Inverse Problems

Article	Citations
A Bayesian approach for CT reconstruction with defect detection for subsea pipelines	45
On direct and inverse obstacle scattering problems for biharmonic waves	43
Uniqueness of an inverse cavity scattering problem for the time-harmonic biharmonic wave equation	32
An analysis of constraint-relaxation in PDE-based inverse problems	25
Multipoint formulas in inverse problems and their numerical implementation	23
Stochastic mirror descent method for linear ill-posed problems in Banach spaces	22
An inverse potential problem for the stochastic heat equation with space-time noise	22
On inverse problems for mean field games with common noise via Carleman estimate*	21
On a quantitative partial imaging problem in vector tomography	20
A Bernstein–von-Mises theorem for the Calderón problem with piecewise constant conductivities	20
Flow recovery from distal pressure in linearized hemodynamics: an optimal control approach	19
Recovering a function from its integrals over conical surfaces through relations with the Radon transform	19
Imaging conductivity from current density magnitude using neural networks*	18
A dataset-free deep learning method for low-dose CT image reconstruction	17
Distributed learning with discretely observed functional data	16
Fictitious null spaces for improving the solution of injective inverse problems	16
Geometric approach for determining stationary phase points in radar imaging	16
A probabilistic approach to tomography and adjoint state methods, with an application to full waveform inversion in medical ultrasound	16
Addendum: On stochastic Kaczmarz type methods for solving large scale systems of ill-posed equations (2022 Inverse Problems 38 025003)	15
A Kirchhoff Migration scheme for elastic obstacle identification	15
Stability of the isotropic conductivity reconstruction using magnetic resonance electrical impedance tomography (MREIT)	15
The reconstruction of surface vibrations from near-field acoustic pressure measurements under steady flow	15
Stability estimate for an inverse stochastic parabolic problem of determining unknown time-varying boundary *	14
Inferring dynamical models from time-series biological data using an interpretable machine learning method based on weighted expression trees	14
Recovering critical parameter for nonlinear Allen–Cahn equation by fully discrete continuous data assimilation algorithms *	13

Determination of a spatial load in a damped Kirchhoff–Love plate equation from final time measured data	13
Chilled sampling for uncertainty quantification: a motivation from a meteorological inverse problem *	13
Uniqueness theorems for tomographic phase retrieval with few coded diffraction patterns	13
Direct inversion of the Longitudinal ray transform for 2D residual elastic strain fields	12
Efficient decomposition-based algorithms for	12
Bayesian design of measurements for magnetorelaxometry imaging *	12
Hearing the shape of a cuboid room using sparse measure recovery	12
3D refractive index reconstruction from phaseless coherent optical microscopy data using multiple scattering-based inverse solvers—a study	12
Radon transform on algebraic Cormack α-curves inversion formula	12
A mathematical framework for nonlinear wavefront reconstruction in adaptive optics systems with Fourier-type wavefront sensing	12
A two-stage numerical approach for the sparse initial source identification of a diffusion–advection equation *	11
Maximum a posteriori estimators in ℓp are well-defined for diagonal Gaussian priors	11
Optimal regularized hypothesis testing in statistical inverse problems	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
Hyperparameter estimation using a resolution matrix for Bayesian sensing	11
Matrix recovery from nonconvex regularized least absolute deviations	10
Minimizing L 1 over L 2 norms on the gradient	10
Strong maximum a posteriori estimation in Banach spaces with Gaussian priors	10
Double-parameter regularization for solving the backward diffusion problem with parallel-in-time algorithm	10
Fast iterative reconstruction for multi-spectral CT by a Schmidt orthogonal modification algorithm (SOMA)	10
Microwave time reversal for nondestructive testing of buried small damage in composite materials	10
On inertial iterated Tikhonov methods for solving ill-posed problems	10
Reconstruction of the initial data from the trace of the solutions on an infinite time cylinder of damped wave equations *	10
Bouligand–Newton type methods for non-smooth ill-posed problems	10
Stochastic asymptotical regularization for linear inverse problems	10
Shape and orientation classification of objects based on their electromagnetic signatures using convolutional neural networks	9
Nonstationary iterated Tikhonov regularization: convergence analysis via Hölder stability	9
Unsupervised knowledge-transfer for learned image reconstruction*	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
Convergence analysis of the discretization of continuous-domain inverse problems	9
A new nonconvex low-rank tensor approximation method with applications to hyperspectral images denoising	9
Low-resolution prior equilibrium network for CT reconstruction	9
Some integral geometry problems for wave equations	9
Iterative regularization in classification via hinge loss diagonal descent	9
Robust signal recovery for ℓ 1–2 minimization via prior support information	9
Reconstructing the image scanning microscopy dataset: an inverse problem	9
Stability estimates for the expected utility in Bayesian optimal experimental design	8
Multi-scale CLEAN for Fourier-based hard x-ray solar imaging	8
DRIP: deep regularizers for inverse problems	8
GPU accelerated 3D source free adaptive wavefield reconstruction inversion for seismic imaging	8
Direct sampling for recovering a clamped cavity from the biharmonic far-field data	8
Adaptive Tikhonov strategies for stochastic ensemble Kalman inversion	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
Full-waveform reconstruction of microseismic events via observations of acoustic pressure in the surrounding fluid	8
Theory and fast learned solver for	8
Reconstructing the shape and material parameters of dissipative obstacles using an impedance model	8
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
Regularization graphs—a unified framework for variational regularization of inverse problems	7
On the stability of recovering two sources and initial status in a stochastic hyperbolic-parabolic system	7
Object based Bayesian full-waveform inversion for shear elastography	7
Inverse source problem for discrete Helmholtz equation	7
A stochastic gradient descent approach with partitioned-truncated singular value decomposition for large-scale inverse problems of magnetic modulus data	7
Solving an inverse source problem by deep neural network method with convergence and error analysis	7
Determining anomalies in a semilinear elliptic equation by a minimal number of measurements	7
Randomized block coordinate descent method for linear ill-posed problems	7
Nearly optimal bounds for the global geometric landscape of phase retrieval	7
Lipschitz stability of recovering the conductivity from internal current densities	7
The C ∞	7
Low-rank tensor completion with non-local self-similarity and multidimensional learnable transforms*	7
Phase retrieval and phaseless inverse scattering with background information	7
On the uniqueness of solutions for the basis pursuit in the continuum	7
Enhanced microscale hydrodynamic near-cloaking using electro-osmosis	7
Uniqueness and numerical method for phaseless inverse diffraction grating problem with known superposition of incident point sources	7
A numerical investigation of matched source waveform inversion applied to acoustic transmission data	7
Non-zero constraints in elliptic PDE with random boundary values and applications to hybrid inverse problems	7
Mixed geometry information regularization for image deblurring with multiplicative noise	7
Analysis of the discrepancy principle for Tikhonov regularization with oversmoothing penalty term under low order source conditions	7
Inverse problems of damped wave equations with Robin boundary conditions: an application to blood perfusion	7
Local saddles of relaxed averaged alternating reflections algorithms on phase retrieval	6
The lower bound of nonlocal gradient for non-convex and non-smooth image patches based regularization	6
Generalized inexact Newton regularization for nonlinear ill-posed problems in Banach spaces	6
An inexact proximal majorization–minimization method for a class of image reconstruction models	6
Bayesian inversion of log-normal eikonal equations	6
Regularization of the factorization method applied to diffuse optical tomography	6
Deep neural-network based optimization for the design of a multi-element surface magnet for MRI applications	6
Global uniqueness for determining an inverse electromagnetic scattering medium and its physical coefficients	6
Convergence of level sets in fractional Laplacian regularization	6
Bayesian interface technique-based inverse estimation of closure coefficients of standard	6
On Bayesian data assimilation for PDEs with ill-posed forward problems	6
In memoriam Pierre Sabatier	6
On uniqueness and stable estimation of multiple parameters in the Cahn–Hilliard equation	6
Reduced order model approach for imaging with waves	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
Convergence analysis of an alternating direction method of multipliers for the identification of nonsmooth diffusion parameters with total variation	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
Some direct and inverse source problems in nonlinear evolutionary PDEs with Volterra operators	5
Solving inverse acoustic obstacle scattering problem from phaseless far-field measurement using deep neural network surrogates*	5
Determining initial conditions for nonlinear hyperbolic equations with time dimensional reduction and the Carleman contraction principle	5
Theoretical and numerical studies of inverse source problem for the linear parabolic equation with sparse boundary measurements	5
Analysis of the monotonicity method for an anisotropic scatterer with a conductive boundary	5
Heuristic rule for inexact Newton-Landweber iteration with convex penalty terms of nonlinear: ill-posed problems	5
Convergence study and regularizing property of a modified Robin–Robin method for the Cauchy problem in linear elasticity	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
Joint Gaussian dictionary learning and tomographic reconstruction	5
Semi-discrete Tikhonov regularization in RKHS with large randomly distributed noise	5
The MLE is a reliable source: sharp performance guarantees for localization problems	5
Corrigendum: On uniqueness of an inverse problem in electromagnetic obstacle scattering for an impedance cylinder (2012 Inverse Problems 28 055012)	5
Crack identification in a multi-layer inhomogeneous domain using the Reciprocity Gap-Linear Sampling Method	5
Projection methods for high numerical aperture phase retrieval	5
An analytical inversion formula for the overdetermined spherical section transform	5
The domain derivative in inverse obstacle scattering with nonlinear impedance boundary condition	5
Recovery of a coefficient in a diffusion equation from large time data*	5
Sound speed uncertainty in acousto-electric tomography	5
MiPhDUO: microwave imaging via physics-informed deep unrolled optimization	5
Vertical autofocus for the phase screen in a turbulent ionosphere	5
Fourier method for inverse source problem using correlation of passive measurements*	5
Local recovery of a piecewise constant anisotropic conductivity in EIT on domains with exposed corners	5
Increasing stability in the linearized inverse Schrödinger potential problem with power type nonlinearities*	5
PatchNR: learning from very few images by patch normalizing flow regularization	5
Estimation of off-the grid sparse spikes with over-parametrized projected gradient descent: theory and application	5
The monotonicity method for inclusion detection and the time harmonic elastic wave equation	5
Fourier reconstruction for diffraction tomography of an object rotated into arbitrary orientations	5
A probabilistic framework for uncertainty quantification in positron emission particle tracking	5
Determination of discontinuous diffusion coefficients for the heat equation on a tree-shaped network	5
An optimal transport approach for 3D electrical impedance tomography	5
Carleman contraction mapping for a 1D inverse scattering problem with experimental time-dependent data	5
Kalman-based estimation of loading conditions from ultrasonic guided wave measurements	5
Multiscale hierarchical decomposition methods for ill-posed problems	5
Heavy-ball enhanced pseudo-inverse-based hard thresholding algorithms for sparse linear inverse problems	5
The inverse Rytov series for diffuse optical tomography	5
Inverse problem for a nonlocal diffuse optical tomography equation	5
Convergence rates of Landweber-type methods for inverse problems in Banach spaces	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
Wirtinger gradient descent methods for low-dose Poisson phase retrieval	4
Color image restoration based on saturation-value total variation plus L1 fidelity*	4
Deep Gaussian process priors for Bayesian image reconstruction	4
Tractable optimal experimental design using transport maps*	4
Direct and inverse scattering in an optical waveguide*	4
Assessing the potential of using a virtual Veselago lens in quantitative microwave imaging	4
Joint estimation of Robin coefficient and domain boundary for the Poisson problem	4
Reduced-order autodifferentiable ensemble Kalman filters	4
Bilevel inverse problems in neuromorphic imaging	4
Adaptive anisotropic Bayesian meshing for inverse problems	4
Bayesian inversion with α-stable priors	4
Stability estimates for an inverse boundary value problem for biharmonic operators with first order perturbation from partial data	4
Accelerating ill-conditioned Hankel matrix recovery via structured Newton-like descent	4
Inverse problem of reconstruction of degenerate diffusion coefficient in a parabolic equation	4
Consistency of Bayesian inference with Gaussian process priors for a parabolic inverse problem	4
On a nonlinear model in domains with cavities arising from cardiac electrophysiology	4
A variational non-linear constrained model for the inversion of FDEM data*	4
On a numerical construction of doubly stochastic matrices with prescribed eigenvalues	4
Error estimates for Golub–Kahan bidiagonalization with Tikhonov regularization for ill–posed operator equations	4
Stability estimates for an inverse problem for Schrödinger operators at high frequencies from arbitrary partial boundary measurements	4
Error bounds for extended source inversion applied to an acoustic transmission inverse problem	4
The inverse obstacle problem for nonlinear inclusions	4
Diffraction tomography for incident Herglotz waves	4
Vector-valued spline method for the spherical multiple-shell electro-magnetoencephalography problem	4
Analysis of the inverse Born series: an approach through geometric function theory	4
Inverse scattering for the multipoint potentials of Bethe−Peierls−Thomas−Fermi type*	4
One-dimensional coefficient inverse problems by transformation operators	4
Lipschitz stability of an inverse conductivity problem with two Cauchy data pairs	4
Corrigendum: Solution of an acoustic transmission inverse problem by extended inversion (2022 Inverse Problems 38 115003)	4
Uncertainty quantification for goal-oriented inverse problems via variational encoder-decoder networks	4
An approximate analytical reconstruction method in inverse problems of cone-beam rotary computed laminography	4
Determining sources in the bioluminescence tomography problem	4
Optimal indirect estimation for linear inverse problems with discretely sampled functional data	4
A Bayesian approach for consistent reconstruction of inclusions	4
Discrete nonlinear Fourier transforms and their inverses	4
Noise-robust one-bit diffraction tomography and optimal dose fractionation	4
Microlocal properties of seven-dimensional lemon and apple Radon transforms with applications in Compton scattering tomography	4
Continuous Gaussian mixture solution for linear Bayesian inversion with application to Laplace priors	4
A direct sampling-based deep learning approach for inverse medium scattering problems	4
Reconstruction of Voronoi diagrams: the case of inverse conductivity problems	4
The Radon transform with finitely many angles *	4
Recovery of piecewise smooth parameters in an acoustic-gravitational system of equations from exterior Cauchy data	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