Multipoint formulas in inverse problems and their numerical implementation

Scattering theory for PDEs (35P25) Inverse problems for PDEs (35R30) Diffraction, scattering (78A45) NLS equations (nonlinear Schrödinger equations) (35Q55) Schrödinger operator, Schrödinger equation (35J10) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21) Inverse problems (including inverse scattering) in optics and electromagnetic theory (78A46)

Cites Work

Multidimensional inverse spectral problem for the equation $-\Delta \psi -(v(x)-Eu(x))\psi =0$
High-energy and smoothness asymptotic expansion of the scattering amplitude.
Phaseless inverse problems that use wave interference
Small angle scattering and $X$-ray transform in classical mechanics
Multidimensional inverse scattering for the Schrödinger equation
Phaseless problem of determination of anisotropic conductivity in electrodynamic equations
The Mathematics of Computerized Tomography
New Stability Estimates for the Inverse Acoustic Inhomogeneous Medium Problem and Applications
Scattering transformation at fixed non-zero energy for the two-dimensional Schrödinger operator with potential decaying at infinity
On inverse scattering at fixed energy for the multidimensional Newton equation in a non-compactly supported field
A Generalization of Theorems of Rellich and Atkinson
The $ \bar\partial$-equation in the multidimensional inverse scattering problem
An iterative approach to monochromatic phaseless inverse scattering
Fixed-distance multipoint formulas for the scattering amplitude from phaseless measurements
Multipoint formulae for inverse scattering at high energies
Multipoint formulas for scattered far field in multidimensions
Fixed Angle Inverse Scattering for Almost Symmetric or Controlled Perturbations
A Numerical Method to Solve a Phaseless Coefficient Inverse Problem from a Single Measurement of Experimental Data
Electron tomography: a short overview with an emphasis on the absorption potential model for the forward problem
Phaseless Inverse Scattering Problems in Three Dimensions
Numerical reconstruction from the Fourier transform on the ball using prolate spheroidal wave functions
Approximate Lipschitz stability for phaseless inverse scattering with background information
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