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Mathematics › Mathematical Physics

Inverse Problems in Mathematical Physics and Imaging

Works Count: 46836

Description

This cluster of papers focuses on the mathematical theory and computational methods for solving inverse problems in various fields, including mathematical physics and imaging. It covers topics such as regularization methods, ill-posed problems, electrical impedance tomography, Calderón's problem, boundary value problems, inverse scattering theory, Tikhonov regularization, transmission eigenvalues, and numerical methods.

Keywords

Inverse Problems; Regularization Methods; Ill-Posed Problems; Electrical Impedance Tomography; Calderón's Problem; Boundary Value Problem; Inverse Scattering Theory; Tikhonov Regularization; Transmission Eigenvalues; Numerical Methods

Most Cited Works

Action Title Date Authors
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Tables of Integral Transforms 2005-01-01 Bateman Manuscript H. Bateman Arthur Erdélyi
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Inverse Acoustic and Electromagnetic Scattering Theory 2012-10-22 David Colton Rainer Kreß
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Spectral Theory and Differential Operators 2018-05-23 D. E. Edmunds Des Evans
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Regularization of Inverse Problems 1996-01-01 Heinz W. Engl Martin Hanke Andreas B. Neubauer
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Multiple Integrals in the Calculus of Variations 1966-01-01 Charles B. Morrey
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Proximal Splitting Methods in Signal Processing 2011-01-01 Patrick L. Combettes Jean‐Christophe Pesquet
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An introduction to stochastic partial differential equations 2006-11-23 John B. Walsh
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The Use of the L-Curve in the Regularization of Discrete Ill-Posed Problems 1993-11-01 Per Christian Hansen Dianne P. O’Leary
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Basic mathematical and electromagnetic concepts of the biomagnetic inverse problem 1987-01-01 Jukka Sarvas
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Total Generalized Variation 2010-01-01 Kristian Bredies Karl Kunisch Thomas Pock
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On the numerical solution of heat conduction problems in two and three space variables 1956-01-01 Jim Douglas H.H. Rachford
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Signal Recovery by Proximal Forward-Backward Splitting 2005-01-01 Patrick L. Combettes Valérie R. Wajs
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An Iterative Regularization Method for Total Variation-Based Image Restoration 2005-01-01 Stanley Osher Martin Burger Donald Goldfarb Jinjun Xu Wotao Yin
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Variable Exponent, Linear Growth Functionals in Image Restoration 2006-01-01 Yunmei Chen Stacey Levine Murali Rao
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Function minimization by conjugate gradients 1964-02-01 R. Fletcher
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Best constant in Sobolev inequality 1976-12-01 Giorgio Talenti
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Inverse Problems for Partial Differential Equations 1998-01-01 Victor Isakov
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Logarithmic Potentials with External Fields 1997-01-01 Edward B. Saff Вилмос Тотик
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A New TwIST: Two-Step Iterative Shrinkage/Thresholding Algorithms for Image Restoration 2007-11-21 José M. Bioucas‐Dias Mário A. T. Figueiredo
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Analysis of Discrete Ill-Posed Problems by Means of the L-Curve 1992-12-01 Per Christian Hansen
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REGULARIZATION TOOLS: A Matlab package for analysis and solution of discrete ill-posed problems 1994-03-01 Per Christian Hansen
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Optimal Global Rates of Convergence for Nonparametric Regression 1982-12-01 Charles J. Stone
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Correlations in Space and Time and Born Approximation Scattering in Systems of Interacting Particles 1954-07-01 Léon Van Hove
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A Global Uniqueness Theorem for an Inverse Boundary Value Problem 1987-01-01 John Sylvester Günther Uhlmann
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Generalized nonlinear inverse problems solved using the least squares criterion 1982-05-01 Albert Tarantola Bernard Valette
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A constrained regularization method for inverting data represented by linear algebraic or integral equations 1982-09-01 Stephen W. Provencher
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A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging 2010-12-20 Antonin Chambolle Thomas Pock
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On the distribution of points in a cube and the approximate evaluation of integrals 1967-01-01 I. M. Sobol
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The Numerical Solution of Parabolic and Elliptic Differential Equations 1955-03-01 D.W. Peaceman H.H. Rachford
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A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems 2009-01-01 Amir Beck Marc Teboulle
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An iterative thresholding algorithm for linear inverse problems with a sparsity constraint 2004-08-26 Ingrid Daubechies Michel Defrise Christine De Mol
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Numerical Methods for the Solution of Ill-Posed Problems 1995-01-01 А. Н. Тихонов A. V. Goncharsky В. В. Степанов A. G. Yagola
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Sparse signal reconstruction from limited data using FOCUSS: a re-weighted minimum norm algorithm 1997-03-01 I.F. Gorodnitsky Bhaskar D. Rao
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Smoothing noisy data with spline functions 1975-10-01 Grace Wahba
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The Split Bregman Method for L1-Regularized Problems 2009-01-01 Tom Goldstein Stanley Osher
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Fast Gradient-Based Algorithms for Constrained Total Variation Image Denoising and Deblurring Problems 2009-07-28 Amir Beck Marc Teboulle
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The Resolving Power of Gross Earth Data 1968-10-01 George Backus Freeman Gilbert
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The Fractional Order Fourier Transform and its Application to Quantum Mechanics 1980-01-01 Victor Namias
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Image Selective Smoothing and Edge Detection by Nonlinear Diffusion. II 1992-06-01 Luis Álvarez Pierre-Louis Lions Jean‐Michel Morel
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A two-dimensional interpolation function for irregularly-spaced data 1968-01-01 Donald S. Shepard
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A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type 1947-01-01 J Crank P. Nicolson
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The Multiple Scattering of Waves. I. General Theory of Isotropic Scattering by Randomly Distributed Scatterers 1945-02-01 L. L. Foldy
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A method for the solution of certain non-linear problems in least squares 1944-07-01 Kenneth Levenberg
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The Analysis of Linear Partial Differential Operators III 2007-01-01 Lars Hörmander
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Singular integral equations 1954-06-01 Howard H. Brown
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Stochastic Differential Equations—An Introduction With Applications 2006-10-01
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On a quasi-linear parabolic equation occurring in aerodynamics 1951-10-01 Julian D. Cole
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An Interior-Point Method for Large-Scale -Regularized Least Squares 2007-12-01 Seung-Jean Kim Kwangmoo Koh Michael Lustig Stephen Boyd Dimitry Gorinevsky
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Spatial Variation of Currents and Fields Due to Localized Scatterers in Metallic Conduction 1957-07-01 Rolf Landauer
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Degenerate Parabolic Equations 1993-01-01 Emmanuele DiBenedetto

Most Recent Works

Action Title Date Authors
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Min-min minimization for the fractional ℓ0-regularized problem 2025-05-02 Jun Wang Qiang Ma Cheng Zhou
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Solvability of Semilinear Operator Equations with Growing Nonlinearity Using Fractional Tikhonov regularization 2025-05-03 Ravinder Katta N. Sukavanam
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Higher order error estimates for regularization of inverse problems under non-additive noise 2025-05-02 Diana Elena Mirciu Elena Resmerita
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Inverse coefficient problems for the heat equation with fractional Laplacian 2025-05-02 Azizbek Mamanazarov Durvudkhan Suragan
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Existence of solutions to Dirichlet boundary value problems of the stationary relativistic Boltzmann equation 2025-05-02 Wang Yi Li Li Zaihong Jiang
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Convexification for the 3D Problem of Travel Time Tomography 2025-05-02 Michael V. Klibanov Jingzhi Li V. G. Romanov Zhipeng Yang
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The generalized photo-thermo-elastic wave dynamics with a double porosity semiconductors under Lord–Shulman theory 2025-05-03 Kh. Lotfy Ibrahim S. Elshazly Imed Bachar Saurav Sharma Ramdan S. Tantawi E. S. Elidy
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A Counterexample Regarding a Two-phase Problem for Harmonic Measure in VMO 2025-05-03 Xavier Tolsa
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Minimizing Schrödinger eigenvalues for confining potentials 2025-05-03 Rupert L. Frank
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Analytical and Geometric Foundations and Modern Applications of Kinetic Equations and Optimal Transport 2025-05-04 Cécile Barbachoux Joseph Kouneiher
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A Framework Unifying Three‐Cell‐Based Scale‐Invariant Exponential and Trigonometric WENO Weighting Functions With Optimal Shape Parameters 2025-05-04 Xi Deng Zhenhua Jiang Bin Xie Chao Yan
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A game interpretation for the weighted <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si7.svg" display="inline" id="d1e41"><mml:mi>p</mml:mi></mml:math>-Laplace equation 2025-05-05 Mamoru Aihara
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Inverse coefficient problem for wave equation with the generalized Riemann–Liouville time-derivative 2025-05-04 D. K. Durdiev H. H. Turdiev
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Mixed local and nonlocal eigenvalue problems in the exterior domain 2025-05-05 R. Lakshmi Sekhar Ghosh
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Metric extrapolation in the Wasserstein space 2025-05-05 Thomas Gallouët Andrea Natale Gabriele Todeschi
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Gradient estimates for nonlinear equations with measurable nonlinearities from composite material 2025-05-05 Yunsoo Jang
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On bound states of Schrödinger equation with vanishing magnetic potential 2025-05-05 Baihong Li Yuanhong Wei
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Projected iterated Tikhonov in general form with adaptive choice of the regularization parameter 2025-05-06 Alessandro Buccini Silvia Gazzola Lucas Onisk Mirjeta Pasha Lothar Reichel
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The half-volume spectrum of a manifold 2025-05-07 Liam Mazurowski Xin Zhou
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Combined <i>L</i> <sub>1</sub> and concave regularization for high-dimensional AFT models under measurement errors 2025-05-06 Qin Yu Zemin Zheng Yang Li
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On Computational Aspects of Least-Squares Projection-Based Model Reduction for Conductive Radiative Systems 2025-05-06 Rajat Chourasia Abhijit A. Adoni Balaji Srinivasan
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An ESCA algorithm for solving the coefficient inverse problem of singularly perturbed parabolic convection–diffusion equation 2025-05-06 Li‐Bin Liu Tian Zhou Ling Li Xiongfa Mai Delong Guo
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Some remarks on a dispersal integral operator 2025-05-06 Francisco Júlio S. A. Corrêa Natan de Assis Lima
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Some Optimal Inequalities for $$\alpha $$-harmonic Functions Estimated by their Boundary Functions 2025-05-06 Bo-Yong Long
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Large Deviations for an Obstacle Problem with T-monotone Operator and Multiplicative Noise 2025-05-06 Yassine Tahraoui
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Stability in inverse problem for a Moore-Gibson-Thompson equation with time-dependent coefficient 2025-05-06 Song-Ren Fu Yongyi Yu
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PERIODIC LAYER POTENTIALS AND DOMAIN PERTURBATIONS 2025-05-06 Roberto Bramati Matteo Dalla Riva Paolo Luzzini Paolo Musolino
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Generalized Optimal AMG Convergence Theory for Nonsymmetric and Indefinite Problems 2025-05-06 Ahsan Ali James Brannick Karsten Kahl Oliver A. Krzysik Jacob B. Schroder Ben S. Southworth
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Parameter Selection by GCV and a \(\boldsymbol {\chi^2}\) Test within Iterative Methods for \(\boldsymbol{\ell_1}\)-Regularized Inverse Problems 2025-05-06 Brian Sweeney Rosemary A. Renaut Malena I. Español
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Multi-scale analysis of minimizers for a second order regularization of the Perona–Malik functional 2025-05-08 Massimo Gobbino Nicola Picenni
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A weighted weak-type multilinear gradient inequality 2025-05-07 Víctor García García Pedro Ortega Salvador
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Quasiclassical approximation of electromagnetic radiation by fermions embedded in a rigidly rotating medium in a strong magnetic field 2025-05-07 Matteo Buzzegoli Kirill Tuchin Nandagopal Vijayakumar
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Weighted Gagliardo–Nirenberg Inequalities via Optimal Transport Theory and Applications 2025-05-07 Zoltán M. Balogh Sebastiano Don Alexandru Kristály
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Perturbative Diagonalization and Spectral Gaps of Quasiperiodic Operators on $$\ell ^2(\mathbb Z^d)$$ with Monotone Potentials 2025-05-07 Ilya Kachkovskiy Leonid Parnovski Roman Shterenberg
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On some general imperfect interface models for conductivity problem 2025-05-07 Nguyễn Trung Kiên Hoang Quan Nguyen
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Spectral Analysis of the Neumann–Poincaré Operator for Thin Doubly Connected Domains 2025-05-07 Doosung Choi Mikyoung Lim Stephen P. Shipman
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Asymptotic Convergence of Restarted Anderson Acceleration for Certain Normal Linear Systems 2025-05-07 Oliver A. Krzysik Hans De Sterck Adam Smith
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Robust First- and Second-Order Differentiation for Regularized Optimal Transport 2025-05-07 Xingjie Helen Li Fei Lu Molei Tao Felix X.-F. Ye
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Modified exterior electromagnetic Steklov eigenvalues in inverse scattering 2025-05-06 Yuan Li Lixin Feng
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Spectral estimates of dynamically-defined and amenable operator families 2025-05-08 Siegfried Beckus Alberto Takase
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An inverse problem for the fractionally damped wave equation 2025-05-08 Li Li Yang Zhang
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Sharp semiclassical spectral asymptotics for Schrödinger operators with non-smooth potentials 2025-05-08 Søren Mikkelsen
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On increasing stability in the <i>n</i> -dimensional inverse source scattering problem with many frequencies 2025-05-09 Suliang Si
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Neural network-driven adaptive parameter selection for the Local Method of Fundamental Solutions 2025-05-09 Liang Han Min Lei Chih‐Che Wu Ruiping Niu Heming Jia Hongwei Wang
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On widely degenerate p-Laplace equations with symmetric data 2025-05-09 Stefania Russo
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Subordinated Bessel heat kernels 2025-05-09 Krzysztof Bogdan Konstantin Merz
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On higher integrability of minimizer to a nonlinear functional in domains perforated along the boundary 2025-05-09 Г. А. Чечкин
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Fractional analysis of time-fractional Emden-Fowler problem in the fluid flow through a porous medium 2025-05-09 Muhammad Nadeem Yabin Shao M. Riaz Khan Azeem Hafiz P A Ebraheem Alzahrani
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Stability and Lorentzian geometry for an inverse problem of a semilinear wave equation 2025-05-10 Matti Lassas Tony Liimatainen Leyter Potenciano‐Machado Teemu Tyni
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Efficient resist modeling and calibration using a Wiener–Padé formulation and convex optimizations 2025-05-10 C Mu Zhiyang Song Cheng Lei Shaopeng Guo Ke Li Song Zhang Hao Jiang David H. Wei Yanlong Sun Jinlong Zhu