Inverse Problems

Article	Citations
Nonlocal robust tensor recovery with nonconvex regularization *	31
Optimal experimental design for infinite-dimensional Bayesian inverse problems governed by PDEs: a review	30
Inverse problems for generalized quasi-variational inequalities with application to elliptic mixed boundary value systems	30
Higher-order total variation approaches and generalisations	27
On a local geometric property of the generalized elastic transmission eigenfunctions and application	25
Learning regularization parameters of inverse problems via deep neural networks	22
High resolution 3D ultrasonic breast imaging by time-domain full waveform inversion	21
Backward problems in time for fractional diffusion-wave equation	21
Adaptive regularisation for ensemble Kalman inversion	20
Simultaneous inversion of the potential term and the fractional orders in a multi-term time-fractional diffusion equation	20
Stability for inverse source problems by Carleman estimates	20
Stabilizing Invertible Neural Networks Using Mixture Models	19
Refraction-corrected ray-based inversion for three-dimensional ultrasound tomography of the breast	19
Deep neural network expression of posterior expectations in Bayesian PDE inversion	18
Task adapted reconstruction for inverse problems	18
Uniqueness in determining fractional orders of derivatives and initial values	17
Hyper-differential sensitivity analysis for inverse problems constrained by partial differential equations	16
Nonlocal low-rank regularized two-phase approach for mixed noise removal	15
Inverse problems for mean field games	14
A direct method for solving inverse Sturm–Liouville problems*	14
Simultaneous recoveries for semilinear parabolic systems	13
Monotonicity Principle in tomography of nonlinear conducting materials *	13
A new interpretation of (Tikhonov) regularization	13
Efficient derivative-free Bayesian inference for large-scale inverse problems	13
A level-set approach based on reaction–diffusion equation applied to inversion problems in acoustic wave propagation	13

Recovery of coefficients for a weighted p-Laplacian perturbed by a linear second order term	12
Data-free likelihood-informed dimension reduction of Bayesian inverse problems	12
Deep synthesis network for regularizing inverse problems	12
A generalized quasi-boundary value method for recovering a source in a fractional diffusion-wave equation	12
A new 3D model for magnetic particle imaging using realistic magnetic field topologies for algebraic reconstruction	12
A second order Calderón’s method with a correction term and a priori information	11
Minimizing L 1 over L 2 norms on the gradient	11
Inverse moving source problem for time-fractional evolution equations: determination of profiles	11
Reconstructing the image scanning microscopy dataset: an inverse problem	11
Data driven regularization by projection	11
Integrable nonlocal derivative nonlinear Schrödinger equations	11
Equivariant neural networks for inverse problems	11
PatchNR: learning from very few images by patch normalizing flow regularization	10
An inverse potential problem for subdiffusion: stability and reconstruction*	10
Processing the 2D and 3D Fresnel experimental databases via topological derivative methods	10
Carleman estimates and the contraction principle for an inverse source problem for nonlinear hyperbolic equations	10
Stochastic asymptotical regularization for linear inverse problems	10
A practical method for recovering Sturm–Liouville problems from the Weyl function	10
Optimal-order convergence of Nesterov acceleration for linear ill-posed problems*	10
Binary sparse signal recovery with binary matching pursuit *	10
Γ -convergence of Onsager–Machlup functionals: I. With applications to maximum a posteriori estimation in Bayesian inverse problems	10
Joint reconstruction of initial pressure distribution and spatial distribution of acoustic properties of elastic media with application to transcranial photoacoustic tomography	10
On Calderón’s inverse inclusion problem with smooth shapes by a single partial boundary measurement	10
Some inverse problems for wave equations with fractional derivative attenuation	9
Un-supervised learning for blind image deconvolution via Monte-Carlo sampling	9
Fourier reconstruction for diffraction tomography of an object rotated into arbitrary orientations	9
A mathematical theory of computational resolution limit in multi-dimensional spaces *	9
Imaging of 3D objects with experimental data using orthogonality sampling methods	9
Shape reconstruction in linear elasticity: standard and linearized monotonicity method	9
Convergence of proximal gradient algorithm in the presence of adjoint mismatch *	9
A numerical algorithm for inverse problem from partial boundary measurement arising from mean field game problem	9
Machine learning enhanced electrical impedance tomography for 2D materials	9
Unique continuation from a generalized impedance edge-corner for Maxwell’s system and applications to inverse problems	9
Ray-based inversion accounting for scattering for biomedical ultrasound tomography	9
An inner–outer iterative method for edge preservation in image restoration and reconstruction *	9
A deterministic-statistical approach to reconstruct moving sources using sparse partial data	9
Bayesian particle filter algorithm for learning epidemic dynamics	9
A transmutation operator method for solving the inverse quantum scattering problem *	9
Recovering the potential and order in one-dimensional time-fractional diffusion with unknown initial condition and source *	9
Lippmann–Schwinger–Lanczos algorithm for inverse scattering problems	8
Uniqueness of orders and parameters in multi-term time-fractional diffusion equations by short-time behavior	8
A new nonconvex low-rank tensor approximation method with applications to hyperspectral images denoising	8
A probabilistic approach to tomography and adjoint state methods, with an application to full waveform inversion in medical ultrasound	8
Approximation error method for imaging the human head by electrical impedance tomography*	8
Structure analysis of direct sampling method in 3D electromagnetic inverse problem: near- and far-field configuration	8
Inverse moving point source problem for the wave equation	8
Optimal transport in full-waveform inversion: analysis and practice of the multidimensional Kantorovich–Rubinstein norm	8
Joint super-resolution image reconstruction and parameter identification in imaging operator: analysis of bilinear operator equations, numerical solution, and application to magnetic particle imaging	8
Deep learning methods for partial differential equations and related parameter identification problems	8
A fast homotopy algorithm for gridless sparse recovery	8

The Dantzig selector: recovery of signal via ℓ 1 − αℓ 2 minimization	8
Edge adaptive hybrid regularization model for image deblurring	8
Sequentially optimized projections in x-ray imaging *	8
A new nonlocal low-rank regularization method with applications to magnetic resonance image denoising	8
The monotonicity principle for magnetic induction tomography	8
On a three-dimensional Compton scattering tomography system with fixed source	8
A globally convergent algorithm for a class of gradient compounded non-Lipschitz models applied to non-additive noise removal	8
Inversion formulae for ray transforms in vector and tensor tomography	8
Feature augmentation for the inversion of the Fourier transform with limited data	7
Near-field linear sampling method for axisymmetric eddy current tomography	7
Hölder-logarithmic stability in Fourier synthesis	7
Variational regularisation for inverse problems with imperfect forward operators and general noise models	7
Nonstationary iterated Tikhonov regularization: convergence analysis via Hölder stability	7
Recovering a quasilinear conductivity from boundary measurements	7
On regularization via frame decompositions with applications in tomography	7
An inverse problem for generalized Kelvin–Voigt equation with p-Laplacian and damping term	7
Imaging conductivity from current density magnitude using neural networks*	7
Regularization of the factorization method applied to diffuse optical tomography	7
Adaptive Tikhonov strategies for stochastic ensemble Kalman inversion	7
Scanning electron diffraction tomography of strain	7
Robust signal recovery for ℓ 1–2 minimization via prior support information	7
Solving an inverse heat convection problem with an implicit forward operator by using a projected quasi-Newton method	7
A stochastic alternating direction method of multipliers for non-smooth and non-convex optimization	7
Reduced order model approach for imaging with waves	7
Adaptively sketched Bregman projection methods for linear systems	7
A variational non-linear constrained model for the inversion of FDEM data*	7
A mathematical framework for nonlinear wavefront reconstruction in adaptive optics systems with Fourier-type wavefront sensing	7
A fast image reconstruction method for planar objects CT inspired by differentiation property of Fourier transform (DPFT)	7
Sparsity-based nonlinear reconstruction of optical parameters in two-photon photoacoustic computed tomography	7
Unsupervised knowledge-transfer for learned image reconstruction*	6
Stable determination of coefficients in semilinear parabolic system with dynamic boundary conditions	6
Phaseless inverse scattering with background information	6
Unique recovery of unknown spatial load in damped Euler–Bernoulli beam equation from final time measured output	6
Robust kernel-based distribution regression	6
Stability in inverse problem of an elastic plate with a curved middle surface	6
Analysis of resolution of tomographic-type reconstruction from discrete data for a class of distributions	6
Maximum a posteriori estimators in ℓp are well-defined for diagonal Gaussian priors	6
Estimation of microtexture region orientation distribution functions using eddy current data	6
Mumford–Shah regularization in electrical impedance tomography with complete electrode model	6
A projective two-point gradient Kaczmarz iteration for nonlinear ill-posed problems	6
Localized ensemble Kalman inversion	6
A noniterative reconstruction method for solving a time-fractional inverse source problem from partial boundary measurements	6
Γ-convergence of Onsager–Machlup functionals: II. Infinite product measures on Banach spaces	6
Rethinking data-driven point spread function modeling with a differentiable optical model	6
Laboratory application of sampling approaches to inverse scattering	6
Error analysis for filtered back projection reconstructions in Besov spaces	6
Ultrasound modulated bioluminescence tomography with a single optical measurement	6
A modified discrepancy principle to attain optimal convergence rates under unknown noise	6
Convergence analysis of inexact Newton–Landweber iteration under Hölder stability	5
Spurious minimizers in non uniform Fourier sampling optimization	5
A novel quantitative inverse scattering scheme using interior resonant modes	5
Graph-based prior and forward models for inverse problems on manifolds with boundaries	5
Analysis of the inverse Born series: an approach through geometric function theory	5
Convergence study and regularizing property of a modified Robin–Robin method for the Cauchy problem in linear elasticity	5
Increasing stability in the linearized inverse Schrödinger potential problem with power type nonlinearities*	5
Material-separating regularizer for multi-energy x-ray tomography	5
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,	5
An inverse random source problem for the one-dimensional Helmholtz equation with attenuation	5
Factorization method with one plane wave: from model-driven and data-driven perspectives	5
A source reconstruction method in two dimensional radiative transport using boundary data measured on an arc	5
Non-stationary multi-layered Gaussian priors for Bayesian inversion	5
Error bounds for extended source inversion applied to an acoustic transmission inverse problem	5
A Bayesian interpretation of the L-curve	5
A projected gradient method for αℓ 1 − βℓ 2 sparsity regularization **	5
Electric impedance tomography problem for surfaces with internal holes *	5
Distributed least squares prediction for functional linear regression*	5
Application of the second domain derivative in inverse electromagnetic scattering	5
Inverse problems for constrained parabolic variational-hemivariational inequalities *	5
Reconstruction of multipolar point sources with multi-frequency sparse far field data	5
Nonconvex multi-view subspace clustering via simultaneously learning the representation tensor and affinity matrix*	5
A distributed resistance inverse method for flow obstacle identification from internal velocity measurements	5
On stochastic Kaczmarz type methods for solving large scale systems of ill-posed equations	5
Prior normalization for certified likelihood-informed subspace detection of Bayesian inverse problems	5
3D Compton scattering imaging with multiple scattering: analysis by FIO and contour reconstruction	5
Uniformly convex neural networks and non-stationary iterated network Tikhonov (iNETT) method	5
A local in time existence and uniqueness result of an inverse problem for the Kelvin-Voigt fluids	5
Imaging of buried obstacles in a two-layered medium with phaseless far-field data	5
Stability of an inverse source problem for the damped biharmonic plate equation	5
Fixed-distance multipoint formulas for the scattering amplitude from phaseless measurements	5
Revisiting the probe and enclosure methods	5

Frame decompositions of bounded linear operators in Hilbert spaces with applications in tomography	5
Parameter estimation in fluid flow models from aliased velocity measurements	5
Stochastic EM methods with variance reduction for penalised PET reconstructions	5
Joint gravity and magnetic inversion with trans-dimensional alpha shapes and autoregressive noise models	4
Recovering point sources for the inhomogeneous Helmholtz equation *	4
An accelerated homotopy perturbation iteration for nonlinear ill-posed problems in Banach spaces with uniformly convex penalty	4
Analysis of a generalized regularized Gauss–Newton method under heuristic rule in Banach spaces	4
On iteratively regularized predictor–corrector algorithm for parameter identification *	4
Co-inversion of a scattering cavity and its internal sources: uniqueness, decoupling and imaging	4
Displacement field estimation from OCT images utilizing speckle information with applications in quantitative elastography	4
Quantitative signal subspace imaging	4
Spatiotemporal imaging with diffeomorphic optimal transportation	4
Identifying source term in the subdiffusion equation with L 2-TV regularization *	4
Learning optical flow for fast MRI reconstruction	4
A projected Bouligand–Landweber iteration for non-smooth ill-posed problems	4
Determining a parabolic system by boundary observation of its non-negative solutions with biological applications	4
Dynamic Fourier ptychography with deep spatiotemporal priors	4
Inverse problem for a nonlocal diffuse optical tomography equation	4
Carleman contraction mapping for a 1D inverse scattering problem with experimental time-dependent data	4
Numerical solution of an inverse random source problem for the time fractional diffusion equation via PhaseLift	4
Inverse potential problem for a semilinear generalized fractional diffusion equation with spatio-temporal dependent coefficients	4
Estimate the spectrum of affine dynamical systems from partial observations of a single trajectory data	4
Tangential cone condition and Lipschitz stability for the full waveform forward operator in the acoustic regime	4
Numerical reconstruction from the Fourier transform on the ball using prolate spheroidal wave functions	4
Weighted Radon transforms of vector fields, with applications to magnetoacoustoelectric tomography	4
Inverse problem of reconstruction of degenerate diffusion coefficient in a parabolic equation	4
Some direct and inverse source problems in nonlinear evolutionary PDEs with Volterra operators	4
Translation invariant diagonal frame decomposition of inverse problems and their regularization	4
A dataset-free deep learning method for low-dose CT image reconstruction	4
Determining damping terms in fractional wave equations	4
Parameter identification for elliptic boundary value problems: an abstract framework and applications	4
On the simultaneous reconstruction of boundary Robin coefficient and internal source in a slow diffusion system	4
Tikhonov regularization for polynomial approximation problems in Gauss quadrature points	4
Regularisation, optimisation, subregularity	4
Non-zero constraints in elliptic PDE with random boundary values and applications to hybrid inverse problems	3
A direct sampling-based deep learning approach for inverse medium scattering problems	3
On block accelerations of quantile randomized Kaczmarz for corrupted systems of linear equations	3
Iterative inversion of the tensor momentum x-ray transform	3
An ADMM-Newton-CNN numerical approach to a TV model for identifying discontinuous diffusion coefficients in elliptic equations: convex case with gradient observations	3
Determining the viscosity of the Navier–Stokes equations from observations of finitely many modes	3
Invertible residual networks in the context of regularization theory for linear inverse problems	3
Stability estimates for the expected utility in Bayesian optimal experimental design	3
Numerical conductivity reconstruction from partial interior current density information in three dimensions	3
Hybrid projection methods for large-scale inverse problems with mixed Gaussian priors	3
Stochastic mirror descent method for linear ill-posed problems in Banach spaces	3
Consistency of Bayesian inference with Gaussian process priors for a parabolic inverse problem	3
Solution of an acoustic transmission inverse problem by extended inversion	3
Range-relaxed strategy applied to the Levenberg–Marquardt method with uniformly convex penalization term in Banach spaces	3
A model reference adaptive system approach for nonlinear online parameter identification	3
The interior inverse electromagnetic scattering for an inhomogeneous cavity	3
Efficient 1.5D full waveform inversion in the Laplace-Fourier domain	3
Monotonicity-based shape reconstruction for an inverse scattering problem in a waveguide	3
Computed tomography with view angle estimation using uncertainty quantification	3
Determination of the reaction coefficient in a time dependent nonlocal diffusion process	3
A general method for extracting the amplitude spectrum of the seismic wavelet from the seismic traces	3
Vertical autofocus for the phase screen in a turbulent ionosphere	3
Stability and numerical analysis of backward problem for subdiffusion with time-dependent coefficients	3
Determination of a spatial load in a damped Kirchhoff–Love plate equation from final time measured data	3
Simultaneous recovery of a locally rough interface and the embedded obstacle with its surrounding medium	3
Theoretical and numerical studies of inverse source problem for the linear parabolic equation with sparse boundary measurements	3
Numerical recovery of a time-dependent potential in subdiffusion *	3
Stability for the Calderón’s problem for a class of anisotropic conductivities via an ad hoc misfit functional	3
Simultaneous determination of different class of parameters for a diffusion equation from a single measurement	3
Analysis of seismic inversion with optimal transportation and softplus encoding	3
An extended primal-dual algorithm framework for nonconvex problems: application to image reconstruction in spectral CT	3
Imaging based on Compton scattering: model uncertainty and data-driven reconstruction methods	3
Reconstruction of sources from time domain scattered waves at sparse sensors	3
An asymptotical regularization with convex constraints for inverse problems	3
Phase recovery from phaseless scattering data for discrete Schrödinger operators	3
Low rank matrix recovery with adversarial sparse noise*	3
Bayesian inversion for electromyography using low-rank tensor formats	3
Adaptive multilevel iteration methods for solving ill-posed integral equations via a coupled system	3
Predictive risk estimation for the expectation maximization algorithm with Poisson data	3
Convergence analyses based on frequency decomposition for the randomized row iterative method	3
Gradient flow structure and convergence analysis of the ensemble Kalman inversion for nonlinear forward models	3
Remarks on the factorization and monotonicity method for inverse acoustic scatterings	3
Discretization of parameter identification in PDEs using neural networks	3
Hierarchical off-diagonal low-rank approximation of Hessians in inverse problems, with application to ice sheet model initialization	3
Adaptive spectral decompositions for inverse medium problems	3
On the simultaneous reconstruction of the nonlinearity coefficient and the sound speed in the Westervelt equation	3
An inversion algorithm for P-functions with applications to multi-energy CT	3
Radial recombination for rigid rotational alignment of images and volumes	3
A statistical reconstruction model for absorption CT with source uncertainty *	3
On the use of nonlinear anisotropic diffusion filters for seismic imaging using the full waveform	3
Oversmoothing Tikhonov regularization in Banach spaces *	3
Posterior consistency of semi-supervised regression on graphs	3
On global normal linear approximations for nonlinear Bayesian inverse problems	3
A range-relaxed criteria for choosing the Lagrange multipliers in the iterated Tikhonov Kaczmarz method for solving systems of linear ill-posed equations	3
Regularization theory of the analytic deep prior approach	3
Stability estimates for the relativistic Schrödinger equation from partial boundary data	3
Hyperparameter estimation using a resolution matrix for Bayesian sensing	3
Distributed spectral pairwise ranking algorithms	2
Uniqueness of a spherically symmetric refractive index from modified transmission eigenvalues	2
Adaptive Spectral Inversion for inverse medium problems	2
Bayesian statistical inference using a regression in electrical impedance tomography	2