Inverse Problems

Article	Citations
NETT: solving inverse problems with deep neural networks	117
Computed tomography reconstruction using deep image prior and learned reconstruction methods	96
Recovering piecewise constant refractive indices by a single far-field pattern	37
Bilevel optimization, deep learning and fractional Laplacian regularization with applications in tomography	36
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	33
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	27
On a local geometric property of the generalized elastic transmission eigenfunctions and application	25
Nonlocal robust tensor recovery with nonconvex regularization *	25
Higher-order total variation approaches and generalisations	24
Inverse problems for generalized quasi-variational inequalities with application to elliptic mixed boundary value systems	24
Numerical solution of inverse problems by weak adversarial networks	24
Optimal experimental design for infinite-dimensional Bayesian inverse problems governed by PDEs: a review	24
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	22
Classification of stroke using neural networks in electrical impedance tomography	21
Stability for inverse source problems by Carleman estimates	20
The inverse problem of reconstructing reaction–diffusion systems	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
Consistency of Bayesian inference with Gaussian process priors in an elliptic inverse problem	18
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

Deep neural network expression of posterior expectations in Bayesian PDE inversion	18
On the local Lipschitz stability of Bayesian inverse problems	17
The quadratic Wasserstein metric for inverse data matching	17
Uniqueness in determining fractional orders of derivatives and initial values	16
Backward problems in time for fractional diffusion-wave equation	16
On a regularization approach to the inverse transmission eigenvalue problem	15
Fisher information analysis of list-mode SPECT emission data for joint estimation of activity and attenuation distribution	15
Stabilizing Invertible Neural Networks Using Mixture Models	14
High resolution 3D ultrasonic breast imaging by time-domain full waveform inversion	14
Inverse problems for one dimensional conformable fractional Dirac type integro differential system	14
Unique determination of fractional order and source term in a fractional diffusion equation from sparse boundary data	14
On existence and regularity of a terminal value problem for the time fractional diffusion equation	13
An inverse source problem for distributed order time-fractional diffusion equation	13
Hyper-differential sensitivity analysis for inverse problems constrained by partial differential equations	13
A revisit on Landweber iteration	13
A level-set approach based on reaction–diffusion equation applied to inversion problems in acoustic wave propagation	13
Carleman estimates for a stochastic degenerate parabolic equation and applications to null controllability and an inverse random source problem	12
Task adapted reconstruction for inverse problems	12
A new class of accelerated regularization methods, with application to bioluminescence tomography	12
A direct method for solving inverse Sturm–Liouville problems*	12
Numerical schemes to reconstruct three-dimensional time-dependent point sources of acoustic waves	12
Refraction-corrected ray-based inversion for three-dimensional ultrasound tomography of the breast	12
Monotonicity Principle in tomography of nonlinear conducting materials *	12
TV-based reconstruction of periodic functions	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
Simultaneous recoveries for semilinear parabolic systems	11
Wavefield reconstruction inversion: an example	11
Continuous limits for constrained ensemble Kalman filter	11
Geometry of the phase retrieval problem	11
Monotonicity in inverse obstacle scattering on unbounded domains	11
Deep synthesis network for regularizing inverse problems	11
Optimal experimental design under irreducible uncertainty for linear inverse problems governed by PDEs	11
Nonlocal low-rank regularized two-phase approach for mixed noise removal	10
A joint reconstruction and lambda tomography regularization technique for energy-resolved x-ray imaging	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
Unique continuation from a generalized impedance edge-corner for Maxwell’s system and applications to inverse problems	10
Integrable nonlocal derivative nonlinear Schrödinger equations	10
A practical method for recovering Sturm–Liouville problems from the Weyl function	10
Shape reconstruction in linear elasticity: standard and linearized monotonicity method	9
Inverse electromagnetic obstacle scattering problems with multi-frequency sparse backscattering far field data	9
The Calderón problem for the fractional magnetic operator	9
An inverse potential problem for subdiffusion: stability and reconstruction*	9
Optimal-order convergence of Nesterov acceleration for linear ill-posed problems*	9
On Calderón’s inverse inclusion problem with smooth shapes by a single partial boundary measurement	9
Ray-based inversion accounting for scattering for biomedical ultrasound tomography	9
One-bit compressed sensing via ℓ p (0 < p < 1)-minimization method	9
Minimizing L 1 over L 2 norms on the gradient	9
A new interpretation of (Tikhonov) regularization	9

A generalized quasi-boundary value method for recovering a source in a fractional diffusion-wave equation	9
Bayesian approach to inverse scattering with topological priors	9
Inverse moving source problem for time-fractional evolution equations: determination of profiles	9
Convergence of proximal gradient algorithm in the presence of adjoint mismatch *	9
Bayesian particle filter algorithm for learning epidemic dynamics	9
A transmutation operator method for solving the inverse quantum scattering problem *	9
Data driven regularization by projection	9
Joint reconstruction of initial pressure distribution and spatial distribution of acoustic properties of elastic media with application to transcranial photoacoustic tomography	9
On the discrepancy principle for stochastic gradient descent	8
On a three-dimensional Compton scattering tomography system with fixed source	8
Global uniqueness in a passive inverse problem of helioseismology	8
Inverse problems for mean field games	8
Optimal transport in full-waveform inversion: analysis and practice of the multidimensional Kantorovich–Rubinstein norm	8
On the inverse spectral stability for the transmission eigenvalue problem with finite data	8
Local solvability of an inverse problem to the Navier–Stokes equation with memory term	8
Efficient derivative-free Bayesian inference for large-scale inverse problems	8
Seismic wavefield redatuming with regularized multi-dimensional deconvolution	8
A shape optimization approach for electrical impedance tomography with point measurements	8
A second order Calderón’s method with a correction term and a priori information	8
A fast homotopy algorithm for gridless sparse recovery	8
Structure analysis of direct sampling method in 3D electromagnetic inverse problem: near- and far-field configuration	8
Some inverse problems for wave equations with fractional derivative attenuation	8
A new 3D model for magnetic particle imaging using realistic magnetic field topologies for algebraic reconstruction	8
An inner–outer iterative method for edge preservation in image restoration and reconstruction *	7
Variational regularisation for inverse problems with imperfect forward operators and general noise models	7
Reduced order models for spectral domain inversion: embedding into the continuous problem and generation of internal data	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
Stochastic asymptotical regularization for linear inverse problems	7
A probabilistic approach to tomography and adjoint state methods, with an application to full waveform inversion in medical ultrasound	7
Near-field linear sampling method for axisymmetric eddy current tomography	7
A mathematical theory of computational resolution limit in multi-dimensional spaces *	7
Imaging of 3D objects with experimental data using orthogonality sampling methods	7
Scanning electron diffraction tomography of strain	7
Reconstructing the image scanning microscopy dataset: an inverse problem	7
A deterministic-statistical approach to reconstruct moving sources using sparse partial data	7
Data-free likelihood-informed dimension reduction of Bayesian inverse problems	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
Recovering the potential and order in one-dimensional time-fractional diffusion with unknown initial condition and source *	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
The monotonicity principle for magnetic induction tomography	7
Un-supervised learning for blind image deconvolution via Monte-Carlo sampling	7
Fourier reconstruction for diffraction tomography of an object rotated into arbitrary orientations	7
Solving phase retrieval via graph projection splitting	7
Stability of the inverse source problem for the Helmholtz equation in R3	6
A globally convergent algorithm for a class of gradient compounded non-Lipschitz models applied to non-additive noise removal	6
Adaptive Tikhonov strategies for stochastic ensemble Kalman inversion	6
3D Compton scattering imaging with multiple scattering: analysis by FIO and contour reconstruction	6
Data-driven forward discretizations for Bayesian inversion	6
On regularization via frame decompositions with applications in tomography	6
A numerical algorithm for inverse problem from partial boundary measurement arising from mean field game problem	6
Mathematical modeling for 2D light-sheet fluorescence microscopy image reconstruction	6
Recovering a quasilinear conductivity from boundary measurements	6
Material-separating regularizer for multi-energy x-ray tomography	6
Feature augmentation for the inversion of the Fourier transform with limited data	6
Bayesian approach to inverse time-harmonic acoustic scattering with phaseless far-field data	6
Convexification for an inverse problem for a 1D wave equation with experimental data	6
Sampled limited memory methods for massive linear inverse problems	6
Inverse moving point source problem for the wave equation	6
Γ-convergence of Onsager–Machlup functionals: II. Infinite product measures on Banach spaces	6
Analysis of resolution of tomographic-type reconstruction from discrete data for a class of distributions	6
Estimation of microtexture region orientation distribution functions using eddy current data	6
A stochastic alternating direction method of multipliers for non-smooth and non-convex optimization	6
Laboratory application of sampling approaches to inverse scattering	6
Equivariant neural networks for inverse problems	6
Error analysis for filtered back projection reconstructions in Besov spaces	6
An inverse problem for generalized Kelvin–Voigt equation with p-Laplacian and damping term	6
Lippmann–Schwinger–Lanczos algorithm for inverse scattering problems	6
The Dantzig selector: recovery of signal via ℓ 1 − αℓ 2 minimization	6
Numerical analysis of backward subdiffusion problems	6
Inverse scattering on the half-line for energy-dependent Schrödinger equations	6
Hölder-logarithmic stability in Fourier synthesis	6
Robust signal recovery for ℓ 1–2 minimization via prior support information	6
Inverse problems with inexact forward operator: iterative regularization and application in dynamic imaging	6
Solving an inverse heat convection problem with an implicit forward operator by using a projected quasi-Newton method	6
Active manipulation of Helmholtz scalar fields: near-field synthesis with directional far-field control	6
A fast image reconstruction method for planar objects CT inspired by differentiation property of Fourier transform (DPFT)	6
Sparse dynamic tomography: a shearlet-based approach for iodine perfusion in plant stems	6
Sparsity-based nonlinear reconstruction of optical parameters in two-photon photoacoustic computed tomography	6

Mumford–Shah regularization in electrical impedance tomography with complete electrode model	6
Stochastic EM methods with variance reduction for penalised PET reconstructions	5
On the solution of direct and inverse multiple scattering problems for mixed sound-soft, sound-hard and penetrable objects	5
Electric impedance tomography problem for surfaces with internal holes *	5
An unbiased approach to compressed sensing	5
Machine learning enhanced electrical impedance tomography for 2D materials	5
Data assimilation finite element method for the linearized Navier–Stokes equations in the low Reynolds regime	5
A noniterative reconstruction method for solving a time-fractional inverse source problem from partial boundary measurements	5
Imaging conductivity from current density magnitude using neural networks*	5
A projective averaged Kaczmarz iteration for nonlinear ill-posed problems	5
Processing the 2D and 3D Fresnel experimental databases via topological derivative methods	5
A local in time existence and uniqueness result of an inverse problem for the Kelvin-Voigt fluids	5
A Bayesian filtering approach to layer stripping for electrical impedance tomography	5
Nonlinear Cauchy problem and identification in contact mechanics: a solving method based on Bregman-gap	5
Reconstruction of multipolar point sources with multi-frequency sparse far field data	5
Uniqueness criteria in multi-energy CT	5
A source reconstruction method in two dimensional radiative transport using boundary data measured on an arc	5
On the simultaneous reconstruction of boundary Robin coefficient and internal source in a slow diffusion system	5
A modified discrepancy principle to attain optimal convergence rates under unknown noise	5
Uniqueness of an inverse source problem in experimental aeroacoustics	5
On stochastic Kaczmarz type methods for solving large scale systems of ill-posed equations	5
Multipoint formulas for scattered far field in multidimensions	5
Graph-based prior and forward models for inverse problems on manifolds with boundaries	5
A parameter choice rule for Tikhonov regularization based on predictive risk	5
Frame decompositions of bounded linear operators in Hilbert spaces with applications in tomography	5
Radiative transport model for coherent acousto-optic tomography	5
Regularization of the factorization method applied to diffuse optical tomography	5
Maximum a posteriori estimators in ℓp are well-defined for diagonal Gaussian priors	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
Analysis of the inverse Born series: an approach through geometric function theory	5
Ultrasound modulated bioluminescence tomography with a single optical measurement	5
A frame decomposition of the atmospheric tomography operator	5
A distributed resistance inverse method for flow obstacle identification from internal velocity measurements	5
A projected gradient method for αℓ 1 − βℓ 2 sparsity regularization **	5
Relax-and-split method for nonconvex inverse problems	5
Fixed-distance multipoint formulas for the scattering amplitude from phaseless measurements	5
Uniqueness of orders and parameters in multi-term time-fractional diffusion equations by short-time behavior	5
Riemannian Newton-CG methods for constructing a positive doubly stochastic matrix from spectral data*	5
A variational non-linear constrained model for the inversion of FDEM data*	5
Unsupervised knowledge-transfer for learned image reconstruction*	5
Inverse scattering reconstruction of a three dimensional sound-soft axis-symmetric impenetrable object *	5
Stable determination of coefficients in semilinear parabolic system with dynamic boundary conditions	5
A projective two-point gradient Kaczmarz iteration for nonlinear ill-posed problems	5
Phaseless inverse scattering with background information	5
Approximation error method for imaging the human head by electrical impedance tomography*	5
Inversion formulae for ray transforms in vector and tensor tomography	5