Notions of support for far fields

@article{Sylvester2006NotionsOS,
  title={Notions of support for far fields},
  author={John Sylvester},
  journal={Inverse Problems},
  year={2006},
  volume={22},
  pages={1273-1288}
}
  • J. Sylvester
  • Published 20 June 2006
  • Mathematics
  • Inverse Problems
In practical remote sensing, faraway sources radiate fields that, within measurement precision, are nearly those radiated by point sources. Algorithms like MUSIC (Devaney J. Acoust. Soc. Am. at press, Kirsch 2002 Inverse Problems 18 1025–40) correctly identify their number, their locations and their strengths based on observations of the near or far fields they radiate. Asymptotic perturbation formulae (Ammari et al 2005 SIAM J. Appl. Math. 65 2107–27, Bruhl et al 2003 Numer. Math. 93 635–54… 

Figures from this paper

Far Field Splitting by Iteratively Reweighted ℓ1 Minimization
TLDR
An iterative strategy is proposed to successively improve the required a priori information by solving a sequence of these weighted $\ell^1$ minimization problems, where estimates of the approximate locations of the individual source components that are used as aPriori information for the next iteration are computed from the value of the current solution.
Far Field Splitting for the Helmholtz Equation
TLDR
An algorithm to approximate the far field data radiated by each of these sources separately is discussed, based on a Galerkin procedure considering subspaces spanned by the singular vectors of “restricted” far field operators that map local source distributions to the corresponding radiated far field patterns.
Uncertainty Principles for Inverse Source Problems, Far Field Splitting, and Data Completion
TLDR
Criteria and algorithms for the recovery of the far field components radiated by each of the individual sources, and the simultaneous restoration of missing data segments are developed, guaranteeing that stable recovery in presence of noise is possible.
Inverse Source Problems in an Inhomogeneous Medium with a Single Far-Field Pattern
TLDR
It is proved that an admissible set of source functions (including harmonic functions) having a convex-polygonal support can be uniquely identified by a single far-field pattern.
Uncertainty Principles for Three-Dimensional Inverse Source Problems
TLDR
This paper considers extensions of the reconstruction schemes for far field splitting and data completion, including their stability analysis, and discusses the sharpness of the results in the three-dimensional case.
Uncertainty principles for inverse source problems for electromagnetic and elastic waves
In isotropic homogeneous media, far fields of time-harmonic electromagnetic waves radiated by compactly supported volume currents, and elastic waves radiated by compactly supported body force
Inverse Source Problems for the Helmholtz Equation and the Windowed Fourier Transform II
TLDR
The theoretical foundation of the method is provided, a numerical implementation of the fully three-dimensional algorithm is discussed, and a series of numerical examples, including an inverse scattering problem, are presented.
Wave-Based Algorithms and Bounds for Target Support Estimation
Abstract : In this research program we developed novel analytical and computational methods to estimate the support of radiating sources and scatterers from knowledge of the corresponding far field
Multi-frequency orthogonality sampling for inverse obstacle scattering problems
We discuss a simple non-iterative method to reconstruct the support of a collection of obstacles from the measurements of far-field patterns of acoustic or electromagnetic waves corresponding to
IDENTIFICATION AND CHARACTERIZATION OF A MOBILE SOURCE IN A GENERAL PARABOLIC DIFFERENTIAL EQUATION
We discuss an inverse source problem for a general parabolic differential equation in Rn x R+ with constant coefficients and a source whose strength and support may vary with time. We demonstrate
...
1
2
3
...

References

SHOWING 1-10 OF 16 REFERENCES
The Convex Scattering Support in a Background Medium
TLDR
The necessary scattering formalism is introduced and the circular Paley-Wiener theorem is restated as a Picard test, as a tool for inverse scattering in an inverse problem for the Helmholtz equation at fixed energy.
A 'range test' for determining scatterers with unknown physical properties
We describe a new scheme for determining the convex scattering support of an unknown scatterer when the physical properties of the scatterers are not known. The convex scattering support is a subset
The MUSIC-algorithm and the factorization method in inverse scattering theory for inhomogeneous media
We consider the scattering of time-harmonic plane waves by an inhomogeneous medium. The far field patterns u∞ of the scattered waves depend on the index of refraction 1 + q, the frequency, and
The Convex Back-Scattering Support
TLDR
It is demonstrated that there is an inhomogeneity supported in any neighborhood of the convex back- scattering support which has exactly that back-scattering kernel.
A direct impedance tomography algorithm for locating small inhomogeneities
TLDR
This paper considers the case where the goal is to find a number of small objects (inhomogeneities) inside an otherwise known conductor, and uses asymptotic analysis to design a direct reconstruction algorithm for the determination of their locations.
The scattering support
We discuss inverse problems for the Helmholtz equation at fixed energy, specifically the inverse source problem and the inverse scattering problem from a medium or an obstacle. We introduce the
Reconstruction of a Small Inclusion in a Two-Dimensional Open Waveguide
TLDR
A MUSIC (multiple signal classification) type of algorithm for locating the inclusion and illustrating its viability in numerical examples is designed.
Notions of Convexity
The first two chapters of the book are devoted to convexity in the classical sense, for functions of one and several real variables respectively. This gives a background for the study in the
Spectral properties of Schrödinger operators and scattering theory
© Scuola Normale Superiore, Pisa, 1975, tous droits réservés. L’accès aux archives de la revue « Annali della Scuola Normale Superiore di Pisa, Classe di Scienze »
Inverse Acoustic and Electromagnetic Scattering Theory
Introduction.- The Helmholtz Equation.- Direct Acoustic Obstacle Scattering.- III-Posed Problems.- Inverse Acoustic Obstacle Scattering.- The Maxwell Equations.- Inverse Electromagnetic Obstacle
...
1
2
...