Uncertainty Principles for Three-Dimensional Inverse Source Problems

DOI10.1137/17M111287XzbMath1380.65347OpenAlexW2770954969MaRDI QIDQ4594902

John Sylvester, Roland Griesmaier

Publication date: 27 November 2017

Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/17m111287x

zbMATH Keywords

Helmholtz equationuncertainty principlesinverse source problemdata completionstable recoveryfar field splitting

Mathematics Subject Classification ID

Inverse problems for PDEs (35R30) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21)

Related Items (10)

Exact and approximate solutions to the Helmholtz, Schrödinger and wave equation in \(\mathbf{R}^3\) with radial data ⋮ Uniqueness and increasing stability in electromagnetic inverse source problems ⋮ Uncertainty principles for inverse source problems for electromagnetic and elastic waves ⋮ Increasing Stability in Acoustic and Elastic Inverse Source Problems ⋮ Determining a random Schrödinger operator: both potential and source are random ⋮ Uniqueness of an inverse source problem in experimental aeroacoustics ⋮ Inverse Source Problems for Maxwell's Equations and the Windowed Fourier Transform ⋮ Determining a Random Schrödinger Equation with Unknown Source and Potential ⋮ Stability and the inverse gravimetry problem with minimal data ⋮ On the inverse gravimetry problem with minimal data

Uses Software

• DLMF
• BEM++

Cites Work

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• Spherical harmonics and approximations on the unit sphere. An introduction
• Computing Fourier transforms and convolutions on the 2-sphere
• Inverse acoustic and electromagnetic scattering theory.
• The analysis of linear partial differential operators. I: Distribution theory and Fourier analysis.
• Time-dependent wave splitting and source separation
• Far Field Splitting by Iteratively Reweighted $\ell^1$ Minimization
• Uncertainty Principles for Inverse Source Problems, Far Field Splitting, and Data Completion
• Uncertainty Principles and Signal Recovery
• Uniform Bounds for Bessel Functions
• Source splitting via the point source method
• The scattering support
• Bessel Functions: Monotonicity and Bounds
• Approximations for the Bessel and Airy functions with an explicit error term
• Solving Boundary Integral Problems with BEM++
• The Convex Scattering Support in a Background Medium
• Far Field Splitting for the Helmholtz Equation
• The Convex Back-Scattering Support
• Notions of support for far fields

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