Inverse Problems

Article	Citations
A Bayesian approach for CT reconstruction with defect detection for subsea pipelines	42
Uniqueness of an inverse cavity scattering problem for the time-harmonic biharmonic wave equation	39
On direct and inverse obstacle scattering problems for biharmonic waves	35
An analysis of constraint-relaxation in PDE-based inverse problems	31
Stochastic mirror descent method for linear ill-posed problems in Banach spaces	28
On inverse problems for mean field games with common noise via Carleman estimate*	21
An inverse potential problem for the stochastic heat equation with space-time noise	21
Multipoint formulas in inverse problems and their numerical implementation	21
A Bernstein–von-Mises theorem for the Calderón problem with piecewise constant conductivities	20
Recovering a function from its integrals over conical surfaces through relations with the Radon transform	19
On a quantitative partial imaging problem in vector tomography	18
Imaging conductivity from current density magnitude using neural networks*	18
A probabilistic approach to tomography and adjoint state methods, with an application to full waveform inversion in medical ultrasound	17
Flow recovery from distal pressure in linearized hemodynamics: an optimal control approach	17
Fictitious null spaces for improving the solution of injective inverse problems	16
Distributed learning with discretely observed functional data	16
Stability of the isotropic conductivity reconstruction using magnetic resonance electrical impedance tomography (MREIT)	16
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
Determination of a spatial load in a damped Kirchhoff–Love plate equation from final time measured data	15
Addendum: On stochastic Kaczmarz type methods for solving large scale systems of ill-posed equations (2022 Inverse Problems 38 025003)	14
Chilled sampling for uncertainty quantification: a motivation from a meteorological inverse problem *	14
Inferring dynamical models from time-series biological data using an interpretable machine learning method based on weighted expression trees	14
Radon transform on algebraic Cormack α-curves inversion formula	14
A Kirchhoff Migration scheme for elastic obstacle identification	14

Geometric approach for determining stationary phase points in radar imaging	14
Direct inversion of the Longitudinal ray transform for 2D residual elastic strain fields	13
Stability estimate for an inverse stochastic parabolic problem of determining unknown time-varying boundary *	13
Bayesian design of measurements for magnetorelaxometry imaging *	12
A dataset-free deep learning method for low-dose CT image reconstruction	12
Maximum a posteriori estimators in ℓp are well-defined for diagonal Gaussian priors	12
Uniqueness theorems for tomographic phase retrieval with few coded diffraction patterns	12
Stability for a multi-frequency inverse random source problem	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
A mathematical framework for nonlinear wavefront reconstruction in adaptive optics systems with Fourier-type wavefront sensing	11
A two-stage numerical approach for the sparse initial source identification of a diffusion–advection equation *	11
Hyperparameter estimation using a resolution matrix for Bayesian sensing	10
Optimal regularized hypothesis testing in statistical inverse problems	10
Unsupervised knowledge-transfer for learned image reconstruction*	10
Matrix recovery from nonconvex regularized least absolute deviations	10
Solving the acousto-electric tomography by the adaptive Nesterov method of Kaczmarz type	10
Minimizing L 1 over L 2 norms on the gradient	10
Double-parameter regularization for solving the backward diffusion problem with parallel-in-time algorithm	10
On inertial iterated Tikhonov methods for solving ill-posed problems	10
Efficient Decomposition-Based Algorithms for ℓ1-Regularized Inverse Problems with Column-Orthogonal and Kronecker Product Matrices	10
Bouligand–Newton type methods for non-smooth ill-posed problems	10
A new nonconvex low-rank tensor approximation method with applications to hyperspectral images denoising	9
Reconstructing the image scanning microscopy dataset: an inverse problem	9
Stable determination of coefficients in semilinear parabolic system with dynamic boundary conditions	9
Nonstationary iterated Tikhonov regularization: convergence analysis via Hölder stability	9
Convergence analysis of the discretization of continuous-domain inverse problems	9
Low-resolution prior equilibrium network for CT reconstruction	9
Microwave time reversal for nondestructive testing of buried small damage in composite materials	9
Strong maximum a posteriori estimation in Banach spaces with Gaussian priors	9
Iterative regularization in classification via hinge loss diagonal descent	9
Robust signal recovery for ℓ 1–2 minimization via prior support information	9
Lipschitz stability of recovering the conductivity from internal current densities	9
Fast iterative reconstruction for multi-spectral CT by a Schmidt orthogonal modification algorithm (SOMA)	9
Reconstructing the shape and material parameters of dissipative obstacles using an impedance model	8
Reconstruction of degenerate conductivity region for parabolic equations	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
Multi-scale CLEAN for Fourier-based hard x-ray solar imaging	8
Norms in sinogram space and stability estimates for the Radon transform	8
GPU accelerated 3D source free adaptive wavefield reconstruction inversion for seismic imaging	8
DRIP: deep regularizers for inverse problems	8
Singular value decomposition for longitudinal, transverse and mixed ray transforms of 2D tensor fields	8
Some integral geometry problems for wave equations	8
Shape and orientation classification of objects based on their electromagnetic signatures using convolutional neural networks	8
Theory and fast learned solver for	8
Inverse problems of damped wave equations with Robin boundary conditions: an application to blood perfusion	8
The C∞ -isomorphism property for a class of singularly-weighted x-ray transforms	7
A numerical investigation of matched source waveform inversion applied to acoustic transmission data	7

In memoriam Pierre Sabatier	7
On bias and its reduction via standardization in discretized electromagnetic source localization problems	7
ASPIRE: iterative amortized posterior inference for Bayesian inverse 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
Stability estimates for the expected utility in Bayesian optimal experimental design	7
Randomized block coordinate descent method for linear ill-posed problems	7
Reduced order model approach for imaging with waves	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
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
Solving an inverse source problem by deep neural network method with convergence and error analysis	7
Uniqueness and numerical method for phaseless inverse diffraction grating problem with known superposition of incident point sources	7
Phase retrieval and phaseless inverse scattering with background information	7
Inverse source problem for discrete Helmholtz equation	7
Enhanced microscale hydrodynamic near-cloaking using electro-osmosis	7
Low-rank tensor completion with non-local self-similarity and multidimensional learnable transforms*	7
Analysis of the discrepancy principle for Tikhonov regularization with oversmoothing penalty term under low order source conditions	7
Nearly optimal bounds for the global geometric landscape of phase retrieval	7
Adaptive Tikhonov strategies for stochastic ensemble Kalman inversion	7
Generalized inexact Newton regularization for nonlinear ill-posed problems in Banach spaces	6
Deep neural-network based optimization for the design of a multi-element surface magnet for MRI applications	6
Regularization of the factorization method applied to diffuse optical tomography	6
Bayesian interface technique-based inverse estimation of closure coefficients of standard	6
Bayesian inversion of log-normal eikonal equations	6
On uniqueness and stable estimation of multiple parameters in the Cahn–Hilliard equation	6
On Bayesian data assimilation for PDEs with ill-posed forward problems	6
Convergence analysis of an alternating direction method of multipliers for the identification of nonsmooth diffusion parameters with total variation	6
Convergence of level sets in fractional Laplacian regularization	6
Uniqueness in determining rectangular grating profiles with a single incoming wave (part II): TM polarization case	6
The lower bound of nonlocal gradient for non-convex and non-smooth image patches based regularization	6
Robust kernel-based distribution regression	6
Heuristic rule for inexact Newton-Landweber iteration with convex penalty terms of nonlinear: ill-posed problems	5
Fourier reconstruction for diffraction tomography of an object rotated into arbitrary orientations	5
Multiscale hierarchical decomposition methods for ill-posed problems	5
The inverse Rytov series for diffuse optical tomography	5
Local saddles of relaxed averaged alternating reflections algorithms on phase retrieval	5
Increasing stability in the linearized inverse Schrödinger potential problem with power type nonlinearities*	5
Determination of discontinuous diffusion coefficients for the heat equation on a tree-shaped network	5
Some direct and inverse source problems in nonlinear evolutionary PDEs with Volterra operators	5
Projection methods for high numerical aperture phase retrieval	5
The domain derivative in inverse obstacle scattering with nonlinear impedance boundary condition	5
The MLE is a reliable source: sharp performance guarantees for localization problems	5
Vertical autofocus for the phase screen in a turbulent ionosphere	5
Convergence rates of Landweber-type methods for inverse problems in Banach spaces	5
Kalman-based estimation of loading conditions from ultrasonic guided wave measurements	5
Stability estimate for the broken non-abelian x-ray transform in Minkowski space	5
An optimal transport approach for 3D electrical impedance tomography	5
Global uniqueness for determining an inverse electromagnetic scattering medium and its physical coefficients	5
Local recovery of a piecewise constant anisotropic conductivity in EIT on domains with exposed corners	5
An inexact proximal majorization–minimization method for a class of image reconstruction models	5
Convergence study and regularizing property of a modified Robin–Robin method for the Cauchy problem in linear elasticity	5
Theoretical and numerical studies of inverse source problem for the linear parabolic equation with sparse boundary measurements	5
Electric impedance tomography problem for surfaces with internal holes *	5
A probabilistic framework for uncertainty quantification in positron emission particle tracking	5
Corrigendum: On uniqueness of an inverse problem in electromagnetic obstacle scattering for an impedance cylinder (2012 Inverse Problems 28 055012)	5
Carleman contraction mapping for a 1D inverse scattering problem with experimental time-dependent data	5
Analysis of the monotonicity method for an anisotropic scatterer with a conductive boundary	5
Heavy-ball enhanced pseudo-inverse-based hard thresholding algorithms for sparse linear inverse problems	5
MiPhDUO: microwave imaging via physics-informed deep unrolled optimization	5
Inverse problem for a nonlocal diffuse optical tomography equation	5
Fourier method for inverse source problem using correlation of passive measurements*	5
Permeability estimation of a porous structure in cancer treatment based on sampled velocity measurement*	5
Recovery of a coefficient in a diffusion equation from large time data*	5
Simultaneous determination of different class of parameters for a diffusion equation from a single measurement	5
Joint Gaussian dictionary learning and tomographic reconstruction	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
Adaptive anisotropic Bayesian meshing for inverse problems	5
Crack identification in a multi-layer inhomogeneous domain using the Reciprocity Gap-Linear Sampling Method	5
Semi-discrete Tikhonov regularization in RKHS with large randomly distributed noise	5
The monotonicity method for inclusion detection and the time harmonic elastic wave equation	4
PatchNR: learning from very few images by patch normalizing flow regularization	4
Stability estimates for an inverse boundary value problem for biharmonic operators with first order perturbation from partial data	4
Uniqueness in determining rectangular grating profiles with a single incoming wave (Part I): TE polarization case	4
Diffraction tomography for incident Herglotz waves	4
Consistency of Bayesian inference with Gaussian process priors for a parabolic inverse problem	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
Inverse scattering for the multipoint potentials of Bethe−Peierls−Thomas−Fermi type*	4
Error bounds for extended source inversion applied to an acoustic transmission inverse problem	4
Optimal indirect estimation for linear inverse problems with discretely sampled functional data	4
A direct sampling-based deep learning approach for inverse medium scattering problems	4
Assessing the potential of using a virtual Veselago lens in quantitative microwave imaging	4
A mixed finite element scheme for three-dimensional Maxwell’s transmission eigenvalue problems	4
Color image restoration based on saturation-value total variation plus L1 fidelity*	4
Corrigendum: Solution of an acoustic transmission inverse problem by extended inversion (2022 Inverse Problems 38 115003)	4
Determining a parabolic system by boundary observation of its non-negative solutions with biological applications	4
Error estimates for Golub–Kahan bidiagonalization with Tikhonov regularization for ill–posed operator equations	4
On a nonlinear model in domains with cavities arising from cardiac electrophysiology	4
On a numerical construction of doubly stochastic matrices with prescribed eigenvalues	4
Microlocal properties of seven-dimensional lemon and apple Radon transforms with applications in Compton scattering tomography	4
Wirtinger gradient descent methods for low-dose Poisson phase retrieval	4
Reduced-order autodifferentiable ensemble Kalman filters	4
Estimation of off-the grid sparse spikes with over-parametrized projected gradient descent: theory and application	4
Analysis of the inverse Born series: an approach through geometric function theory	4
Lipschitz stability of an inverse conductivity problem with two Cauchy data pairs	4
Discrete nonlinear Fourier transforms and their inverses	4
Bayesian inversion with α-stable priors	4
Accelerating Ill-conditioned Hankel Matrix Recovery via Structured Newton-like Descent	4
One-dimensional coefficient inverse problems by transformation operators	4
Determining sources in the bioluminescence tomography problem	4
A variational non-linear constrained model for the inversion of FDEM data*	4
Tractable optimal experimental design using transport maps*	4