2012, ISBN 052111974X, ages cm

Inverse problems are of interest and importance across many branches of physics, mathematics, engineering and medical imaging...

Wave equation | Mathematics | Inverse problems (Differential equations)

Wave equation | Mathematics | Inverse problems (Differential equations)

Book

2018, ISBN 9789813220966, xiv, 604 pages

Book

2016, CBMS-NSF regional conference series in applied mathematics, ISBN 1611974453, Volume 88, x, 193 pages

Book

2001, Chapman & Hall/CRC research notes in mathematics series, ISBN 1584882522, Volume 427, xi, 261

Book

Inverse Problems, ISSN 0266-5611, 09/2015, Volume 31, Issue 9, pp. 93001 - 93021

This paper is concerned with computational approaches and mathematical analysis for solving inverse scattering problems in the frequency domain...

diffraction limit | multiple frequency | inverse scattering | LOCATION | NONUNIQUENESS | MATHEMATICS, APPLIED | RECONSTRUCTION | STABILITY | ALGORITHM | PHYSICS, MATHEMATICAL | NUMERICAL-SOLUTION | HELMHOLTZ-EQUATION | OBSTACLE | MAP | LINEAR SAMPLING METHOD | Reconstruction | Algorithms | Inverse problems | Diffraction | Inverse scattering | Mathematical analysis | Mathematical models | Inverse | Analysis of PDEs | Mathematics

diffraction limit | multiple frequency | inverse scattering | LOCATION | NONUNIQUENESS | MATHEMATICS, APPLIED | RECONSTRUCTION | STABILITY | ALGORITHM | PHYSICS, MATHEMATICAL | NUMERICAL-SOLUTION | HELMHOLTZ-EQUATION | OBSTACLE | MAP | LINEAR SAMPLING METHOD | Reconstruction | Algorithms | Inverse problems | Diffraction | Inverse scattering | Mathematical analysis | Mathematical models | Inverse | Analysis of PDEs | Mathematics

Journal Article

6.
Full Text
Inverse scattering transform for the integrable nonlocal nonlinear Schrödinger equation

Nonlinearity, ISSN 0951-7715, 02/2016, Volume 29, Issue 3, pp. 915 - 946

... out. The direct and inverse scattering problems are analyzed. Key symmetries of the eigenfunctions and scattering data and conserved quantities are obtained...

left-right Riemann-Hilbert problem | integrable nonlocal NLS equation | PT symmetry | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL | Inverse scattering | Mathematical analysis | Transforms | Solitons | Nonlinearity | Evolution | Schroedinger equation | Cauchy problem

left-right Riemann-Hilbert problem | integrable nonlocal NLS equation | PT symmetry | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL | Inverse scattering | Mathematical analysis | Transforms | Solitons | Nonlinearity | Evolution | Schroedinger equation | Cauchy problem

Journal Article

SIAM Journal on Applied Mathematics, ISSN 0036-1399, 2016, Volume 76, Issue 3, pp. 1000 - 1030

In this work we first review the (phased) inverse scattering problem and then pursue the phaseless reconstruction from far-field data with the help of the concept of scattering coefficients...

Inverse medium scattering | Reconstruction algorithm | Condition numbers | Farfield measurements | Phaseless reconstruction | Scattering coefficients | MATHEMATICS, APPLIED | far-field measurements | APPROXIMATION | inverse medium scattering | FIELD | ALGORITHM | condition numbers | scattering coefficients | IDENTIFICATION | phaseless reconstruction | RECOVERY | CONTRAST SOURCE INVERSION | FREQUENCY | reconstruction algorithm | LINEAR SAMPLING METHOD | ELECTROMAGNETIC INVERSION

Inverse medium scattering | Reconstruction algorithm | Condition numbers | Farfield measurements | Phaseless reconstruction | Scattering coefficients | MATHEMATICS, APPLIED | far-field measurements | APPROXIMATION | inverse medium scattering | FIELD | ALGORITHM | condition numbers | scattering coefficients | IDENTIFICATION | phaseless reconstruction | RECOVERY | CONTRAST SOURCE INVERSION | FREQUENCY | reconstruction algorithm | LINEAR SAMPLING METHOD | ELECTROMAGNETIC INVERSION

Journal Article

2002, ISBN 0126137609, 2 v. (xxi, 1831 p.)

Scattering is the collision of two objects that results in a change of trajectory and energy...

Scattering (Mathematics) | Scattering (Physics)

Scattering (Mathematics) | Scattering (Physics)

Book

Computers and Mathematics with Applications, ISSN 0898-1221, 03/2019, Volume 77, Issue 6, pp. 1681 - 1702

A version of the so-called “convexification” numerical method for a coefficient inverse scattering problem for the 3D Helmholtz equation is developed analytically and tested numerically...

Coefficient inverse scattering problem | Carleman weight function | Globally convergent numerical method | MATHEMATICS, APPLIED | CAUCHY-PROBLEMS | CONVEXITY | BURIED OBJECTS | SINGLE MEASUREMENT | CONVERGENT NUMERICAL-METHOD | Information science | Algorithms | Operators (mathematics) | Helmholtz equations | Wave propagation | Inverse scattering | Backscattering | Numerical methods | Plane waves | Hilbert space | Weighting functions | Convergence

Coefficient inverse scattering problem | Carleman weight function | Globally convergent numerical method | MATHEMATICS, APPLIED | CAUCHY-PROBLEMS | CONVEXITY | BURIED OBJECTS | SINGLE MEASUREMENT | CONVERGENT NUMERICAL-METHOD | Information science | Algorithms | Operators (mathematics) | Helmholtz equations | Wave propagation | Inverse scattering | Backscattering | Numerical methods | Plane waves | Hilbert space | Weighting functions | Convergence

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 10/2012, Volume 253, Issue 8, pp. 2380 - 2419

.... One motivation for this investigation comes from the Camassa–Holm equation for which the solution of the Cauchy problem can be achieved by the inverse scattering transform for −u″+14u=λwu.

Camassa–Holm equation | Inverse scattering theory | Left-definite problems | Scattering theory | Camassa-Holm equation | SPECTRAL THEORY | MATHEMATICS | BREAKING | LINE | CRITERION | SHALLOW-WATER EQUATION | OPERATORS | CIRCLE | Atmospheric physics | Naturvetenskap | Mathematics | Natural Sciences | Matematik

Camassa–Holm equation | Inverse scattering theory | Left-definite problems | Scattering theory | Camassa-Holm equation | SPECTRAL THEORY | MATHEMATICS | BREAKING | LINE | CRITERION | SHALLOW-WATER EQUATION | OPERATORS | CIRCLE | Atmospheric physics | Naturvetenskap | Mathematics | Natural Sciences | Matematik

Journal Article

Inverse Problems, ISSN 0266-5611, 02/2012, Volume 28, Issue 2, pp. 025003 - 11

In this work we present a novel sampling method for time harmonic inverse medium scattering problems...

PHYSICS, MATHEMATICAL | MATHEMATICS, APPLIED | Scattering | Inhomogeneous media | Tools | Derivation | Sampling methods | Mathematical models | Inverse | Computational efficiency | Three dimensional

PHYSICS, MATHEMATICAL | MATHEMATICS, APPLIED | Scattering | Inhomogeneous media | Tools | Derivation | Sampling methods | Mathematical models | Inverse | Computational efficiency | Three dimensional

Journal Article

12.
Full Text
Algorithm 1001

: IPscatt-A MATLAB Toolbox for the Inverse Medium Problem in Scattering

ACM Transactions on Mathematical Software (TOMS), ISSN 0098-3500, 12/2019, Volume 45, Issue 4, pp. 1 - 20

IPscatt is a free, open-source MATLAB toolbox facilitating the solution for time-independent scattering...

denoising | total variation regularization | primal-dual algorithm | MATLAB toolbox | Helmholtz equation | Inverse scattering problem | sparsity regularization | parameter identification | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | REGULARIZATION

denoising | total variation regularization | primal-dual algorithm | MATLAB toolbox | Helmholtz equation | Inverse scattering problem | sparsity regularization | parameter identification | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | REGULARIZATION

Journal Article

2011, CBMS-NSF regional conference series in applied mathematics, ISBN 0898719399, Volume 80, x, 138

Book

JOURNAL OF MATHEMATICAL PHYSICS, ISSN 0022-2488, 10/2014, Volume 55, Issue 10, p. 103502

.... This problem arises in particular in the acoustic tomography of moving fluid. We consider linearized and nonlinearized reconstruction algorithms for this problem of inverse scattering...

TRANSFORM | POTENTIALS | FIXED-ENERGY | PHYSICS, MATHEMATICAL | DEPENDENT SCHRODINGER-EQUATION | Mathematics | Functional Analysis | Mathematical Physics | Analysis of PDEs | TOMOGRAPHY | DISTURBANCES | WAVE EQUATIONS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | INVERSE SCATTERING PROBLEM | PERTURBATION THEORY | ALGORITHMS | TWO-DIMENSIONAL CALCULATIONS

TRANSFORM | POTENTIALS | FIXED-ENERGY | PHYSICS, MATHEMATICAL | DEPENDENT SCHRODINGER-EQUATION | Mathematics | Functional Analysis | Mathematical Physics | Analysis of PDEs | TOMOGRAPHY | DISTURBANCES | WAVE EQUATIONS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | INVERSE SCATTERING PROBLEM | PERTURBATION THEORY | ALGORITHMS | TWO-DIMENSIONAL CALCULATIONS

Journal Article

Inverse Problems, ISSN 0266-5611, 10/2013, Volume 29, Issue 10, pp. 104011 - 21

...) > 0 and the accumulation point 1 of the eigenvalues of the scattering operator S(k) when k approaches k sub(0...

Operators | Inverse problems | Scattering | Transforms | Far fields | Eigenvalues | Inhomogeneous media | Constants | Factorization

Operators | Inverse problems | Scattering | Transforms | Far fields | Eigenvalues | Inhomogeneous media | Constants | Factorization

Journal Article

2008, Oxford lecture series in mathematics and its applications, ISBN 9780199213535, Volume 36, xiv, 201

This book is devoted to problems of shape identification in the context of (inverse) scattering problems and problems of impedance tomography...

Inverse problems (Differential equations) | Factorization (Mathematics) | Inverse scattering problem | Shape identification | Boundary condition | Sampling method | Factorization method

Inverse problems (Differential equations) | Factorization (Mathematics) | Inverse scattering problem | Shape identification | Boundary condition | Sampling method | Factorization method

Book

New Journal of Physics, ISSN 1367-2630, 02/2019, Volume 21, Issue 2, p. 22001

...) for reactive molecular systems using feedback from quantum scattering calculations. The method is designed to correct for the uncertainties of quantum chemistry...

bayesian optimization | gaussian processes | inverse scattering problem | APPROXIMATION | PHYSICS, MULTIDISCIPLINARY | POTENTIAL-ENERGY SURFACES | RESONANCES | Potential energy | Organic chemistry | Quantum chemistry | Inverse scattering | Mathematical analysis | Machine learning | Feedback loops | Bayesian analysis | Optimization | Physics - Chemical Physics

bayesian optimization | gaussian processes | inverse scattering problem | APPROXIMATION | PHYSICS, MULTIDISCIPLINARY | POTENTIAL-ENERGY SURFACES | RESONANCES | Potential energy | Organic chemistry | Quantum chemistry | Inverse scattering | Mathematical analysis | Machine learning | Feedback loops | Bayesian analysis | Optimization | Physics - Chemical Physics

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 03/2014, Volume 55, Issue 3, p. 31506

The inverse scattering transform for the focusing nonlinear Schrödinger equation with non-zero boundary conditions at infinity is presented, including...

WAVE-TRAINS | EIGENVALUES | MODULATION INSTABILITY | PHYSICS, MATHEMATICAL | PROPAGATION | WATER | Riemann surfaces | Inverse problems | Inverse scattering | Mathematical analysis | Boundary conditions | Schroedinger equation | Eigenvectors | SOLITONS | SYMMETRY | NONLINEAR PROBLEMS | INVERSE SCATTERING PROBLEM | EQUATIONS | CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY | RIEMANN SHEET | EIGENFUNCTIONS | SPECTRA | ASYMPTOTIC SOLUTIONS | SCATTERING | BOUNDARY CONDITIONS

WAVE-TRAINS | EIGENVALUES | MODULATION INSTABILITY | PHYSICS, MATHEMATICAL | PROPAGATION | WATER | Riemann surfaces | Inverse problems | Inverse scattering | Mathematical analysis | Boundary conditions | Schroedinger equation | Eigenvectors | SOLITONS | SYMMETRY | NONLINEAR PROBLEMS | INVERSE SCATTERING PROBLEM | EQUATIONS | CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY | RIEMANN SHEET | EIGENFUNCTIONS | SPECTRA | ASYMPTOTIC SOLUTIONS | SCATTERING | BOUNDARY CONDITIONS

Journal Article

Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 03/2020, Volume 82, p. 105056

...–Shabat scattering problem and the Ablowitz–Ladik problems.•A simple intuitive derivation of the discrete Darboux transformation is provided for each of the discrete systems considered...

Zakharov–Shabat problem | Direct scattering | Nonlinear fourier transform | MATHEMATICS, APPLIED | Zakharov-Shabat problem | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | INVERSE SCATTERING | PHYSICS, FLUIDS & PLASMAS | EQUATIONS | PHYSICS, MATHEMATICAL

Zakharov–Shabat problem | Direct scattering | Nonlinear fourier transform | MATHEMATICS, APPLIED | Zakharov-Shabat problem | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | INVERSE SCATTERING | PHYSICS, FLUIDS & PLASMAS | EQUATIONS | PHYSICS, MATHEMATICAL

Journal Article

IEEE Transactions on Antennas and Propagation, ISSN 0018-926X, 04/2009, Volume 57, Issue 4, pp. 1133 - 1149

The nonlinear electromagnetic inverse scattering problem of reconstructing a possibly quasi-piecewise constant inhomogeneous complex permittivity profile is solved by iterative minimization of a pixel...

Smoothing methods | regularization | optimization methods | Least squares methods | Degradation | Inverse problems | microwave imaging | Electromagnetic scattering | Cost function | Permittivity | Newton method | Recursive estimation | Testing | Regularization | Optimization methods | Microwave imaging | SET | RECONSTRUCTION | ALGORITHM | OBJECTS | TELECOMMUNICATIONS | CONJUGATE-GRADIENT | ENGINEERING, ELECTRICAL & ELECTRONIC | CONTRAST SOURCE INVERSION | EDGE-PRESERVING REGULARIZATION | inverse problems | Electromagnetic waves | Scattering | Imaging systems | Research | Observations | Mathematical optimization | Methods | Microwave communications | Studies | Optimization techniques | Engineering Sciences | Electromagnetism

Smoothing methods | regularization | optimization methods | Least squares methods | Degradation | Inverse problems | microwave imaging | Electromagnetic scattering | Cost function | Permittivity | Newton method | Recursive estimation | Testing | Regularization | Optimization methods | Microwave imaging | SET | RECONSTRUCTION | ALGORITHM | OBJECTS | TELECOMMUNICATIONS | CONJUGATE-GRADIENT | ENGINEERING, ELECTRICAL & ELECTRONIC | CONTRAST SOURCE INVERSION | EDGE-PRESERVING REGULARIZATION | inverse problems | Electromagnetic waves | Scattering | Imaging systems | Research | Observations | Mathematical optimization | Methods | Microwave communications | Studies | Optimization techniques | Engineering Sciences | Electromagnetism

Journal Article

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