Inverse Problems

Article	Citations
NETT: solving inverse problems with deep neural networks	120
Computed tomography reconstruction using deep image prior and learned reconstruction methods	101
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
The D-bar method for electrical impedance tomography—demystified	35
Convexification and experimental data for a 3D inverse scattering problem with the moving point source	33
ℓ 1 − αℓ 2 minimization methods for signal and image reconstruction with impulsive noise removal	29
The bound-state soliton solutions of the complex modified KdV equation	28
Nonlocal robust tensor recovery with nonconvex regularization *	27
Optimal experimental design for infinite-dimensional Bayesian inverse problems governed by PDEs: a review	26
On a local geometric property of the generalized elastic transmission eigenfunctions and application	25
Higher-order total variation approaches and generalisations	25
Inverse problems for generalized quasi-variational inequalities with application to elliptic mixed boundary value systems	25
Numerical solution of inverse problems by weak adversarial networks	25
Non-unique games over compact groups and orientation estimation in cryo-EM	24
The inverse problem of reconstructing reaction–diffusion systems	22
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	22
Convexification for an inverse parabolic problem	20
Stability for inverse source problems by Carleman estimates	19
Simultaneous inversion of the potential term and the fractional orders in a multi-term time-fractional diffusion equation	19
On the local Lipschitz stability of Bayesian inverse problems	18
Adaptive regularisation for ensemble Kalman inversion	18
Learning regularization parameters of inverse problems via deep neural networks	18
Consistency of Bayesian inference with Gaussian process priors in an elliptic inverse problem	18

Deep neural network expression of posterior expectations in Bayesian PDE inversion	18
Modulus-based iterative methods for constrained ℓ p – ℓ q minimization	18
Backward problems in time for fractional diffusion-wave equation	17
The quadratic Wasserstein metric for inverse data matching	17
Uniqueness in determining fractional orders of derivatives and initial values	16
High resolution 3D ultrasonic breast imaging by time-domain full waveform inversion	15
Stabilizing Invertible Neural Networks Using Mixture Models	15
Fisher information analysis of list-mode SPECT emission data for joint estimation of activity and attenuation distribution	15
Task adapted reconstruction for inverse problems	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
Inverse problems for one dimensional conformable fractional Dirac type integro differential system	14
On existence and regularity of a terminal value problem for the time fractional diffusion equation	13
A level-set approach based on reaction–diffusion equation applied to inversion problems in acoustic wave propagation	13
Hyper-differential sensitivity analysis for inverse problems constrained by partial differential equations	13
A revisit on Landweber iteration	13
An inverse source problem for distributed order time-fractional diffusion equation	13
Refraction-corrected ray-based inversion for three-dimensional ultrasound tomography of the breast	12
Numerical schemes to reconstruct three-dimensional time-dependent point sources of acoustic waves	12
A new class of accelerated regularization methods, with application to bioluminescence tomography	12
Wavefield reconstruction inversion: an example	12
Monotonicity Principle in tomography of nonlinear conducting materials *	12
Simultaneous recoveries for semilinear parabolic systems	12
A direct method for solving inverse Sturm–Liouville problems*	12
Integrable nonlocal derivative nonlinear Schrödinger equations	11
Carleman estimates for a stochastic degenerate parabolic equation and applications to null controllability and an inverse random source problem	11
Continuous limits for constrained ensemble Kalman filter	11
Optimal experimental design under irreducible uncertainty for linear inverse problems governed by PDEs	11
Geometry of the phase retrieval problem	11
A new interpretation of (Tikhonov) regularization	11
Deep synthesis network for regularizing inverse problems	11
TV-based reconstruction of periodic functions	11
Monotonicity in inverse obstacle scattering on unbounded domains	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
Inverse moving source problem for time-fractional evolution equations: determination of profiles	10
A second order Calderón’s method with a correction term and a priori information	10
A generalized quasi-boundary value method for recovering a source in a fractional diffusion-wave equation	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
Inverse problems for mean field games	10
An inverse potential problem for subdiffusion: stability and reconstruction*	10
Shape reconstruction in linear elasticity: standard and linearized monotonicity method	10
Nonlocal low-rank regularized two-phase approach for mixed noise removal	10
Γ -convergence of Onsager–Machlup functionals: I. With applications to maximum a posteriori estimation in Bayesian inverse problems	10
A practical method for recovering Sturm–Liouville problems from the Weyl function	10
A transmutation operator method for solving the inverse quantum scattering problem *	9
Unique continuation from a generalized impedance edge-corner for Maxwell’s system and applications to inverse 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

Inverse electromagnetic obstacle scattering problems with multi-frequency sparse backscattering far field data	9
Bayesian particle filter algorithm for learning epidemic dynamics	9
Machine learning enhanced electrical impedance tomography for 2D materials	9
Optimal-order convergence of Nesterov acceleration for linear ill-posed problems*	9
Bayesian approach to inverse scattering with topological priors	9
Efficient derivative-free Bayesian inference for large-scale inverse problems	9
Minimizing L 1 over L 2 norms on the gradient	9
The Calderón problem for the fractional magnetic operator	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
Convergence of proximal gradient algorithm in the presence of adjoint mismatch *	9
Data-free likelihood-informed dimension reduction of Bayesian inverse problems	9
Fourier reconstruction for diffraction tomography of an object rotated into arbitrary orientations	8
A shape optimization approach for electrical impedance tomography with point measurements	8
A fast homotopy algorithm for gridless sparse recovery	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
On a three-dimensional Compton scattering tomography system with fixed source	8
A mathematical theory of computational resolution limit in multi-dimensional spaces *	8
Structure analysis of direct sampling method in 3D electromagnetic inverse problem: near- and far-field configuration	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
Optimal transport in full-waveform inversion: analysis and practice of the multidimensional Kantorovich–Rubinstein norm	8
Local solvability of an inverse problem to the Navier–Stokes equation with memory term	8
Carleman estimates and the contraction principle for an inverse source problem for nonlinear hyperbolic equations	8
On the discrepancy principle for stochastic gradient descent	8
On the inverse spectral stability for the transmission eigenvalue problem with finite data	8
Imaging of 3D objects with experimental data using orthogonality sampling methods	8
Seismic wavefield redatuming with regularized multi-dimensional deconvolution	8
Un-supervised learning for blind image deconvolution via Monte-Carlo sampling	8
Recovering the potential and order in one-dimensional time-fractional diffusion with unknown initial condition and source *	7
Scanning electron diffraction tomography of strain	7
Numerical analysis of backward subdiffusion problems	7
A dual approach to Kohn–Vogelius regularization applied to data completion problem	7
Stochastic asymptotical regularization for linear inverse problems	7
Error analysis for filtered back projection reconstructions in Besov spaces	7
Bayesian approach to inverse time-harmonic acoustic scattering with phaseless far-field data	7
The Dantzig selector: recovery of signal via ℓ 1 − αℓ 2 minimization	7
An inner–outer iterative method for edge preservation in image restoration and reconstruction *	7
Inverse moving point source problem for the wave equation	7
Inverse problems with inexact forward operator: iterative regularization and application in dynamic imaging	7
A deterministic-statistical approach to reconstruct moving sources using sparse partial data	7
The monotonicity principle for magnetic induction tomography	7
Unique recovery of unknown spatial load in damped Euler–Bernoulli beam equation from final time measured output	7
Inverse scattering on the half-line for energy-dependent Schrödinger equations	7
Near-field linear sampling method for axisymmetric eddy current tomography	7
Variational regularisation for inverse problems with imperfect forward operators and general noise models	7
Analysis of a heuristic rule for the IRGNM in Banach spaces with convex regularization terms	7
Reconstructing the image scanning microscopy dataset: an inverse problem	7
Equivariant neural networks for inverse problems	7
Recovering a quasilinear conductivity from boundary measurements	7
A probabilistic approach to tomography and adjoint state methods, with an application to full waveform inversion in medical ultrasound	7
Solving phase retrieval via graph projection splitting	7
Lippmann–Schwinger–Lanczos algorithm for inverse scattering problems	6
Sequentially optimized projections in x-ray imaging *	6
3D Compton scattering imaging with multiple scattering: analysis by FIO and contour reconstruction	6
A parameter choice rule for Tikhonov regularization based on predictive risk	6
Estimation of microtexture region orientation distribution functions using eddy current data	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
Uniqueness of an inverse source problem in experimental aeroacoustics	6
Feature augmentation for the inversion of the Fourier transform with limited data	6
Processing the 2D and 3D Fresnel experimental databases via topological derivative methods	6
Convexification for an inverse problem for a 1D wave equation with experimental data	6
Adaptive Tikhonov strategies for stochastic ensemble Kalman inversion	6
Γ-convergence of Onsager–Machlup functionals: II. Infinite product measures on Banach spaces	6
Data-driven forward discretizations for Bayesian inversion	6
Solving an inverse heat convection problem with an implicit forward operator by using a projected quasi-Newton method	6
A numerical algorithm for inverse problem from partial boundary measurement arising from mean field game problem	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
Mumford–Shah regularization in electrical impedance tomography with complete electrode model	6
A globally convergent algorithm for a class of gradient compounded non-Lipschitz models applied to non-additive noise removal	6
Relax-and-split method for nonconvex inverse problems	6
Uniqueness of orders and parameters in multi-term time-fractional diffusion equations by short-time behavior	6
Hölder-logarithmic stability in Fourier synthesis	6
Robust signal recovery for ℓ 1–2 minimization via prior support information	6
Analysis of resolution of tomographic-type reconstruction from discrete data for a class of distributions	6
A stochastic alternating direction method of multipliers for non-smooth and non-convex optimization	6
On regularization via frame decompositions with applications in tomography	6
Mathematical modeling for 2D light-sheet fluorescence microscopy image reconstruction	6

Sparsity-based nonlinear reconstruction of optical parameters in two-photon photoacoustic computed tomography	6
An inverse problem for generalized Kelvin–Voigt equation with p-Laplacian and damping term	6
Approximation error method for imaging the human head by electrical impedance tomography*	5
A distributed resistance inverse method for flow obstacle identification from internal velocity measurements	5
A frame decomposition of the atmospheric tomography operator	5
On the simultaneous reconstruction of boundary Robin coefficient and internal source in a slow diffusion system	5
A mathematical framework for nonlinear wavefront reconstruction in adaptive optics systems with Fourier-type wavefront sensing	5
An unbiased approach to compressed sensing	5
Multipoint formulas for scattered far field in multidimensions	5
Graph-based prior and forward models for inverse problems on manifolds with boundaries	5
Co-inversion of a scattering cavity and its internal sources: uniqueness, decoupling and imaging	5
A projective averaged Kaczmarz iteration for nonlinear ill-posed problems	5
Frame decompositions of bounded linear operators in Hilbert spaces with applications in tomography	5
A variational non-linear constrained model for the inversion of FDEM data*	5
Regularization of the factorization method applied to diffuse optical tomography	5
A local in time existence and uniqueness result of an inverse problem for the Kelvin-Voigt fluids	5
Inverse scattering reconstruction of a three dimensional sound-soft axis-symmetric impenetrable object *	5
An inverse random source problem for the one-dimensional Helmholtz equation with attenuation	5
On the solution of direct and inverse multiple scattering problems for mixed sound-soft, sound-hard and penetrable objects	5
A source reconstruction method in two dimensional radiative transport using boundary data measured on an arc	5
Adaptively sketched Bregman projection methods for linear systems	5
A projected gradient method for αℓ 1 − βℓ 2 sparsity regularization **	5
A Bayesian interpretation of the L-curve	5
Material-separating regularizer for multi-energy x-ray tomography	5
A noniterative reconstruction method for solving a time-fractional inverse source problem from partial boundary measurements	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
Radiative transport model for coherent acousto-optic tomography	5
Uniqueness criteria in multi-energy CT	5
Maximum a posteriori estimators in ℓp are well-defined for diagonal Gaussian priors	5
A projective two-point gradient Kaczmarz iteration for nonlinear ill-posed problems	5
Electric impedance tomography problem for surfaces with internal holes *	5
Inversion formulae for ray transforms in vector and tensor tomography	5
Localized ensemble Kalman inversion	5
Stochastic EM methods with variance reduction for penalised PET reconstructions	5
A modified discrepancy principle to attain optimal convergence rates under unknown noise	5
On stochastic Kaczmarz type methods for solving large scale systems of ill-posed equations	5
Nonlinear Cauchy problem and identification in contact mechanics: a solving method based on Bregman-gap	5
Data assimilation finite element method for the linearized Navier–Stokes equations in the low Reynolds regime	5
Riemannian Newton-CG methods for constructing a positive doubly stochastic matrix from spectral data*	5
Unsupervised knowledge-transfer for learned image reconstruction*	5
Imaging conductivity from current density magnitude using neural networks*	5
Stable determination of coefficients in semilinear parabolic system with dynamic boundary conditions	5
Reconstruction of multipolar point sources with multi-frequency sparse far field data	5
Analysis of the inverse Born series: an approach through geometric function theory	5
Ultrasound modulated bioluminescence tomography with a single optical measurement	5