduced order model approach for imaging with waves	7
Non-zero constraints in elliptic PDE with random boundary values and applications to hybrid inverse problems	7
Randomized block coordinate descent method for linear ill-posed problems	7
Regularization graphs—a unified framework for variational regularization of inverse problems	7
Deep neural-network based optimization for the design of a multi-element surface magnet for MRI applications	7
The lower bound of nonlocal gradient for non-convex and non-smooth image patches based regularization	7
Enhanced microscale hydrodynamic near-cloaking using electro-osmosis	7
On bias and its reduction via standardization in discretized electromagnetic source localization problems	7
A stochastic gradient descent approach with partitioned-truncated singular value decomposition for large-scale inverse problems of magnetic modulus data	7
On the uniqueness of solutions for the basis pursuit in the continuum	7
Coercivity-based analysis and its application to an inverse source problem for a subdiffusion equation with time-dependent principal parts	7
Low-rank tensor completion with non-local self-similarity and multidimensional learnable transforms*	7
Bayesian inversion of log-normal eikonal equations	7
Uniqueness in determining rectangular grating profiles with a single incoming wave (part II): TM polarization case	7
Inverse source problem for discrete Helmholtz equation	7
In memoriam Pierre Sabatier	7
Nearly optimal bounds for the global geometric landscape of phase retrieval	7
The C∞ -isomorphism property for a class of singularly-weighted x-ray transforms	7
Object based Bayesian full-waveform inversion for shear elastography	7
On the stability of recovering two sources and initial status in a stochastic hyperbolic-parabolic system	7
On Bayesian data assimilation for PDEs with ill-posed forward problems	6
Fourier reconstruction for diffraction tomography of an object rotated into arbitrary orientations	6
The inverse Rytov series for diffuse optical tomography	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
Regularization of the factorization method applied to diffuse optical tomography	6
Permeability estimation of a porous structure in cancer treatment based on sampled velocity measurement*	6
Fourier method for inverse source problem using correlation of passive measurements*	6
Robust kernel-based distribution regression	6
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
Local recovery of a piecewise constant anisotropic conductivity in EIT on domains with exposed corners	6
An inexact proximal majorization–minimization method for a class of image reconstruction models	6
Convergence of level sets in fractional Laplacian regularization	6
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
Increasing stability in the linearized inverse Schrödinger potential problem with power type nonlinearities*	5
MiPhDUO: microwave imaging via physics-informed deep unrolled optimization	5
The MLE is a reliable source: sharp performance guarantees for localization problems	5
Analysis of the inverse Born series: an approach through geometric function theory	5
Projection methods for high numerical aperture phase retrieval	5
Determining initial conditions for nonlinear hyperbolic equations with time dimensional reduction and the Carleman contraction principle	5
An optimal transport approach for 3D electrical impedance tomography	5
Kalman-based estimation of loading conditions from ultrasonic guided wave measurements	5
Convergence study and regularizing property of a modified Robin–Robin method for the Cauchy problem in linear elasticity	5
Convergence rates of Landweber-type methods for inverse problems in Banach spaces	5
Stability estimate for the broken non-abelian x-ray transform in Minkowski space	5
Recovery of a coefficient in a diffusion equation from large time data*	5
Analysis of the monotonicity method for an anisotropic scatterer with a conductive boundary	5
Joint Gaussian dictionary learning and tomographic reconstruction	5
Electric impedance tomography problem for surfaces with internal holes *	5
Corrigendum: On uniqueness of an inverse problem in electromagnetic obstacle scattering for an impedance cylinder (2012 Inverse Problems 28 055012)	5
The domain derivative in inverse obstacle scattering with nonlinear impedance boundary condition	5
Adaptive anisotropic Bayesian meshing for inverse problems	5
Theoretical and numerical studies of inverse source problem for the linear parabolic equation with sparse boundary measurements	5
Carleman contraction mapping for a 1D inverse scattering problem with experimental time-dependent data	5
Vertical autofocus for the phase screen in a turbulent ionosphere	5
Multiscale hierarchical decomposition methods for ill-posed problems	5
Semi-discrete Tikhonov regularization in RKHS with large randomly distributed noise	5
Reduced-order autodifferentiable ensemble Kalman filters	5
Some direct and inverse source problems in nonlinear evolutionary PDEs with Volterra operators	5
Stability estimates for an inverse boundary value problem for biharmonic operators with first order perturbation from partial data	5
Sound speed uncertainty in acousto-electric tomography	5
The monotonicity method for inclusion detection and the time harmonic elastic wave equation	5
A probabilistic framework for uncertainty quantification in positron emission particle tracking	5
Inverse problem for a nonlocal diffuse optical tomography equation	5
A variational non-linear constrained model for the inversion of FDEM data*	4
Joint estimation of Robin coefficient and domain boundary for the Poisson problem	4
Continuous Gaussian mixture solution for linear Bayesian inversion with application to Laplace priors	4
The inverse obstacle problem for nonlinear inclusions	4
Stability estimates for an inverse problem for Schrödinger operators at high frequencies from arbitrary partial boundary measurements	4

Optimal indirect estimation for linear inverse problems with discretely sampled functional data	4
Stability of data-dependent ridge-regularization for inverse problems	4
Uncertainty quantification for goal-oriented inverse problems via variational encoder-decoder networks	4
The Radon transform with finitely many angles *	4
Lipschitz stability of an inverse conductivity problem with two Cauchy data pairs	4
Determining sources in the bioluminescence tomography problem	4
Assessing the potential of using a virtual Veselago lens in quantitative microwave imaging	4
PatchNR: learning from very few images by patch normalizing flow regularization	4
A direct sampling-based deep learning approach for inverse medium scattering problems	4
A mixed finite element scheme for three-dimensional Maxwell’s transmission eigenvalue problems	4
Consistency of Bayesian inference with Gaussian process priors for a parabolic inverse problem	4
Error bounds for extended source inversion applied to an acoustic transmission inverse problem	4
A posterior contraction for Bayesian inverse problems in Banach spaces	4
Bilevel inverse problems in neuromorphic imaging	4
Vector-valued spline method for the spherical multiple-shell electro-magnetoencephalography problem	4
Wirtinger gradient descent methods for low-dose Poisson phase retrieval	4
Deep Gaussian Process Priors for Bayesian Image Reconstruction	4
Error estimates for Golub–Kahan bidiagonalization with Tikhonov regularization for ill–posed operator equations	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
On a numerical construction of doubly stochastic matrices with prescribed eigenvalues	4
Inverse problem of reconstruction of degenerate diffusion coefficient in a parabolic equation	4
Estimation of off-the grid sparse spikes with over-parametrized projected gradient descent: theory and application	4
Diffraction tomography for incident Herglotz waves	4
One-dimensional coefficient inverse problems by transformation operators	4
Microlocal properties of seven-dimensional lemon and apple Radon transforms with applications in Compton scattering tomography	4
Direct and inverse scattering in an optical waveguide*	4
A Bayesian approach for consistent reconstruction of inclusions	4
Color image restoration based on saturation-value total variation plus L1 fidelity*	4
Reconstruction of Voronoi diagrams: the case of inverse conductivity problems	4
Tractable optimal experimental design using transport maps*	4
Nonlocal low-rank regularized two-phase approach for mixed noise removal	4
Corrigendum: Solution of an acoustic transmission inverse problem by extended inversion (2022 Inverse Problems 38 115003)	4
On a nonlinear model in domains with cavities arising from cardiac electrophysiology	4
Discrete nonlinear Fourier transforms and their inverses	4
Sequentially optimized projections in x-ray imaging *	4
Determining a parabolic system by boundary observation of its non-negative solutions with biological applications	4
A fast image reconstruction method for planar objects CT inspired by differentiation property of Fourier transform (DPFT)	4
Convergence of non-linear diagonal frame filtering for regularizing inverse problems	3
Conforming and nonconforming finite element methods for biharmonic inverse source problem	3
Initial state estimation from limited observations of the heat equation in metric graphs	3
Bayesian image segmentation under varying blur with triplet Markov random field	3
Simultaneous recovery of a locally rough interface and the embedded obstacle with its surrounding medium	3
Discrete Calderón problem with partial data	3
Corrigendum: Unique reconstruction of the potential for the interior transmission eigenvalue problem for spherically stratified media (2020 Inverse Problems 36 035017)	3
Precursors for synthetic aperture radar	3
Distributed spectral pairwise ranking algorithms	3
A new interpretation of (Tikhonov) regularization	3
Divide-and-conquer DNN approach for the inverse point source problem using a few single frequency measurements	3
Restoring the discontinuous heat equation source using sparse boundary data and dynamic sensors	3
Microtexture region segmentation of eddy current testing data using a structural prior	3
TRAC method in dissipative media—a first analysis in frequency domain and homogeneous media	3
V-line 2-tensor tomography in the plane	3
Uniqueness results for inverse source problems for semilinear elliptic equations	3
Inverse conductivity problem with one measurement: uniqueness of multi-layer structures	3
Image analysis and resolution for detection-based synthetic-aperture passive source localization	3
Relaxation approach for learning neural network regularizers for a class of identification problems	3
An inverse Cauchy problem of a stochastic hyperbolic equation	3
Subgradient-based Lavrentiev regularisation of monotone ill-posed problems	3
Approximation of discontinuous inverse operators with neural networks	3
Bayesian view on the training of invertible residual networks for solving linear inverse problems *	3
Eigenvalue-free iterative shrinkage-thresholding algorithm for solving the linear inverse problems	3
Solving time-fractional diffusion equations with a singular source term	3
On the uniqueness of inverse problems for the reduced wave equation with unknown embedded obstacles	3
State estimation approach to dual-modal imaging of two-phase flow based on electromagnetic flow tomography and electrical tomography	3
Fixed-distance multipoint formulas for the scattering amplitude from phaseless measurements	3
Reconstruction of the doping profile in Vlasov–Poisson system	3
Sampling for the V-line transform with vertex on a circle	3
Dynamic thresholding algorithm with memory for linear inverse problems	3
The Dantzig selector: recovery of signal via ℓ 1 − αℓ 2 minimization	3
A local in time existence and uniqueness result of an inverse problem for the Kelvin-Voigt fluids	3
Numerical conductivity reconstruction from partial interior current density information in three dimensions	3
Determining the viscosity of the Navier–Stokes equations from observations of finitely many modes	3
Sampling complexity on phase retrieval from masked Fourier measurements via Wirtinger flow*	3
Machine learning enhanced electrical impedance tomography for 2D materials	3
High resolution 3D ultrasonic breast imaging by time-domain full waveform inversion	3
Size estimates for nanoplates	3
In memoriam Mario Bertero	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
Inversion of α-sine and α-cosine transforms on R	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
Feature augmentation for the inversion of the Fourier transform with limited data	3
A modified discrepancy principle to attain optimal convergence rates under unknown noise	3
fg-ORKA: fast and gridless reconstruction of moving and deforming objects in multidimensional data	3
Potential coefficient identification problem in parabolic equation with deep neural networks	3
Far field operator splitting and completion in inverse medium scattering	3
Un-supervised learning for blind image deconvolution via Monte-Carlo sampling	3
Solution of the EEG inverse problem by random dipole sampling	3
Relaxation-based schemes for on-the-fly parameter estimation in dissipative dynamical systems	3
Spectral decomposition of atomic structures in heterogeneous cryo-EM	3
A novel epidemiologically informed particle filter for assessing epidemic phenomena. Application to the monkeypox outbreak of 2022	3
Piecewise nonlinear materials and Monotonicity Principle	3
A novel Newton method for inverse elastic scattering problems	3