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An Initial Value Approach to the Inverse Helmholtz Problem at Fixed Frequency

  • Frank Natterer

Abstract

The inverse Helmholtz problem calls for the determination of the function f in \(\Omega \subseteq \bold{R}^{n}\) from the boundary values \(g(\theta, x) = u(x), x \in \partial \Omega\) of the solution u of the Helmholtz equation
$$\bigtriangleup u(x)+k^{2}(1+f(x))u(x) = 0$$
$$u(x) = e^{ikx.\boldsymbol{\theta}}+w(x)$$
in R n, where w satisfies the Sommerfeld radiation condition. The number k > 0 is the frequency of the incident plane wave with direction \(\theta \in S^{n-1}\). We assume f = 0 outside Ω. g is measured for a single fixed frequency k and all \(\theta \in S^{n-1}\).

Keywords

Inverse Problem Helmholtz Equation Hankel Function Incident Plane Wave Ultrasonic Image 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Wien 1997

Authors and Affiliations

  • Frank Natterer
    • 1
  1. 1.Institut für Numerische und instrumentelle MathematikUniversität MünsterMünsterGermany

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