Inverse Problems

Article	Citations
Unique reconstruction of simple magnetizations from their magnetic potential	30
TRAC method in dissipative media—a first analysis in frequency domain and homogeneous media	30
Frame decompositions of bounded linear operators in Hilbert spaces with applications in tomography	26
Towards optimal sensor placement for inverse problems in spaces of measures	25
Radial recombination for rigid rotational alignment of images and volumes	22
Inversion formulae for ray transforms in vector and tensor tomography	21
On the exactness of the universal backprojection formula for the spherical means Radon transform	20
Reduced order model approach for imaging with waves	18
An analysis of constraint-relaxation in PDE-based inverse problems	17
Regularization of ill-posed problems involving constant-coefficient pseudo-differential operators	17
Recovering a function from its integrals over conical surfaces through relations with the Radon transform	17
Carleman estimate for the Navier–Stokes equations and applications	14
Convergence of level sets in fractional Laplacian regularization	14
Carleman estimates and the contraction principle for an inverse source problem for nonlinear hyperbolic equations	13
Determination of a small elliptical anomaly in electrical impedance tomography using minimal measurements	13
In memoriam Pierre Sabatier	13
On Bayesian data assimilation for PDEs with ill-posed forward problems	12
Flow recovery from distal pressure in linearized hemodynamics: an optimal control approach	11
Generalized inexact Newton regularization for nonlinear ill-posed problems in Banach spaces	11
Stochastic mirror descent method for linear ill-posed problems in Banach spaces	11
Reconstruction of sources from time domain scattered waves at sparse sensors	11
On uniqueness and stable estimation of multiple parameters in the Cahn–Hilliard equation	11
A Bernstein–von-Mises theorem for the Calderón problem with piecewise constant conductivities	10
Regularization of the factorization method applied to diffuse optical tomography	10
Adaptive anadromic regularization method for the Cauchy problem of the Helmholtz equation	10

Convergence rate analysis of the coefficient identification problems in a Kuramoto–Sivashinsky equation	10
Parameter identification for elliptic boundary value problems: an abstract framework and applications	10
Convexification for the viscocity solution for a coefficient inverse problem for the radiative transfer equation	10
Multi-channel Potts-based reconstruction for multi-spectral computed tomography	10
Monotonicity Principle in tomography of nonlinear conducting materials *	10
A model reference adaptive system approach for nonlinear online parameter identification	10
Co-inversion of a scattering cavity and its internal sources: uniqueness, decoupling and imaging	10
Adaptive Spectral Inversion for inverse medium problems	10
Masked unbiased principles for parameter selection in variational image restoration under Poisson noise	10
Reconstruction of multipolar point sources with multi-frequency sparse far field data	9
Bayesian statistical inference using a regression in electrical impedance tomography	9
Inverse medium scattering problems with Kalman filter techniques	9
Local saddles of relaxed averaged alternating reflections algorithms on phase retrieval	9
Numerical conductivity reconstruction from partial interior current density information in three dimensions	9
Stochastic linear regularization methods: random discrepancy principle and applications	9
On extension of the data driven ROM inverse scattering framework to partially nonreciprocal arrays	9
Feasibility of acousto-electric tomography	9
Jointly determining the point sources and obstacle from Cauchy data	9
Posterior consistency of semi-supervised regression on graphs	9
Uniqueness and numerical inversion in the time-domain fluorescence diffuse optical tomography	9
Corrigendum: The enclosure method for a generalized anisotropic complex conductivity equation (2021 Inverse Problems 37 055010)	8
Deep neural-network based optimization for the design of a multi-element surface magnet for MRI applications	8
Simultaneous determination of different class of parameters for a diffusion equation from a single measurement	8
Numerical resolution of the inverse source problem for EEG using the quasi-reversibility method	8
Uniqueness of an inverse cavity scattering problem for the time-harmonic biharmonic wave equation	8
A Bayesian approach for CT reconstruction with defect detection for subsea pipelines	8
The lower bound of nonlocal gradient for non-convex and non-smooth image patches based regularization	8
Bayesian inversion of log-normal eikonal equations	8
Multipoint formulas in inverse problems and their numerical implementation	8
Gradient flows and randomised thresholding: sparse inversion and classification*	8
Convergence analysis of an alternating direction method of multipliers for the identification of nonsmooth diffusion parameters with total variation	8
Uniqueness results for inverse source problems for semilinear elliptic equations	8
Sparse Bayesian inference with regularized Gaussian distributions *	8
An autoencoder compression approach for accelerating large-scale inverse problems	8
Learning a stable approximation of an existing but unknown inverse mapping: application to the half-time circular Radon transform	7
Sampling complexity on phase retrieval from masked Fourier measurements via Wirtinger flow*	7
Processing the 2D and 3D Fresnel experimental databases via topological derivative methods	7
Blood and breath alcohol concentration from transdermal alcohol biosensor data: estimation and uncertainty quantification via forward and inverse filtering for a covariate-dependent, physics-informed,	7
Structure analysis of direct sampling method in 3D electromagnetic inverse problem: near- and far-field configuration	7
Inverse problems for constrained parabolic variational-hemivariational inequalities *	7
Task adapted reconstruction for inverse problems	7
A deep learning enhanced inverse scattering framework for microwave imaging of piece-wise homogeneous targets	7
A novel Newton method for inverse elastic scattering problems	7
An inverse problem for a transmission wave equation with a flat interface in Rn	7
Enhanced total variation minimization for stable image reconstruction	7
On Calderón’s inverse inclusion problem with smooth shapes by a single partial boundary measurement	7
Robust kernel-based distribution regression	7
Revisiting the probe and enclosure methods	7
On the simultaneous reconstruction of the nonlinearity coefficient and the sound speed in the Westervelt equation	7
On bias and its reduction via standardization in discretized electromagnetic source localization problems	7

Machine learning for structural design models of continuous beam systems via influence zones	7
Unique continuation from a generalized impedance edge-corner for Maxwell’s system and applications to inverse problems	7
Uniqueness in determining rectangular grating profiles with a single incoming wave (part II): TM polarization case	7
Subsampling in ensemble Kalman inversion	7
Support condition identification of wind turbines based on a statistical time-domain damping parameter	6
Bayesian model error method for the passive inverse scattering problem	6
Numerical solution of an inverse random source problem for the time fractional diffusion equation via PhaseLift	6
Bayesian interface technique-based inverse estimation of closure coefficients of standard	6
Adaptive Bregman–Kaczmarz: an approach to solve linear inverse problems with independent noise exactly	6
New trends in electromagnetic inverse problems	6
Total least squares problems on infinite dimensional spaces	6
A projective two-point gradient Kaczmarz iteration for nonlinear ill-posed problems	6
The Dantzig selector: recovery of signal via ℓ 1 − αℓ 2 minimization	6
Regularized factorization method for a perturbed positive compact operator applied to inverse scattering	6
Imaging conductivity from current density magnitude using neural networks*	6
Near-field linear sampling method for axisymmetric eddy current tomography	6
On the use of nonlinear anisotropic diffusion filters for seismic imaging using the full waveform	6
Imaging in lossy media	6
Numerical recovery of a time-dependent potential in subdiffusion *	6
Distributed spectral pairwise ranking algorithms	6
Structured model selection via ℓ1−ℓ2 optimization	6
Recovering critical parameter for nonlinear Allen–Cahn equation by fully discrete continuous data assimilation algorithms *	5
Inverse problems for a generalized fractional diffusion equation with unknown history	5
Solution of an acoustic transmission inverse problem by extended inversion	5
When artificial parameter evolution gets real: particle filtering for time-varying parameter estimation in deterministic dynamical systems	5
Global Lipschitz stability of multiple space dependent ionic parameters for the MEA/hiPSC-CM assays	5
Adaptive tempered reversible jump algorithm for Bayesian curve fitting	5
Distributed least squares prediction for functional linear regression*	5
Statistical modelling and Bayesian inversion for a Compton imaging system: application to radioactive source localization	5
ADJUST: a dictionary-based joint reconstruction and unmixing method for spectral tomography	5
Computational approaches to non-convex, sparsity-inducing multi-penalty regularization	5
Discrete Calderón problem with partial data	5
Approximation error method for imaging the human head by electrical impedance tomography*	5
An extended primal-dual algorithm framework for nonconvex problems: application to image reconstruction in spectral CT	5
Optimal-order convergence of Nesterov acceleration for linear ill-posed problems*	5
Uniqueness of a spherically symmetric refractive index from modified transmission eigenvalues	5
Regularization of the inverse Laplace transform by mollification	5
On direct and inverse obstacle scattering problems for biharmonic waves	5
Invertible residual networks in the context of regularization theory for linear inverse problems	5
Reconstruction of averaging indicators for highly heterogeneous media	5
Chilled sampling for uncertainty quantification: a motivation from a meteorological inverse problem *	5
Convergence of non-linear diagonal frame filtering for regularizing inverse problems	5
Gradient flow structure and convergence analysis of the ensemble Kalman inversion for nonlinear forward models	5
Uniqueness and modified Newton method for cracks from the far field patterns with a fixed incident direction	5
A mathematical theory of computational resolution limit in multi-dimensional spaces *	5
Consistency of the Bayes method for the inverse scattering problem	5
Inverse problems for generalized quasi-variational inequalities with application to elliptic mixed boundary value systems	5
On the ensemble Kalman inversion under inequality constraints	5
A three-stage method for reconstructing multiple coefficients in coupled photoacoustic and diffuse optical imaging	5
Radon transform on algebraic Cormack α-curves inversion formula	5
Determining damping terms in fractional wave equations	5
MiPhDUO: microwave imaging via physics-informed deep unrolled optimization	5
Direct sampling method to inverse wave-number-dependent source problems: determination of the support of a stationary source	5
Geometric approach for determining stationary phase points in radar imaging	4
Eigenvalue-free iterative shrinkage-thresholding algorithm for solving the linear inverse problems	4
Estimation of the cell membrane permeability for gas transport from surface pH measurements	4
Reconstructing a state-independent cost function in a mean-field game model	4
Analysis of sampling methods for imaging a periodic layer and its defects	4
Local recovery of a piecewise constant anisotropic conductivity in EIT on domains with exposed corners	4
Cones with convoluted geometry that always scatter or radiate	4
A content-adaptive unstructured grid based regularized CT reconstruction method with a SART-type preconditioned fixed-point proximity algorithm	4
A practical method for recovering Sturm–Liouville problems from the Weyl function	4
Material-separating regularizer for multi-energy x-ray tomography	4
Permeability estimation of a porous structure in cancer treatment based on sampled velocity measurement*	4
Carleman contraction mapping for a 1D inverse scattering problem with experimental time-dependent data	4
Feature augmentation for the inversion of the Fourier transform with limited data	4
CUQIpy: I. Computational uncertainty quantification for inverse problems in Python	4
Inexact Newton regularization combined with two-point gradient methods for nonlinear ill-posed problems *	4
Stably determining time-dependent convection–diffusion coefficients from a partial Dirichlet-to-Neumann map	4
Fast inverse elastic scattering of multiple particles in three dimensions*	4
Multiscale hierarchical decomposition methods for ill-posed problems	4
Bayesian image segmentation under varying blur with triplet Markov random field	4
MB-DAMPNet: a novel multi-branch denoising-based approximate message passing algorithm via deep neural network for image reconstruction	4
Addendum: On stochastic Kaczmarz type methods for solving large scale systems of ill-posed equations (2022 Inverse Problems 38 025003)	4
Parametrix for the inverse source problem of thermoacoustic tomography with reduced data	4
Solving, tracking and stopping streaming linear inverse problems	4
The inverse Rytov series for diffuse optical tomography	4
Sampling for the V-line transform with vertex on a circle	4
Fourier reconstruction for diffraction tomography of an object rotated into arbitrary orientations	3
Reconstruction of a source domain from the Cauchy data: II. Three-dimensional case	3

A Kirchhoff Migration scheme for elastic obstacle identification	3
Theoretical and numerical studies of inverse source problem for the linear parabolic equation with sparse boundary measurements	3
Unique recovery of unknown spatial load in damped Euler–Bernoulli beam equation from final time measured output	3
L2SR: learning to sample and reconstruct for accelerated MRI via reinforcement learning	3
Spectral decomposition of atomic structures in heterogeneous cryo-EM	3
A structured L-BFGS method and its application to inverse problems	3
Direct inversion of the Longitudinal ray transform for 2D residual elastic strain fields	3
Positive Jacobian constraints for elliptic boundary value problems with piecewise-regular coefficients arising from multi-wave inverse problems	3
Fictitious null spaces for improving the solution of injective inverse problems	3
Stability estimate for an inverse stochastic parabolic problem of determining unknown time-varying boundary *	3
Stability and regularization for ill-posed Cauchy problem of a stochastic parabolic differential equation	3
Learning regularization parameters of inverse problems via deep neural networks	3
Inferring dynamical models from time-series biological data using an interpretable machine learning method based on weighted expression trees	3
A generalized quasi-boundary value method for recovering a source in a fractional diffusion-wave equation	3
A phase-field approach for detecting cavities via a Kohn–Vogelius type functional	3
Optimal experimental design for infinite-dimensional Bayesian inverse problems governed by PDEs: a review	3
Fixed-distance multipoint formulas for the scattering amplitude from phaseless measurements	3
Precursors for synthetic aperture radar	3
Convergence of Poisson point processes and of optimal transport regularization with application in variational analysis of PET reconstruction	3
fg-ORKA: fast and gridless reconstruction of moving and deforming objects in multidimensional data	3
Stability estimate for the broken non-abelian x-ray transform in Minkowski space	3
An inverse problem for generalized Kelvin–Voigt equation with p-Laplacian and damping term	3
Parameter choices for sparse regularization with the ℓ1 norm *	3
Ill-posedness of time-dependent inverse problems in Lebesgue-Bochner spaces	3
Heuristic rule for inexact Newton-Landweber iteration with convex penalty terms of nonlinear: ill-posed problems	3
On the uniqueness of inverse problems for the reduced wave equation with unknown embedded obstacles	3
Mumford–Shah regularization in electrical impedance tomography with complete electrode model	3
A new interpretation of (Tikhonov) regularization	3
Fourier method for inverse source problem using correlation of passive measurements*	3
Normalizing flow regularization for photoacoustic tomography	3
Inverse conductivity problem with one measurement: uniqueness of multi-layer structures	3
Iterative inversion of the tensor momentum x-ray transform	3
Discretization of parameter identification in PDEs using neural networks	3
Inverse problem for a nonlocal diffuse optical tomography equation	3
Local near-field scattering data enables unique reconstruction of rough electric potentials	3
Stability of the isotropic conductivity reconstruction using magnetic resonance electrical impedance tomography (MREIT)	3
A single level set function approach for multiple material-phases applied to full-waveform inversion in the time domain	3
Determination of a spatial load in a damped Kirchhoff–Love plate equation from final time measured data	3
Solving Bayesian inverse problems with expensive likelihoods using constrained Gaussian processes and active learning	3
A unified approach to inversion formulae for vector and tensor ray and radon transforms and the Natterer inequality	3
Determining the viscosity of the Navier–Stokes equations from observations of finitely many modes	3
Piecewise nonlinear materials and Monotonicity Principle	3
Uniqueness theorems for tomographic phase retrieval with few coded diffraction patterns	3
Linearized boundary control method for density reconstruction in acoustic wave equations	3
Size estimates for nanoplates	3
Vertical autofocus for the phase screen in a turbulent ionosphere	3
Bilevel optimal parameter learning for a high-order nonlocal multiframe super-resolution problem	3
Reconstruction of the doping profile in Vlasov–Poisson system	3
On a three-dimensional Compton scattering tomography system with fixed source	3
Stability of an inverse source problem for the damped biharmonic plate equation	3
Solving inverse obstacle scattering problem with latent surface representations	3
Increasing stability in the linearized inverse Schrödinger potential problem with power type nonlinearities*	3
Foreword to special issue of Inverse Problems on modern challenges in imaging	2
A novel variational approach for multiphoton microscopy image restoration: from PSF estimation to 3D deconvolution	2
Joint Gaussian dictionary learning and tomographic reconstruction	2
Stabilizing Invertible Neural Networks Using Mixture Models	2
Generalized variational framework with minimax optimization for parametric blind deconvolution	2
Imaging of buried obstacles in a two-layered medium with phaseless far-field data	2
3D Poissonian image deblurring via patch-based tensor logarithmic Schatten-p minimization	2
Quantitative parameter reconstruction from optical coherence tomographic data	2
Efficient, multimodal, and derivative-free bayesian inference with Fisher–Rao gradient flows	2
The MLE is a reliable source: sharp performance guarantees for localization problems	2
A dataset-free deep learning method for low-dose CT image reconstruction	2
Imaging sound-soft targets in waveguides using the topological derivative	2
An accelerated homotopy perturbation iteration for nonlinear ill-posed problems in Banach spaces with uniformly convex penalty	2
A two-stage numerical approach for the sparse initial source identification of a diffusion–advection equation *	2
Dynamic Fourier ptychography with deep spatiotemporal priors	2
Restoring the discontinuous heat equation source using sparse boundary data and dynamic sensors	2
The domain derivative in inverse obstacle scattering with nonlinear impedance boundary condition	2
Sound speed uncertainty in acousto-electric tomography	2
Double-parameter regularization for solving the backward diffusion problem with parallel-in-time algorithm	2
The monotonicity method for inclusion detection and the time harmonic elastic wave equation	2
A numerical algorithm for inverse problem from partial boundary measurement arising from mean field game problem	2
Projection methods for high numerical aperture phase retrieval	2
Translation invariant diagonal frame decomposition of inverse problems and their regularization	2
The reconstruction of surface vibrations from near-field acoustic pressure measurements under steady flow	2
Bayesian particle filter algorithm for learning epidemic dynamics	2
A heterogeneous patient-specific model of glioblastoma multiforme tumor through an inverse problem	2
Recovery of a coefficient in a diffusion equation from large time data*	2
Detection of scatterers using an XFEM-BEM level set solver based on the topological derivative	2
Distributed parameter identification for the Navier–Stokes equations for obstacle detection	2
Relaxation approach for learning neural network regularizers for a class of identification problems	2
Image reconstruction based on nonlinear diffusion model for limited-angle computed tomography	2
An image inpainting algorithm using exemplar matching and low-rank sparse prior	2
Bi-level iterative regularization for inverse problems in nonlinear PDEs	2
Some direct and inverse source problems in nonlinear evolutionary PDEs with Volterra operators	2
Divide-and-conquer DNN approach for the inverse point source problem using a few single frequency measurements	2
Reconstruction of the initial data from the trace of the solutions on an infinite time cylinder of damped wave equations *	2
Analysis of a generalized regularized Gauss–Newton method under heuristic rule in Banach spaces	2
On regularization via frame decompositions with applications in tomography	2
Machine learning enhanced electrical impedance tomography for 2D materials	2
A probabilistic framework for uncertainty quantification in positron emission particle tracking	2
Parametric level-sets enhanced to improve reconstruction (PaLEnTIR)	2
Optimal regularized hypothesis testing in statistical inverse problems	2
An accelerated majorization-minimization algorithm with convergence guarantee for non-Lipschitz wavelet synthesis model *	2