# 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} }

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…

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## 30 Citations

Far Field Splitting by Iteratively Reweighted ℓ1 Minimization

- Computer Science, MathematicsSIAM J. Appl. Math.
- 2016

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

- Mathematics, Computer ScienceSIAM J. Numer. Anal.
- 2014

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

- Mathematics, Computer ScienceSIAM J. Appl. Math.
- 2017

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

- Computer Science, MathematicsSIAM J. Math. Anal.
- 2020

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

- Mathematics, Computer ScienceSIAM J. Appl. Math.
- 2017

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

- Mathematics
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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

- Mathematics, Computer ScienceSIAM J. Sci. Comput.
- 2013

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

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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

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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…

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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…

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