Inverse Problems

Article	Citations
NETT: solving inverse problems with deep neural networks	116
Computed tomography reconstruction using deep image prior and learned reconstruction methods	92
Bilevel optimization, deep learning and fractional Laplacian regularization with applications in tomography	36
Recovering piecewise constant refractive indices by a single far-field pattern	35
Convexification and experimental data for a 3D inverse scattering problem with the moving point source	33
The D-bar method for electrical impedance tomography—demystified	31
ℓ 1 − αℓ 2 minimization methods for signal and image reconstruction with impulsive noise removal	27
The bound-state soliton solutions of the complex modified KdV equation	25
Nonlocal robust tensor recovery with nonconvex regularization *	24
Optimal experimental design for infinite-dimensional Bayesian inverse problems governed by PDEs: a review	24
Higher-order total variation approaches and generalisations	24
Numerical solution of inverse problems by weak adversarial networks	23
On a local geometric property of the generalized elastic transmission eigenfunctions and application	23
Non-unique games over compact groups and orientation estimation in cryo-EM	23
Stable determination of polygonal inclusions in Calderón’s problem by a single partial boundary measurement	20
Inverse problems for generalized quasi-variational inequalities with application to elliptic mixed boundary value systems	20
The inverse problem of reconstructing reaction–diffusion systems	20
Stability for inverse source problems by Carleman estimates	20
Convexification for an inverse parabolic problem	20
Simultaneous inversion of the potential term and the fractional orders in a multi-term time-fractional diffusion equation	19
Learning regularization parameters of inverse problems via deep neural networks	18
Adaptive regularisation for ensemble Kalman inversion	18
Modulus-based iterative methods for constrained ℓ p – ℓ q minimization	18
Classification of stroke using neural networks in electrical impedance tomography	18
Consistency of Bayesian inference with Gaussian process priors in an elliptic inverse problem	18

Hyper-molecules: on the representation and recovery of dynamical structures for applications in flexible macro-molecules in cryo-EM	17
The quadratic Wasserstein metric for inverse data matching	17
Deep neural network expression of posterior expectations in Bayesian PDE inversion	17
Uniqueness in determining fractional orders of derivatives and initial values	16
On the local Lipschitz stability of Bayesian inverse problems	16
Fisher information analysis of list-mode SPECT emission data for joint estimation of activity and attenuation distribution	15
Backward problems in time for fractional diffusion-wave equation	15
On a regularization approach to the inverse transmission eigenvalue problem	15
Unique determination of fractional order and source term in a fractional diffusion equation from sparse boundary data	14
Stabilizing Invertible Neural Networks Using Mixture Models	14
Inverse problems for one dimensional conformable fractional Dirac type integro differential system	14
An image sharpening operator combined with framelet for image deblurring	13
High resolution 3D ultrasonic breast imaging by time-domain full waveform inversion	13
Hyper-differential sensitivity analysis for inverse problems constrained by partial differential equations	13
Consistency of a phase field regularisation for an inverse problem governed by a quasilinear Maxwell system	13
An inverse source problem for distributed order time-fractional diffusion equation	13
A level-set approach based on reaction–diffusion equation applied to inversion problems in acoustic wave propagation	12
Task adapted reconstruction for inverse problems	12
A revisit on Landweber iteration	12
On existence and regularity of a terminal value problem for the time fractional diffusion equation	12
Numerical schemes to reconstruct three-dimensional time-dependent point sources of acoustic waves	12
Momentum ray transforms, II: range characterization in the Schwartz space	12
A direct method for solving inverse Sturm–Liouville problems*	12
Monotonicity Principle in tomography of nonlinear conducting materials *	12
Refraction-corrected ray-based inversion for three-dimensional ultrasound tomography of the breast	12
A new class of accelerated regularization methods, with application to bioluminescence tomography	11
Wavefield reconstruction inversion: an example	11
Continuous limits for constrained ensemble Kalman filter	11
TV-based reconstruction of periodic functions	11
Carleman estimates for a stochastic degenerate parabolic equation and applications to null controllability and an inverse random source problem	11
Deep synthesis network for regularizing inverse problems	11
Optimal experimental design under irreducible uncertainty for linear inverse problems governed by PDEs	11
Geometry of the phase retrieval problem	11
Recovery of coefficients for a weighted p-Laplacian perturbed by a linear second order term	11
Convergence rates of Tikhonov regularizations for elliptic and parabolic inverse radiativity problems	11
Binary sparse signal recovery with binary matching pursuit *	10
Monotonicity in inverse obstacle scattering on unbounded domains	10
Unique continuation from a generalized impedance edge-corner for Maxwell’s system and applications to inverse problems	10
Simultaneous recoveries for semilinear parabolic systems	10
Γ -convergence of Onsager–Machlup functionals: I. With applications to maximum a posteriori estimation in Bayesian inverse problems	10
A joint reconstruction and lambda tomography regularization technique for energy-resolved x-ray imaging	10
Nonlocal low-rank regularized two-phase approach for mixed noise removal	10
A practical method for recovering Sturm–Liouville problems from the Weyl function	10
Inverse electromagnetic obstacle scattering problems with multi-frequency sparse backscattering far field data	9
A transmutation operator method for solving the inverse quantum scattering problem *	9
Data driven regularization by projection	9
Ray-based inversion accounting for scattering for biomedical ultrasound tomography	9
Convergence of proximal gradient algorithm in the presence of adjoint mismatch *	9
Bayesian particle filter algorithm for learning epidemic dynamics	9
A generalized quasi-boundary value method for recovering a source in a fractional diffusion-wave equation	9

Optimal-order convergence of Nesterov acceleration for linear ill-posed problems*	9
Shape reconstruction in linear elasticity: standard and linearized monotonicity method	9
Integrable nonlocal derivative nonlinear Schrödinger equations	9
The Calderón problem for the fractional magnetic operator	9
An inverse potential problem for subdiffusion: stability and reconstruction*	9
Bayesian approach to inverse scattering with topological priors	9
Inverse moving source problem for time-fractional evolution equations: determination of profiles	9
Inverse problems for mean field games	8
Seismic wavefield redatuming with regularized multi-dimensional deconvolution	8
A shape optimization approach for electrical impedance tomography with point measurements	8
On the two-step estimation of the cross-power spectrum for dynamical linear inverse problems	8
One-bit compressed sensing via ℓ p (0 < p < 1)-minimization method	8
A second order Calderón’s method with a correction term and a priori information	8
A new interpretation of (Tikhonov) regularization	8
Joint reconstruction of initial pressure distribution and spatial distribution of acoustic properties of elastic media with application to transcranial photoacoustic tomography	8
A fast homotopy algorithm for gridless sparse recovery	8
A new 3D model for magnetic particle imaging using realistic magnetic field topologies for algebraic reconstruction	8
Optimal transport in full-waveform inversion: analysis and practice of the multidimensional Kantorovich–Rubinstein norm	8
Global uniqueness in a passive inverse problem of helioseismology	8
On the discrepancy principle for stochastic gradient descent	8
On the inverse spectral stability for the transmission eigenvalue problem with finite data	8
The monotonicity principle for magnetic induction tomography	7
A probabilistic approach to tomography and adjoint state methods, with an application to full waveform inversion in medical ultrasound	7
Fourier reconstruction for diffraction tomography of an object rotated into arbitrary orientations	7
A mathematical theory of computational resolution limit in multi-dimensional spaces *	7
Near-field linear sampling method for axisymmetric eddy current tomography	7
Efficient derivative-free Bayesian inference for large-scale inverse problems	7
Scanning electron diffraction tomography of strain	7
Variational regularisation for inverse problems with imperfect forward operators and general noise models	7
Joint super-resolution image reconstruction and parameter identification in imaging operator: analysis of bilinear operator equations, numerical solution, and application to magnetic particle imaging	7
Un-supervised learning for blind image deconvolution via Monte-Carlo sampling	7
Unique recovery of unknown spatial load in damped Euler–Bernoulli beam equation from final time measured output	7
Carleman estimates and the contraction principle for an inverse source problem for nonlinear hyperbolic equations	7
Structure analysis of direct sampling method in 3D electromagnetic inverse problem: near- and far-field configuration	7
Recovering the potential and order in one-dimensional time-fractional diffusion with unknown initial condition and source *	7
Numerical analysis of backward subdiffusion problems	7
Analysis of a heuristic rule for the IRGNM in Banach spaces with convex regularization terms	7
A dual approach to Kohn–Vogelius regularization applied to data completion problem	7
Stochastic asymptotical regularization for linear inverse problems	7
Data-free likelihood-informed dimension reduction of Bayesian inverse problems	7
On a three-dimensional Compton scattering tomography system with fixed source	7
Solving phase retrieval via graph projection splitting	7
On Calderón’s inverse inclusion problem with smooth shapes by a single partial boundary measurement	7
An inner–outer iterative method for edge preservation in image restoration and reconstruction *	7
Reduced order models for spectral domain inversion: embedding into the continuous problem and generation of internal data	7
Some inverse problems for wave equations with fractional derivative attenuation	7
A deterministic-statistical approach to reconstruct moving sources using sparse partial data	7
Estimation of microtexture region orientation distribution functions using eddy current data	6
Minimizing L 1 over L 2 norms on the gradient	6
Solving an inverse heat convection problem with an implicit forward operator by using a projected quasi-Newton method	6
Feature augmentation for the inversion of the Fourier transform with limited data	6
Sparsity-based nonlinear reconstruction of optical parameters in two-photon photoacoustic computed tomography	6
Unique continuation of the normal operator of the x-ray transform and applications in geophysics	6
A globally convergent algorithm for a class of gradient compounded non-Lipschitz models applied to non-additive noise removal	6
Lippmann–Schwinger–Lanczos algorithm for inverse scattering problems	6
Hölder-logarithmic stability in Fourier synthesis	6
Γ-convergence of Onsager–Machlup functionals: II. Infinite product measures on Banach spaces	6
Robust signal recovery for ℓ 1–2 minimization via prior support information	6
Active manipulation of Helmholtz scalar fields: near-field synthesis with directional far-field control	6
Laboratory application of sampling approaches to inverse scattering	6
Mathematical modeling for 2D light-sheet fluorescence microscopy image reconstruction	6
Local solvability of an inverse problem to the Navier–Stokes equation with memory term	6
Sparse dynamic tomography: a shearlet-based approach for iodine perfusion in plant stems	6
The Dantzig selector: recovery of signal via ℓ 1 − αℓ 2 minimization	6
Stability of the inverse source problem for the Helmholtz equation in R3	6
Convexification for an inverse problem for a 1D wave equation with experimental data	6
Analysis of resolution of tomographic-type reconstruction from discrete data for a class of distributions	6
Reconstructing the image scanning microscopy dataset: an inverse problem	6
A stochastic alternating direction method of multipliers for non-smooth and non-convex optimization	6
Equivariant neural networks for inverse problems	6
A fast image reconstruction method for planar objects CT inspired by differentiation property of Fourier transform (DPFT)	6
Recovering a quasilinear conductivity from boundary measurements	6
Error analysis for filtered back projection reconstructions in Besov spaces	6
Mumford–Shah regularization in electrical impedance tomography with complete electrode model	6
Bayesian approach to inverse time-harmonic acoustic scattering with phaseless far-field data	6
Imaging of 3D objects with experimental data using orthogonality sampling methods	6
Adaptive Tikhonov strategies for stochastic ensemble Kalman inversion	6
Data-driven forward discretizations for Bayesian inversion	6
Inverse problems with inexact forward operator: iterative regularization and application in dynamic imaging	6
Uniqueness of orders and parameters in multi-term time-fractional diffusion equations by short-time behavior	5

Nonlinear Cauchy problem and identification in contact mechanics: a solving method based on Bregman-gap	5
Stable determination of coefficients in semilinear parabolic system with dynamic boundary conditions	5
Machine learning enhanced electrical impedance tomography for 2D materials	5
A noniterative reconstruction method for solving a time-fractional inverse source problem from partial boundary measurements	5
Material-separating regularizer for multi-energy x-ray tomography	5
Radiative transport model for coherent acousto-optic tomography	5
Regularization of the factorization method applied to diffuse optical tomography	5
On regularization via frame decompositions with applications in tomography	5
Reconstruction of multipolar point sources with multi-frequency sparse far field data	5
Ultrasound modulated bioluminescence tomography with a single optical measurement	5
Sampled limited memory methods for massive linear inverse problems	5
A distributed resistance inverse method for flow obstacle identification from internal velocity measurements	5
Relax-and-split method for nonconvex inverse problems	5
A modified discrepancy principle to attain optimal convergence rates under unknown noise	5
Phaseless inverse scattering with background information	5
On stochastic Kaczmarz type methods for solving large scale systems of ill-posed equations	5
Unsupervised knowledge-transfer for learned image reconstruction*	5
Uniqueness of an inverse source problem in experimental aeroacoustics	5
Graph-based prior and forward models for inverse problems on manifolds with boundaries	5
Multipoint formulas for scattered far field in multidimensions	5
A parameter choice rule for Tikhonov regularization based on predictive risk	5
Riemannian Newton-CG methods for constructing a positive doubly stochastic matrix from spectral data*	5
3D Compton scattering imaging with multiple scattering: analysis by FIO and contour reconstruction	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
A projective two-point gradient Kaczmarz iteration for nonlinear ill-posed problems	5
Inverse scattering reconstruction of a three dimensional sound-soft axis-symmetric impenetrable object *	5
A source reconstruction method in two dimensional radiative transport using boundary data measured on an arc	5
Stochastic EM methods with variance reduction for penalised PET reconstructions	5
An unbiased approach to compressed sensing	5
A projected gradient method for αℓ 1 − βℓ 2 sparsity regularization **	5
Inverse moving point source problem for the wave equation	5
A new nonlocal low-rank regularization method with applications to magnetic resonance image denoising	5
An inverse problem for generalized Kelvin–Voigt equation with p-Laplacian and damping term	5
A variational non-linear constrained model for the inversion of FDEM data*	5
Fixed-distance multipoint formulas for the scattering amplitude from phaseless measurements	5
A projective averaged Kaczmarz iteration for nonlinear ill-posed problems	5
A Bayesian filtering approach to layer stripping for electrical impedance tomography	5
A numerical algorithm for inverse problem from partial boundary measurement arising from mean field game problem	5
Inverse scattering on the half-line for energy-dependent Schrödinger equations	5
Imaging conductivity from current density magnitude using neural networks*	5
Approximation error method for imaging the human head by electrical impedance tomography*	5
On the simultaneous reconstruction of boundary Robin coefficient and internal source in a slow diffusion system	5
On the solution of direct and inverse multiple scattering problems for mixed sound-soft, sound-hard and penetrable objects	5
A frame decomposition of the atmospheric tomography operator	5
Electric impedance tomography problem for surfaces with internal holes *	5
The two-point gradient methods for nonlinear inverse problems based on Bregman projections	5
Rethinking data-driven point spread function modeling with a differentiable optical model	4
Determination of a spatial load in a damped Kirchhoff–Love plate equation from final time measured data	4
Application of the second domain derivative in inverse electromagnetic scattering	4
Robust kernel-based distribution regression	4
Reduced order model approach for imaging with waves	4
Factorization method with one plane wave: from model-driven and data-driven perspectives	4
Co-inversion of a scattering cavity and its internal sources: uniqueness, decoupling and imaging	4
Tikhonov regularization for polynomial approximation problems in Gauss quadrature points	4
Revisiting the probe and enclosure methods	4
The low rank approximations and Ritz values in LSQR for linear discrete ill-posed problem	4
A projected Bouligand–Landweber iteration for non-smooth ill-posed problems	4
A convex inversion framework for identifying parameters in saddle point problems with applications to inverse incompressible elasticity	4
Microlocally accurate solution of the inverse source problem of thermoacoustic tomography	4
An accelerated homotopy perturbation iteration for nonlinear ill-posed problems in Banach spaces with uniformly convex penalty	4
Analysis of the inverse Born series: an approach through geometric function theory	4
Stability of an inverse source problem for the damped biharmonic plate equation	4
An inverse random source problem for the one-dimensional Helmholtz equation with attenuation	4
Modified forward and inverse Born series for the Calderon and diffuse-wave problems	4
Localized ensemble Kalman inversion	4
Numerical solution of an inverse random source problem for the time fractional diffusion equation via PhaseLift	4
Identifying source term in the subdiffusion equation with L 2-TV regularization *	4
Processing the 2D and 3D Fresnel experimental databases via topological derivative methods	4
Recovering a potential in damped wave equation from Neumann-to-Dirichlet operator	4
Well-conditioned ptychographic imaging via lost subspace completion	4
Nonstationary iterated Tikhonov regularization: convergence analysis via Hölder stability	4
Stability for the Calderón’s problem for a class of anisotropic conductivities via an ad hoc misfit functional	4
A local in time existence and uniqueness result of an inverse problem for the Kelvin-Voigt fluids	4
Inverse scattering for the one-dimensional Helmholtz equation with piecewise constant wave speed	4
Maximum a posteriori estimators in ℓp are well-defined for diagonal Gaussian priors	4
Carleman contraction mapping for a 1D inverse scattering problem with experimental time-dependent data	4
Convergence study and regularizing property of a modified Robin–Robin method for the Cauchy problem in linear elasticity	4
Inversion formulae for ray transforms in vector and tensor tomography	4
Uniqueness criteria in multi-energy CT	4
Quantitative signal subspace imaging	4
Displacement field estimation from OCT images utilizing speckle information with applications in quantitative elastography	4
Sequentially optimized projections in x-ray imaging *	4
Frame decompositions of bounded linear operators in Hilbert spaces with applications in tomography	4
Non-stationary multi-layered Gaussian priors for Bayesian inversion	4
Data assimilation finite element method for the linearized Navier–Stokes equations in the low Reynolds regime	4
A mathematical framework for nonlinear wavefront reconstruction in adaptive optics systems with Fourier-type wavefront sensing	4
Motion reconstruction for optical tomography of trapped objects	4
Imaging of buried obstacles in a two-layered medium with phaseless far-field data	4
Inverse problems for constrained parabolic variational-hemivariational inequalities *	3
Simultaneous determination of different class of parameters for a diffusion equation from a single measurement	3
A model reference adaptive system approach for nonlinear online parameter identification	3
Posterior consistency of semi-supervised regression on graphs	3
Stochastic mirror descent method for linear ill-posed problems in Banach spaces	3
Reconstruction of sources from time domain scattered waves at sparse sensors	3
Solution of an acoustic transmission inverse problem by extended inversion	3