Inverse Problems

Article	Citations
Nonlocal robust tensor recovery with nonconvex regularization *	31
Inverse problems for generalized quasi-variational inequalities with application to elliptic mixed boundary value systems	30
Optimal experimental design for infinite-dimensional Bayesian inverse problems governed by PDEs: a review	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
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
Adaptive regularisation for ensemble Kalman inversion	20
Refraction-corrected ray-based inversion for three-dimensional ultrasound tomography of the breast	19
Stabilizing Invertible Neural Networks Using Mixture Models	19
Task adapted reconstruction for inverse problems	18
Deep neural network expression of posterior expectations in Bayesian PDE inversion	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
A direct method for solving inverse Sturm–Liouville problems*	14
Inverse problems for mean field games	14
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
Simultaneous recoveries for semilinear parabolic systems	13
Monotonicity Principle in tomography of nonlinear conducting materials *	13
A new interpretation of (Tikhonov) regularization	13

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
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
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
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
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
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
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
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
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
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
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
Reduced order model approach for imaging with waves	7
Sparsity-based nonlinear reconstruction of optical parameters in two-photon photoacoustic computed 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
Feature augmentation for the inversion of the Fourier transform with limited data	7
On regularization via frame decompositions with applications in tomography	7
Near-field linear sampling method for axisymmetric eddy current tomography	7
An inverse problem for generalized Kelvin–Voigt equation with p-Laplacian and damping term	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
Imaging conductivity from current density magnitude using neural networks*	7
A stochastic alternating direction method of multipliers for non-smooth and non-convex optimization	7
Regularization of the factorization method applied to diffuse optical tomography	7
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
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
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
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
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
Quantitative signal subspace imaging	4
A dataset-free deep learning method for low-dose CT image reconstruction	4
Spatiotemporal imaging with diffeomorphic optimal transportation	4
Identifying source term in the subdiffusion equation with L 2-TV regularization *	4
Determining damping terms in fractional wave equations	4
Learning optical flow for fast MRI reconstruction	4
Parameter identification for elliptic boundary value problems: an abstract framework and applications	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
Inverse potential problem for a semilinear generalized fractional diffusion equation with spatio-temporal dependent coefficients	4
Analysis of a generalized regularized Gauss–Newton method under heuristic rule in Banach spaces	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
On iteratively regularized predictor–corrector algorithm for parameter identification *	4
Numerical reconstruction from the Fourier transform on the ball using prolate spheroidal wave functions	4
Co-inversion of a scattering cavity and its internal sources: uniqueness, decoupling and imaging	4
Weighted Radon transforms of vector fields, with applications to magnetoacoustoelectric tomography	4
Displacement field estimation from OCT images utilizing speckle information with applications in quantitative elastography	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
On the simultaneous reconstruction of boundary Robin coefficient and internal source in a slow diffusion system	4
Inverse problem for a nonlocal diffuse optical tomography equation	4
Tikhonov regularization for polynomial approximation problems in Gauss quadrature points	4
Regularisation, optimisation, subregularity	4
Carleman contraction mapping for a 1D inverse scattering problem with experimental time-dependent data	4
Joint gravity and magnetic inversion with trans-dimensional alpha shapes and autoregressive noise models	4
Numerical solution of an inverse random source problem for the time fractional diffusion equation via PhaseLift	4