Inverse Problems

Article	Citations
A Bayesian approach for CT reconstruction with defect detection for subsea pipelines	43
An analysis of constraint-relaxation in PDE-based inverse problems	41
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*	31
Recovering a function from its integrals over conical surfaces through relations with the Radon transform	29
On a quantitative partial imaging problem in vector tomography	22
A Bernstein–von-Mises theorem for the Calderón problem with piecewise constant conductivities	21
Imaging conductivity from current density magnitude using neural networks*	21
Stochastic mirror descent method for linear ill-posed problems in Banach spaces	20
Flow recovery from distal pressure in linearized hemodynamics: an optimal control approach	20
On direct and inverse obstacle scattering problems for biharmonic waves	19
Uniqueness of an inverse cavity scattering problem for the time-harmonic biharmonic wave equation	18
Multipoint formulas in inverse problems and their numerical implementation	17
A probabilistic approach to tomography and adjoint state methods, with an application to full waveform inversion in medical ultrasound	17
Determination of a spatial load in a damped Kirchhoff–Love plate equation from final time measured data	16
Geometric approach for determining stationary phase points in radar imaging	16
A dataset-free deep learning method for low-dose CT image reconstruction	16
Chilled sampling for uncertainty quantification: a motivation from a meteorological inverse problem *	15
Stability of the isotropic conductivity reconstruction using magnetic resonance electrical impedance tomography (MREIT)	15
Inferring dynamical models from time-series biological data using an interpretable machine learning method based on weighted expression trees	15
Stability estimate for an inverse stochastic parabolic problem of determining unknown time-varying boundary *	15
Distributed learning with discretely observed functional data	14
Recovering critical parameter for nonlinear Allen–Cahn equation by fully discrete continuous data assimilation algorithms *	14
Uniqueness theorems for tomographic phase retrieval with few coded diffraction patterns	14
Fictitious null spaces for improving the solution of injective inverse problems	14

A Kirchhoff Migration scheme for elastic obstacle identification	13
The reconstruction of surface vibrations from near-field acoustic pressure measurements under steady flow	13
Direct inversion of the Longitudinal ray transform for 2D residual elastic strain fields	12
Efficient decomposition-based algorithms for	12
Addendum: On stochastic Kaczmarz type methods for solving large scale systems of ill-posed equations (2022 Inverse Problems 38 025003)	12
Hearing the Shape of a Cuboid Room Using Sparse Measure Recovery	12
Bayesian design of measurements for magnetorelaxometry imaging *	12
Radon transform on algebraic Cormack α-curves inversion formula	12
3D refractive index reconstruction from phaseless coherent optical microscopy data using multiple scattering-based inverse solvers—a study	12
Minimizing L 1 over L 2 norms on the gradient	11
Hyperparameter estimation using a resolution matrix for Bayesian sensing	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
Optimal regularized hypothesis testing in statistical inverse problems	11
Solving the acousto-electric tomography by the adaptive Nesterov method of Kaczmarz type	11
Matrix recovery from nonconvex regularized least absolute deviations	10
Double-parameter regularization for solving the backward diffusion problem with parallel-in-time algorithm	10
Maximum a posteriori estimators in ℓp are well-defined for diagonal Gaussian priors	10
Reconstruction of the initial data from the trace of the solutions on an infinite time cylinder of damped wave equations *	10
Stochastic asymptotical regularization for linear inverse problems	10
A two-stage numerical approach for the sparse initial source identification of a diffusion–advection equation *	10
Stability for a multi-frequency inverse random source problem	10
Bouligand–Newton type methods for non-smooth ill-posed problems	10
Iterative regularization in classification via hinge loss diagonal descent	9
Unsupervised knowledge-transfer for learned image reconstruction*	9
Microwave time reversal for nondestructive testing of buried small damage in composite materials	9
Multi-scale CLEAN for Fourier-based hard x-ray solar imaging	9
Strong maximum a posteriori estimation in Banach spaces with Gaussian priors	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
Nonstationary iterated Tikhonov regularization: convergence analysis via Hölder stability	9
Low-resolution prior equilibrium network for CT reconstruction	9
Convergence analysis of the discretization of continuous-domain inverse problems	9
Reconstructing the image scanning microscopy dataset: an inverse problem	9
Stable determination of coefficients in semilinear parabolic system with dynamic boundary conditions	9
Fast iterative reconstruction for multi-spectral CT by a Schmidt orthogonal modification algorithm (SOMA)	9
Some integral geometry problems for wave equations	8
GPU accelerated 3D source free adaptive wavefield reconstruction inversion for seismic imaging	8
Norms in sinogram space and stability estimates for the Radon transform	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
Theory and fast learned solver for	8
Reconstruction of degenerate conductivity region for parabolic equations	8
Lipschitz stability of recovering the conductivity from internal current densities	8
Inverse problems of damped wave equations with Robin boundary conditions: an application to blood perfusion	8
DRIP: deep regularizers for inverse problems	8
Reconstructing the shape and material parameters of dissipative obstacles using an impedance model	8
Uniqueness and numerical method for phaseless inverse diffraction grating problem with known superposition of incident point sources	8
The C∞ -isomorphism property for a class of singularly-weighted x-ray transforms	7
Stability estimates for the expected utility in Bayesian optimal experimental design	7

Full-waveform reconstruction of microseismic events via observations of acoustic pressure in the surrounding fluid	7
A stochastic gradient descent approach with partitioned-truncated singular value decomposition for large-scale inverse problems of magnetic modulus data	7
Low-rank tensor completion with non-local self-similarity and multidimensional learnable transforms*	7
Regularization graphs—a unified framework for variational regularization of inverse problems	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
Coercivity-based analysis and its application to an inverse source problem for a subdiffusion equation with time-dependent principal parts	7
Adaptive Tikhonov strategies for stochastic ensemble Kalman inversion	7
Solving an inverse source problem by deep neural network method with convergence and error analysis	7
Phase retrieval and phaseless inverse scattering with background information	7
Object based Bayesian full-waveform inversion for shear elastography	7
Randomized block coordinate descent method for linear ill-posed problems	7
ASPIRE: iterative amortized posterior inference for Bayesian inverse problems	7
On the uniqueness of solutions for the basis pursuit in the continuum	7
Determining anomalies in a semilinear elliptic equation by a minimal number of measurements	7
Direct sampling for recovering a clamped cavity from the biharmonic far-field data	7
On the stability of recovering two sources and initial status in a stochastic hyperbolic-parabolic system	7
Enhanced microscale hydrodynamic near-cloaking using electro-osmosis	7
Inverse source problem for discrete Helmholtz equation	7
Analysis of the discrepancy principle for Tikhonov regularization with oversmoothing penalty term under low order source conditions	7
The lower bound of nonlocal gradient for non-convex and non-smooth image patches based regularization	6
In memoriam Pierre Sabatier	6
On bias and its reduction via standardization in discretized electromagnetic source localization problems	6
On uniqueness and stable estimation of multiple parameters in the Cahn–Hilliard equation	6
An inexact proximal majorization–minimization method for a class of image reconstruction models	6
Local saddles of relaxed averaged alternating reflections algorithms on phase retrieval	6
Bayesian inversion of log-normal eikonal equations	6
Reduced order model approach for imaging with waves	6
Mixed geometry information regularization for image deblurring with multiplicative noise	6
Deep neural-network based optimization for the design of a multi-element surface magnet for MRI applications	6
Convergence analysis of an alternating direction method of multipliers for the identification of nonsmooth diffusion parameters with total variation	6
Simultaneous determination of different class of parameters for a diffusion equation from a single measurement	6
Bayesian interface technique-based inverse estimation of closure coefficients of standard	6
Generalized inexact Newton regularization for nonlinear ill-posed problems in Banach spaces	6
Nearly optimal bounds for the global geometric landscape of phase retrieval	6
Uniqueness in determining rectangular grating profiles with a single incoming wave (part II): TM polarization case	6
Regularization of the factorization method applied to diffuse optical tomography	6
Robust kernel-based distribution regression	6
Global uniqueness for determining an inverse electromagnetic scattering medium and its physical coefficients	6
Convergence of level sets in fractional Laplacian regularization	6
Projection methods for high numerical aperture phase retrieval	5
The domain derivative in inverse obstacle scattering with nonlinear impedance boundary condition	5
Semi-discrete Tikhonov regularization in RKHS with large randomly distributed noise	5
Determination of discontinuous diffusion coefficients for the heat equation on a tree-shaped network	5
A probabilistic framework for uncertainty quantification in positron emission particle tracking	5
Multiscale hierarchical decomposition methods for ill-posed problems	5
Permeability estimation of a porous structure in cancer treatment based on sampled velocity measurement*	5
Stability estimate for the broken non-abelian x-ray transform in Minkowski space	5
Local recovery of a piecewise constant anisotropic conductivity in EIT on domains with exposed corners	5
Convergence rates of Landweber-type methods for inverse problems in Banach spaces	5
Increasing stability in the linearized inverse Schrödinger potential problem with power type nonlinearities*	5
Stability estimates for an inverse boundary value problem for biharmonic operators with first order perturbation from partial data	5
Electric impedance tomography problem for surfaces with internal holes *	5
Assessing the potential of using a virtual Veselago lens in quantitative microwave imaging	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
Theoretical and numerical studies of inverse source problem for the linear parabolic equation with sparse boundary measurements	5
Recovery of a coefficient in a diffusion equation from large time data*	5
Heavy-ball enhanced pseudo-inverse-based hard thresholding algorithms for sparse linear inverse problems	5
Fourier method for inverse source problem using correlation of passive measurements*	5
Bayesian compressive sensing using generative models	5
MiPhDUO: microwave imaging via physics-informed deep unrolled optimization	5
Inverse problem for a nonlocal diffuse optical tomography equation	5
Analysis of the inverse Born series: an approach through geometric function theory	5
Sound speed uncertainty in acousto-electric tomography	5
Determining initial conditions for nonlinear hyperbolic equations with time dimensional reduction and the Carleman contraction principle	5
Analysis of the monotonicity method for an anisotropic scatterer with a conductive boundary	5
Fourier reconstruction for diffraction tomography of an object rotated into arbitrary orientations	5
Vertical autofocus for the phase screen in a turbulent ionosphere	5
An analytical inversion formula for the overdetermined spherical section transform	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
The inverse Rytov series for diffuse optical tomography	5
On Bayesian data assimilation for PDEs with ill-posed forward problems	5
Convergence study and regularizing property of a modified Robin–Robin method for the Cauchy problem in linear elasticity	5
Diffraction tomography for incident Herglotz waves	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	4
Inverse scattering for the multipoint potentials of Bethe−Peierls−Thomas−Fermi type*	4

Deep Gaussian process priors for Bayesian image reconstruction	4
A direct sampling-based deep learning approach for inverse medium scattering problems	4
Error bounds for extended source inversion applied to an acoustic transmission inverse problem	4
Inverse problem of reconstruction of degenerate diffusion coefficient in a parabolic equation	4
Uncertainty quantification for goal-oriented inverse problems via variational encoder-decoder networks	4
Recovery of piecewise smooth parameters in an acoustic-gravitational system of equations from exterior Cauchy data	4
Uniqueness in determining rectangular grating profiles with a single incoming wave (Part I): TE polarization case	4
Accelerating ill-conditioned Hankel matrix recovery via structured Newton-like descent	4
PatchNR: learning from very few images by patch normalizing flow regularization	4
Joint Gaussian dictionary learning and tomographic reconstruction	4
Determining sources in the bioluminescence tomography problem	4
Corrigendum: On uniqueness of an inverse problem in electromagnetic obstacle scattering for an impedance cylinder (2012 Inverse Problems 28 055012)	4
Bayesian inversion with α-stable priors	4
Reduced-order autodifferentiable ensemble Kalman filters	4
A variational non-linear constrained model for the inversion of FDEM data*	4
Microlocal properties of seven-dimensional lemon and apple Radon transforms with applications in Compton scattering tomography	4
The MLE is a reliable source: sharp performance guarantees for localization problems	4
Consistency of Bayesian inference with Gaussian process priors for a parabolic inverse problem	4
Error estimates for Golub–Kahan bidiagonalization with Tikhonov regularization for ill–posed operator equations	4
Stability of data-dependent ridge-regularization for inverse problems	4
Color image restoration based on saturation-value total variation plus L1 fidelity*	4
An approximate analytical reconstruction method in inverse problems of cone-beam rotary computed laminography	4
Adaptive anisotropic Bayesian meshing for inverse problems	4
Estimation of off-the grid sparse spikes with over-parametrized projected gradient descent: theory and application	4
One-dimensional coefficient inverse problems by transformation operators	4
The monotonicity method for inclusion detection and the time harmonic elastic wave equation	4
On a numerical construction of doubly stochastic matrices with prescribed eigenvalues	4
Optimal indirect estimation for linear inverse problems with discretely sampled functional data	4
Wirtinger gradient descent methods for low-dose Poisson phase retrieval	4
Vector-valued spline method for the spherical multiple-shell electro-magnetoencephalography problem	4
Tractable optimal experimental design using transport maps*	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
The Radon transform with finitely many angles *	4
Discrete nonlinear Fourier transforms and their inverses	4
Some direct and inverse source problems in nonlinear evolutionary PDEs with Volterra operators	4
On a nonlinear model in domains with cavities arising from cardiac electrophysiology	4