Inverse Problems

Article	Citations
An analysis of constraint-relaxation in PDE-based inverse problems	37
Simultaneous estimation of electrical conductivity and permittivity in quantitative thermoacoustic tomography	33
Subgradient-based Lavrentiev regularisation of monotone ill-posed problems	28
Inverse problems for generalized quasi-variational inequalities with application to elliptic mixed boundary value systems	26
Discrete inverse problems with internal functionals*	26
Carleman estimates and the contraction principle for an inverse source problem for nonlinear hyperbolic equations	23
Inverse problems for constrained parabolic variational-hemivariational inequalities *	23
A three-stage method for reconstructing multiple coefficients in coupled photoacoustic and diffuse optical imaging	21
Stability analysis of inverse problems for coupled magnetic Schrödinger equations	20
Reconstruction of sources from time domain scattered waves at sparse sensors	18
Regularization of the factorization method applied to diffuse optical tomography	18
The lower bound of nonlocal gradient for non-convex and non-smooth image patches based regularization	18
Carleman estimate for the Navier–Stokes equations and applications	17
Reduced order model approach for imaging with waves	16
Parameter identification for elliptic boundary value problems: an abstract framework and applications	15
Regularization of ill-posed problems involving constant-coefficient pseudo-differential operators	15
The Dantzig selector: recovery of signal via ℓ 1 − αℓ 2 minimization	15
A model reference adaptive system approach for nonlinear online parameter identification	15
Optimal-order convergence of Nesterov acceleration for linear ill-posed problems*	15
Numerical conductivity reconstruction from partial interior current density information in three dimensions	14
Uniqueness of a spherically symmetric refractive index from modified transmission eigenvalues	14
Robust kernel-based distribution regression	13
Reconstruction of multipolar point sources with multi-frequency sparse far field data	13
Processing the 2D and 3D Fresnel experimental databases via topological derivative methods	13
Unique reconstruction of simple magnetizations from their magnetic potential	13

An extended primal-dual algorithm framework for nonconvex problems: application to image reconstruction in spectral CT	13
Deep neural-network based optimization for the design of a multi-element surface magnet for MRI applications	12
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,	12
Near-field linear sampling method for axisymmetric eddy current tomography	12
Inversion formulae for ray transforms in vector and tensor tomography	12
Generalized inexact Newton regularization for nonlinear ill-posed problems in Banach spaces	11
Imaging conductivity from current density magnitude using neural networks*	11
Determination of a small elliptical anomaly in electrical impedance tomography using minimal measurements	11
Simultaneous determination of different class of parameters for a diffusion equation from a single measurement	11
Bayesian statistical inference using a regression in electrical impedance tomography	11
Revisiting the probe and enclosure methods	11
Regularization of the inverse Laplace transform by mollification	11
On extension of the data driven ROM inverse scattering framework to partially nonreciprocal arrays	11
A Bayesian approach for CT reconstruction with defect detection for subsea pipelines	11
Numerical recovery of a time-dependent potential in subdiffusion *	11
Uniqueness results for inverse source problems for semilinear elliptic equations	10
Imaging in lossy media	10
Learning a stable approximation of an existing but unknown inverse mapping: application to the half-time circular Radon transform	10
New trends in electromagnetic inverse problems	10
Bayesian model error method for the passive inverse scattering problem	9
Multipoint formulas in inverse problems and their numerical implementation	9
A novel Newton method for inverse elastic scattering problems	9
TRAC method in dissipative media—a first analysis in frequency domain and homogeneous media	9
An inverse problem for a transmission wave equation with a flat interface in Rn	9
On bias and its reduction via standardization in discretized electromagnetic source localization problems	9
Inverse problems for a generalized fractional diffusion equation with unknown history	9
Convergence analysis of an alternating direction method of multipliers for the identification of nonsmooth diffusion parameters with total variation	9
Uniqueness and modified Newton method for cracks from the far field patterns with a fixed incident direction	9
Machine learning for structural design models of continuous beam systems via influence zones	9
A Bernstein–von-Mises theorem for the Calderón problem with piecewise constant conductivities	9
On the ensemble Kalman inversion under inequality constraints	9
In memoriam Pierre Sabatier	8
Convexification for the viscocity solution for a coefficient inverse problem for the radiative transfer equation	8
Adaptive tempered reversible jump algorithm for Bayesian curve fitting	8
Monotonicity Principle in tomography of nonlinear conducting materials *	8
A deep learning enhanced inverse scattering framework for microwave imaging of piece-wise homogeneous targets	8
Sparse Bayesian inference with regularized Gaussian distributions *	8
Towards optimal sensor placement for inverse problems in spaces of measures	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
Regularized factorization method for a perturbed positive compact operator applied to inverse scattering	8
Uniqueness in determining rectangular grating profiles with a single incoming wave (part II): TM polarization case	8
An autoencoder compression approach for accelerating large-scale inverse problems	8
Feasibility of acousto-electric tomography	8
Adaptive Bregman–Kaczmarz: an approach to solve linear inverse problems with independent noise exactly	8
A mathematical theory of computational resolution limit in multi-dimensional spaces *	7
Statistical modelling and Bayesian inversion for a Compton imaging system: application to radioactive source localization	7
Structure analysis of direct sampling method in 3D electromagnetic inverse problem: near- and far-field configuration	7
Structured model selection via ℓ1−ℓ2 optimization	7
Recovering a function from its integrals over conical surfaces through relations with the Radon transform	7

On uniqueness and stable estimation of multiple parameters in the Cahn–Hilliard equation	7
A projective two-point gradient Kaczmarz iteration for nonlinear ill-posed problems	7
Uniqueness and numerical inversion in the time-domain fluorescence diffuse optical tomography	7
On direct and inverse obstacle scattering problems for biharmonic waves	7
Convergence rate analysis of the coefficient identification problems in a Kuramoto–Sivashinsky equation	7
When artificial parameter evolution gets real: particle filtering for time-varying parameter estimation in deterministic dynamical systems	7
Inverse medium scattering problems with Kalman filter techniques	7
Global Lipschitz stability of multiple space dependent ionic parameters for the MEA/hiPSC-CM assays	7
Corrigendum: The enclosure method for a generalized anisotropic complex conductivity equation (2021 Inverse Problems 37 055010)	7
Task adapted reconstruction for inverse problems	7
Posterior consistency of semi-supervised regression on graphs	7
Convergence of level sets in fractional Laplacian regularization	7
Sampling complexity on phase retrieval from masked Fourier measurements via Wirtinger flow*	7
On the simultaneous reconstruction of the nonlinearity coefficient and the sound speed in the Westervelt equation	7
Enhanced total variation minimization for stable image reconstruction	7
Local saddles of relaxed averaged alternating reflections algorithms on phase retrieval	7
On the exactness of the universal backprojection formula for the spherical means Radon transform	6
Adaptive Spectral Inversion for inverse medium problems	6
Distributed spectral pairwise ranking algorithms	6
Co-inversion of a scattering cavity and its internal sources: uniqueness, decoupling and imaging	6
Support condition identification of wind turbines based on a statistical time-domain damping parameter	6
Consistency of the Bayes method for the inverse scattering problem	6
Adaptive anadromic regularization method for the Cauchy problem of the Helmholtz equation	6
Gradient flows and randomised thresholding: sparse inversion and classification*	6
Bayesian inversion of log-normal eikonal equations	6
Jointly determining the point sources and obstacle from Cauchy data	6
Approximation error method for imaging the human head by electrical impedance tomography*	6
Masked unbiased principles for parameter selection in variational image restoration under Poisson noise	6
Radial recombination for rigid rotational alignment of images and volumes	6
Solution of an acoustic transmission inverse problem by extended inversion	6
On Calderón’s inverse inclusion problem with smooth shapes by a single partial boundary measurement	6
Flow recovery from distal pressure in linearized hemodynamics: an optimal control approach	6
Convergence of Poisson point processes and of optimal transport regularization with application in variational analysis of PET reconstruction	5
CUQIpy: I. Computational uncertainty quantification for inverse problems in Python	5
The inverse Rytov series for diffuse optical tomography	5
Theoretical and numerical studies of inverse source problem for the linear parabolic equation with sparse boundary measurements	5
Imaging sound-soft targets in waveguides using the topological derivative	5
Crack identification in a multi-layer inhomogeneous domain using the Reciprocity Gap-Linear Sampling Method	5
On inverse problems for mean field games with common noise via Carleman estimate*	5
On Bayesian data assimilation for PDEs with ill-posed forward problems	5
Stochastic mirror descent method for linear ill-posed problems in Banach spaces	5
Discretization of parameter identification in PDEs using neural networks	5
L2SR: learning to sample and reconstruct for accelerated MRI via reinforcement learning	5
On mathematical problems of two-coefficient inverse problems of ultrasonic tomography	5
Analysis of sampling methods for imaging a periodic layer and its defects	5
Iterative inversion of the tensor momentum x-ray transform	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
Parametric level-sets enhanced to improve reconstruction (PaLEnTIR)	5
Deep learning methods for partial differential equations and related parameter identification problems	5
On the use of nonlinear anisotropic diffusion filters for seismic imaging using the full waveform	5
Stochastic linear regularization methods: random discrepancy principle and applications	5
An accelerated preconditioned proximal gradient algorithm with a generalized Nesterov momentum for PET image reconstruction	5
A phase-field approach for detecting cavities via a Kohn–Vogelius type functional	5
Precursors for synthetic aperture radar	5
Geometric approach for determining stationary phase points in radar imaging	5
Determining the viscosity of the Navier–Stokes equations from observations of finitely many modes	5
ADJUST: a dictionary-based joint reconstruction and unmixing method for spectral tomography	5
A dataset-free deep learning method for low-dose CT image reconstruction	5
Lipschitz stability of an inverse problem of transmission waves with variable jumps	5
Distributed learning with discretely observed functional data	5
Subsampling in ensemble Kalman inversion	5
Bayesian interface technique-based inverse estimation of closure coefficients of standard	5
Fourier reconstruction for diffraction tomography of an object rotated into arbitrary orientations	5
A generalized quasi-boundary value method for recovering a source in a fractional diffusion-wave equation	5
Heuristic rule for inexact Newton-Landweber iteration with convex penalty terms of nonlinear: ill-posed problems	5
Radon transform on algebraic Cormack α-curves inversion formula	4
Fast inverse elastic scattering of multiple particles in three dimensions*	4
Solving, tracking and stopping streaming linear inverse problems	4
Direct sampling method to inverse wave-number-dependent source problems: determination of the support of a stationary source	4
Bayesian image segmentation under varying blur with triplet Markov random field	4
Increasing stability in the linearized inverse Schrödinger potential problem with power type nonlinearities*	4
An inverse problem for generalized Kelvin–Voigt equation with p-Laplacian and damping term	4
Addendum: On stochastic Kaczmarz type methods for solving large scale systems of ill-posed equations (2022 Inverse Problems 38 025003)	4
Spectral decomposition of atomic structures in heterogeneous cryo-EM	4
Recovering critical parameter for nonlinear Allen–Cahn equation by fully discrete continuous data assimilation algorithms *	4
Linearized boundary control method for density reconstruction in acoustic wave equations	4
Solving inverse obstacle scattering problem with latent surface representations	4
Eigenvalue-free iterative shrinkage-thresholding algorithm for solving the linear inverse problems	4
fg-ORKA: fast and gridless reconstruction of moving and deforming objects in multidimensional data	4

Inverse conductivity problem with one measurement: uniqueness of multi-layer structures	4
Convergence study and regularizing property of a modified Robin–Robin method for the Cauchy problem in linear elasticity	4
Permeability estimation of a porous structure in cancer treatment based on sampled velocity measurement*	4
Determination of a spatial load in a damped Kirchhoff–Love plate equation from final time measured data	4
Reconstruction of a source domain from the Cauchy data: II. Three-dimensional case	4
Convergence of non-linear diagonal frame filtering for regularizing inverse problems	4
Material-separating regularizer for multi-energy x-ray tomography	4
Reconstruction of averaging indicators for highly heterogeneous media	4
Direct inversion of the Longitudinal ray transform for 2D residual elastic strain fields	4
Reconstruction of the doping profile in Vlasov–Poisson system	4
A unified approach to inversion formulae for vector and tensor ray and radon transforms and the Natterer inequality	4
Carleman contraction mapping for a 1D inverse scattering problem with experimental time-dependent data	4
Piecewise nonlinear materials and Monotonicity Principle	4
Uniqueness theorems for tomographic phase retrieval with few coded diffraction patterns	4
Bilevel optimal parameter learning for a high-order nonlocal multiframe super-resolution problem	4
A practical method for recovering Sturm–Liouville problems from the Weyl function	4
MB-DAMPNet: a novel multi-branch denoising-based approximate message passing algorithm via deep neural network for image reconstruction	4
Unique recovery of unknown spatial load in damped Euler–Bernoulli beam equation from final time measured output	4
Local near-field scattering data enables unique reconstruction of rough electric potentials	4
Local recovery of a piecewise constant anisotropic conductivity in EIT on domains with exposed corners	4